- Ask a Scientist! -

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Mitch Chubb, a teacher, asks:

I'm currently reading A Beak of Finch. There is a passage referring to two different species of finches mating and having viable offspring. The passage continues discussing other hybrids that occur, ligers, mallards and pintails breeding, and mules. I was under the impression that hybrids such as mules did not occur naturally, rather mated artificially by man. Could you clarify this for me?

Richard Lampe, a biologist, replies:

The biological species concept uses reproductive isolation as its emphasis in identifying the taxon known as species. Useful as it may be in most situation, it is not without its problems. Some organisms have not yet sufficiently diverged genetically to cause a loss of reproductive fitness when they breed with "the other kind". When this happens, there can be an exchange of genetic material across a zone where organisms of two insipient species encounter each other. This can occur naturally but when it does, the two different populations are likely to be quite similar morphologically and hence genetically.
     In other situations where this reproductive isolation has been caused by an ecological barrier (for example, one group has adapted for marsh and the second for forest), if these two habitats are brought into contact then the organisms within them face the chance of making an improper mating decision. This happens especially where human intervention has caused habitats to shift or where species from vastly different regions are introduced to each other.  Though it's not perfect, Ernst Mayr's biological species concept seems to provide biologists with a sound working definition of what is happening in nature.
Hope that this helps.

Johnny, a grade school student, asks:

Can one really see steam? What I mean to say is, when one boils water doesn't the vaporization happen, which is invisible to us? So the "white cloud" or whatever it is we see coming up and off of the result, then, would just be condensation?

Jon Hutchins, a chemist, replies:

You are correct! One cannot see pure steam as it is a colorless gas. The cloudy appearance of steam is due to light diffraction by tiny water droplets suspended in the steam.

Shaun Ng, a middle school student, asks:

Is it possible to safely mutate anybody so that he/she could achieve positive results like growing wings, growing bigger, getting superhuman strength? And how is a person mutated?

Brian A. Lenzmeier, a biologist, replies:

As of now there is not a safe way to specifically mutate a human being to achieve some of the phenotypic descriptions you have given. Exposures to mutagens like radiation that might give you the results you seek will also mutate the rest of the genes and will cause a lot of damage to the person, even perhaps killing them.

There have been experiments using viruses to try to replace defective genes in people who have diseases, but those experiments have not been overly successful.

Your question also raises an important ethical dilemma. I don't think that as a society we would accept mutating human beings. Just think if you made the mutations you suggested in your best friend or mother or father and it ended up killing them. The risks are too great to justify experimenting in this manner on humans.

Neil Jones, a high school student, asks:

I am currently studying in the UK and need to complete an assignment to demonstrate that a non-toxic chemical substance can change colour over a period of days.  Do you have any ideas/suggestions from which I can use as the basis of my experiment and develop to meet the requirements of the assignment?

Jon Hutchins, a chemist, replies:

I would suggest a very weak base (like sodium bicarbonate solution at pH about 8) in water, plus an indicator which changes colour at pH about 6-7. Leave out in a beaker exposed to air. It will pick up C02 and become more acid (pH about 5). If it goes too fast, add more bicarb.

A middle school student asks:

Is Leukemia the opposite of AIDS/HIV? Because AIDS is when you don't have enough working white blood cells to fight off diseases and germs, but Leukemia is when you have too many white blood cells?

Dr. Brian Lenzmeier, a biologist, replies:

Your explanation of Leukemia being the opposite of AIDS is a very good way to explain the two diseases and understand the immune system.

AIDS is caused by a virus called Human Immunodeficiency Virus, or HIV. HIV infects (gets inside) and kills your white blood cells, leaving you unable to fight off any infections by other bacteria and viruses and causing you to have AIDS.

Leukemia is a cancer where your white blood cells gain the ability to divide uncontrollably and your body cannot control their growth, leading to so many white blood cells that your body gets overwhelmed.
Excellent observations!

Sabrina, a high school student, asks:

I'm doing an experiment on reaction times between sight and sound. Can you please tell me which of the two travels faster to the brain to send a reaction to a part of the body? And could you also explain why one is faster that the other?

Dr. Bob Ferguson, a psychologist, replies:

That's an interesting question, and one that is surprisingly complex to answer.

The main problem is that there are several different components that go into determining even a "simple" reaction time response. Here is an excellent web page that details these components: http://www.visualexpert.com/Resources/reactiontime.html The specific component that you have asked about is the neural conduction time from the eye to the primary visual cortex in the occipital lobe or from the ear to the corresponding auditory cortex in the temporal lobe. Since these distances are approximately the same, the difference in conduction times should be minimal.

Nonetheless, most researchers find that, overall, auditory RT's are SLIGHTLY faster than visual. These differences are small (on the order of 10-20 msec) and so can only be identified by calculating averages over large numbers of trials. Some typical data are available at: http://www.euronet.nl/users/fepsy/reac.htm

Since neural conduction times should not play a role here, the differences must be elsewhere. My guess is that the processing of the two types of signals by the cortex is where the difference lies (visual processing may be more complex and thus slower than auditory) but that is only a hypothesis. Another possibility is that once the cortex has recognized the signal, it simply takes longer for the visual cortex to initiate the motor response. But in either case, the time it takes the sensory signal to reach the brain is not likely the culprit.

Before finishing, you should know one last thing. RTs will change depending on the loudness of the tone or the brightness of the light...louder and brighter is faster. Maybe the aud/vis difference just reflects intensity differences of the stimuli used in the two parts of the experiment.

Told ya it was more complicated than you'd think!

Shay, a high school student, asks:

What are the generally excepted requirements an item needs to have to be
considered alive?

Dr. James Eliason, a biologist, replies:

This question is a profound one and surprisingly difficult to answer in
a way that covers all the possibilities.  The following definition works
most of the time:
Something is considered alive if it could have done in the past, or can
do now, or should be able to do in the future, all of the following
"life processes".

Growth:  it gets bigger and more complex with time.
Metabolism:  It uses up energy to convert molecules to other molecules
and obtains energy in a similar way.
It absorbs material from its environment.
It excretes wastes to its environment.
It reproduces, makes more of its own kind.
It responds to its environment.
It adapts, changes its own structure in response to changes in the
environment.
It exhibits homeostasis, that is it maintains some properties of itself
constant despite changes in the environment.
It transports materials from one part of itself to another.
Some, but not all, living things move.
Some, but not all, living things senesce, that is show aging.
Over the course of generations, living organisms evolve.

Not all of these processes have to be present at the same time, but in
general at least one of them should always be present, probably the most
important being metabolism.  For example, a young child cannot
reproduce, but is alive since he/she will be able to after reaching
adulthood.  An old woman past menopause can no longer reproduce but is
alive since she could in the past.  Grass is alive since it shows all
the life processes.  Astroturf is not alive since it never reproduces.
Fire exhibits almost all life processes but is not alive since it does
not evolve.

Traditionally a person "died" when transport stopped, that is when the
heart stopped and blood stopped flowing, but this is no longer used
since in many cases the heart can be restarted and life continued.  In
some cases death is taken to be when the person stops responding to the
environment, that is when the brain ceases function and cannot be
restarted.  Determining the instant of death of a person is very
difficult.  It depends on which life process(es) are required to be
present and on what scale.  Hours after a person is declared dead many
of the person's cells function essentially normally even though the
whole person can never recover.  It may be in the future that a person
is only truly dead if no cells remain "alive" and the person can no
longer be cloned!

Rick Lampe, a biologist, replies:

Hickman, Roberts and Larson (Integrated Principles of Zoology, 2001) answer this question by saying that living systems have a unique chemical organization, unique hierarchical organization, reproduction, genetic programs that enable fidelity in inheritance yet make it possible to change, a characteristic life cycle and the ability to interact with their environment.

Maleki Ray, a high school student, asks:

I'm trying to see if sound waves created by a computer (monotonous ring) could be redirected/misdirected/etc. by using wind created by fans (the purpose is to see if wind could misdirect sound waves). The fans would be lined up on one side of the testing area while a row of microphones aligned perpendicular to the fans record the sounds. The recordings are then placed into a program in the computer which displays the frequency and its value in decibels. I'm just trying to figure out if this is a logical experiment at all, and if using fans is the correct way to provide the interference necessary to answer my question. If there is another way to do this experiment by using different equipment or using a different setup please let me know. Any and all advice would be greatly appreciated.

Joe Traylor, a physicist, replies:

Malek, you pose a very interesting experiment! Yes, I recommend you try to do it. A couple of suggestions: make the source sound a pulse instead of continuous tone for part of the experiment. Then, you might try to see if there is a time delay for sound moving through wind as compared to that in more steady air. Questions to investigate: Does wind affect the velocity of sound? The frequency of sound? The loudness (amplitude) of sound? And, is moving into the wind different from moving with the wind, although these may be harder to do experimentally with fans and mics. The real underlying question is this: Does motion of the molecules in a medium affect the travel of waves in that medium? While I think there may be theoretical answers to those questions, it will be fun for you to investigate. Go for it!

PS. If you're looking for books on sound, check out the new 2002 3rd edition of The Science of Sound by Rossing, Moore, and Wheeler from Addison-Wesley. Pg. 53 talks about your subject.

Tom Hendricks, a microbiologist, asks:
     A colleague of mine and I have a dispute about designing experiments. He states that if you are just looking for main effects, it is just as good to change one variable at a time as it is to run a factorial experiment. I believe that the factorial experiment will give you the main effects cleared of interactions, in other words the effect is valid at multiple levels of the other factors. Who is correct? 

Bob Blodgett, a psychologist, replies:
     The issue, it seems to me, is related to the analysis issue of experimentwise error that accrues from doing individual tests each of which is evaluated for significance at 5%. That is the design and analysis problem that the factorial design addresses with the understanding that there are limitations on the number of factors that should be used for sheer comprehensibility of the design. If multiple, single variable experiments are conducted to test the same hypothesis, the potential for error in the experimental procedures is increased in the same manner as is experimentwise error in analysis. If we consider the potential for error in the experimental procedures is compounded by experimentwise error in analysis, the probability of a type-1 error increases dramatically. Consider the errors that occur in replications (which is encouraged far too little by journal editors these days) of experiments that yield different levels of significance in analysis. Of course replications of experiments has different scientific implications than does multiple experiments testing the same hypothesis. In short, don't do it! Use the factorial design. That's my two cents worth of advice for the day.

Harry Shingleton, a parent, asks:

I have children in secondary school but have had a wholly classics education (which may explain my appalling keyboard skill which cramps my style as you will quickly find out). I find though that my son (aged 12) has a promising mathematical mind and a potential for complex math. We frequently discuss astronomy and science subjects and I wish to encourage him to a higher level of insight.
     If under the Relativity theory mass and energy are equivalent why is the equation not simply e=mc? What is the relevance of the square and since we are in a three dimensional universe why is relativity not energy equals mass times the speed of light cubed?
   This question is more to do with the square and cube in equations than relativity itself - the most obvious place to find the square is in the equation for the area of a circle but it is a multiplier that in mathematics, physics and science generally crops up again and again. I understand the arithmetical square easily enough but as a factor in geometry and algebra it seems to have a much wider implication - please explain including answering the first part. Many thanks.

Shawn Stone, a physicist, replies:

We describe quantities in the universe with units. For instance, 3 meters for distance (m), 10 kilograms for mass (kg), and 5 seconds for time (s). The units for energy (e) are called the Joule which in these fundamental units 1 Joule= 1 (kg*m^2)/(s^2). The speed of light is a constant c= 3X10^8 m/s. The equivalence of mass and energy is some what of a misstatement since they do not have the same units. To make them equal we need a factor of c^2. This makes the units of e=mc^2 match up (both sides have (kg*m^2)/(s^2)). That answers the c^2 question as far as why it must be c^2 arithmetically.

The physical reasons for e=mc^2 are much more complex. It boils down to what two people observe when they are moving relative to each other. As an example, a person is on the ground (not moving relative to the ground) is watching a person in a train passing by at some constant speed. The person in the train drops a ball. Both people observe the ball falling, but both would describe what is happening a little bit differently. The person on the train sees the ball fall in a straight line, the person on the ground sees the ball move in an arc with the train. Even though they describe the motion differently both must agree that the laws of physics are obeyed. Using there observations they both can describe where the ball is and how fast it is moving relative to them. And they both would be correct. Where relativity really comes in is when the train is moving at speeds near c. Since the physics must be the same for both observers the speed of light must be c for both observers. Then when we consider what energy the person on the train measures the ball to have vs what energy the person on the ground measures the ball to have we come up with e=mc^2 (from the math it is like a proportionality constant). This is very general and glosses over a lot. But I hope this may help a little.

Dana asks:

A friend of mine says that a glass of soda sitting on a table in warm weather actually gets cooler through condensation on the glass. So lets say the the glass of soda is at +3 degrees C and the temperature of the air is +30 degrees C. Will the glass of soda become cooler for any period of time? I say no. Can you answer this for me please. Thank You.

Steve Tonsfeldt, a physicist, replies:

Your question was whether a glass of soda sitting on a table in warm weather actually gets cooler through condensation on the glass.  You are correct and your friend is wrong.  If your friend were right, such a process would violate the second law of thermodynamics and in the vast realm of experience, no violation has ever been seen.  Condensation releases heat when it occurs, so it goes the other way.  Evaporation is a cooling process, so that if the glass were surrounded by a damp cover, like some canteens are, evaporation of water cools the canteen.  Dogs panting and people sweating are similar examples.

Roger Durham, a grade school student, asks:

How do sharks smell underwater without water going up their noses?

Carolyn Ashbaugh, a biologist, replies:

Sharks need to get water "up their noses" in order to "smell".  Sharks can detect tiny quantities of substances in the water, but only if the substance comes in contact with special chemosensory structures which are located in something similar to a "nose".  The "nose" of a shark is not used for breathing, so it is not like getting water up your nose when you go swimming.  Human noses are good at (but not nearly so good as a dog's nose) detecting chemicals or aromas (smells) in air. 

A shark is not obtaining oxygen through its "nose"; instead, it takes oxygen from the water using its gills (which are completely separate from its "nose"). The air around us is approximately 20% oxygen.  Oxygen in oceans and lakes is usually measured in parts per million.  There is very little molecular oxygen in water when compared to air, and fish obtain oxygen very differently from air breathing creatures.  A shark uses its "nose" for detecting chemicals (or substances like blood) which may mean that a meal is nearby; it uses its gills for taking in oxygen.  

Jono, a high school student, asks:

If you were traveling at the speed of light carrying a flash light and turned it on what would happen to the light coming out of the flashlight?

Steve Tonsfeldt, a physicist, replies:

Your question is a classic, in that it is exactly the question Einstein himself asked. The answer is not a common sense thing however. The answer is that in your reference frame you still measure the light to proceed away from you at c, 300 million meters per second. ALL OBSERVERS in so-called inertial reference frames, which are those moving at constant speeds with respect to each other, all measure the light to be moving at speed c. Since speed c is distance divided by time, that means that every one of these reference frames will measure different lengths and time intervals, all of which is called the special theory of relativity. The truth of the constancy of the speed of light has been experimentally checked by many experiments, originally by the Michelson-Morley experiment and the anti-common-sense result has been confirmed over and over again. You might want to look in the library for some physics books that go into this in more detail. Happy learning!

James, a middle school student, asks: 

   Why does a salt water solution take longer to freeze than a sugar water solution or plain tap water? When I tried this experiment the salt separated from the water but the sugar stayed dissolved.  Why didn't it separate? I have looked under water soluble solutions but I can't find the answer?

Steve Tonsfeldt, a physicist, replies:

     Your chemistry question is a good one and the answer depends on what the chemists call colligative properties, or properties that depend mostly on the ratio of the number of solute particles (sugar molecules or sodium and chlorine ions) to the number of solvent particles (water), and NOT on the particular chemical identity of the solute (whether it is sugar, salt or whatever). For your situation involving the freezing of the solutions of salt (NaCl) and sugar, consider what the water molecules have to do, in order to bond together in that hexagonal pattern that we see so well in snowflakes. The molecules of sugar get in the way to delay this happening and we get a certain amount of freezing temperature lowering, compared to plain tap water. With salt, the Na and Cl detach and become ions and you have TWICE as many obstacles for the water molecules to overcome, compared to the case for sugar. Therefore the freezing point depression for ordinary salt will be twice that for the same concentration or molarity of sugar solution. I would say that the ability to visualize things on the molecular level is a skill worth cultivating and that starts by asking good questions such as you have! 

Michelle, a high school student, asks: 

     I am starting an experiment this year in my school's research program and I have a few questions that I hope you can help me with. I am going to have four groups of rats: Group "A" will be put into a stimulating environment- a lot of colorful toys, and things to climb on and play with. Group "B" will also be stimulated, but they will be older than group "A". Group "C" will be younger, but they will not be stimulated. Group "D" will be older and not stimulated. To find out if the stimulated groups are better learners, I will have them run through a maze and time them. The faster times will be the smarter rats. 
     Here are my questions: 1. How many rats should I have in each group? (I was thinking three) 2. How many times should I run them through the maze? I know I would have to do it several times to see if the rats learn where to go, but I do not know how soon and how often. 

Jeanne Tinsley, an experimental psychologist, replies:

     This sounds like a very interesting project which you are  beginning.  I will try to answer your questions. 1.   You should try to have 5 or 6 rats in each group.  Many experiments will use as many as 10 in a group.  For your young rats, you should place them in the stimulating environment as soon as they are weaned.  2.  How long it takes the rats to learn the maze will depend on how complicated the maze is.  You could set a fairly long period of  time for a trial and remove the rat after the time is finished – whether the animal has reached the end of the maze or not.  You want to keep running them through the maze in a series of timed trials until they have learned it very well.  You could set a criterion for this –perhaps 5 consecutive trials less than a particular time(probably just a few seconds).  Your rats will need a reason to travel through the maze quickly.  One of the easiest ways is to make them hungry and give them a very small food reward at the end of the maze.  An easy way to make the rats hungry without hurting them is to feed them as much as they want to eat for one hour after you have run them through the maze.  Then remove all of the food.  Make sure the rats have water available at all times.  Then the next day when you are ready to run the rats through the maze again, they will not have eaten for 23 hours and will be hungry.  They will be motivated by the small food reward at the end of the maze.  If you are going to run each rat in a block of trials each day (lets say 5), you need to be certain that the food reward is fairly small so the rat’s appetite is not satisfied.  Noyes pellets work will for this.  Good luck with your project.

Tessa, a middle school student, asks:

    Why can you only see the red dust around the moon when there is a lunar eclipse?  Why is the dust a red color when there is a lunar eclipse?  Can there be other colors then red in the dust around the moon when there is a lunar eclipse?  What would happen if some astronauts went up a few days before a lunar eclipse and waited?  What would they see and would they see the red dust?

Shawn Stone, a physicist, replies:

    The moon is not red because of dust during a lunar eclipse. In fact, the dust of the moon is quite gray all the time!
   
Light from the sun contains all the colors of the spectrum, red, blue, yellow and so on. When it hits the atmosphere of our Earth, the blue light is scattered in all directions leaving the red light passing right through. That is why our sky is blue during the day when the sun is high in the sky. The blue deficient (mostly red) light keeps on going through our upper atmosphere. There it is bent to focus behind the Earth because the Earth's atmosphere also acts like a lens. During a lunar eclipse, the moon is directly behind the Earth where only the focused red light is. That is why the moon looks red! It is reflecting the red light back to your eyes.

Brenda Jennings, a parent, asks:

    What is the definition of a true amphibian? Would a frog still be classified as an amphibian since it loses its ability to breathe in water as an adult? And if so, how would a frog be classified?

Rick Lampe, a biologist, replies:

    Yes, frogs are amphibians. They spend part of their life in a stage that is totally in water and a second stage in which they are able to live on land. However, this second stage is still tied closely to the availability of water. The outer covering of amphibians in quite pervious to water and thus an amphibian can dry out quickly if it does not protect itself. There are three major grouping within the class Amphibia. One is the grouping including frogs and toads. Another includes salamanders and the third is a lesser known group consisting of a legless organism that lives in tropical soils. It's called the caecilian and is quite unusual.

Chris, a high school student, asks:

     In Young's Double-Slit Experiment, it was shown that bright and dark bands were formed on a screen after passing through the double slits. We know that light is not a continuous wave, but rather made up of photons. Why do some photons go one way while the other photons move in a different direction?

Steve Tonsfeldt, a physicist, replies:

     You have asked an excellent question that many other people have come up with. Richard Feynman once said something to the effect that the double slit experiment contains the fundamental mystery of quantum mechanics.

The first point to make is that our concepts of wave and particle are somewhat contradictory (complementary, as we say in physics). A particle is a point, just like you were told in geometry, but it has no dimensions! Awful hard to make a period for this sentence with no dimensions. On the other hand, an example of a perfect wave is y = sin kx, a pattern that extends from minus infinity to plus infinity. Again, it's hard to imagine any real object that can do that. So we need both particle and wave properties to describe real-world things and events.

The essential thing about light is that it travels like a wave and hits like a particle. So in transit the light wave passes through essentially both slits and yet when it comes to the screen, a tiny spot is made as a record of the detection of a photon or particle. This experiment has been done many times with extremely low intensity light and the researchers have seen the interference or diffraction pattern build up slowly, spot by spot, impact by impact.

Such behavior violates our so-called common sense, yet we must remember that our language and concepts reflect our experience in the macroscopic, everyday world and maybe should not be expected to apply to other realms of investigation. That's why experiments are so valuable in physics. We ask nature itself how it operates.

I hope this discussion helps. Please feel free to get back in touch. There are many excellent little books to read more about this topic.

Crystal M., a high school student, asks:

     We were going over intermolecular forces in chemistry and my teacher mentioned the London Dispersion Forces. The question is, what is the reasoning behind why they are named the "London" dispersion forces?

Jon Hutchins, a physicist, replies:

     London dispersion forces, the weakest type of Van der Waal's forces between atoms or molecules, were described using quantum mechanics by physicist F. (Frank?) London, I would guess about 1930.

Brenda, a high school student, asks:

     Why does hammering on a magnetized rod make the rod lose its magnetism?

Steve Tonsfeldt, a physicist, replies:

     Hello Brenda! Your question is a good one and it might be good to look up a photomicrograph of a ferromagnet in order to see the microscopic crystalline structure. Ferromagnets can be iron, steel, magnetite, cobalt, etc. and are all characterized by the existence of magnetic domains, little islands of order, in which tremendous numbers of atoms have their spins aligned in the same direction. Knowing that current loops are the cause of magnetism, that makes each domain a little magnet in its own right. If the iron, for example is unmagnetized, all of these little domain magnets are randomly oriented and cancel each other out. If there are more pointing in one direction than the other, then it is a "permanent" magnet. However these little magnets can be randomized by either hammering on the magnet or by heating the magnet above a characteristic temperature called the Curie temperature (after Pierre Curie, the researcher). For iron this is 770 deg. C.
     Magnetism is a fascinating subject and I hope you look up more on magnetic domains and ferromagnetism in particular. Enjoy!

Teresa Nichols asks:

     Here is the problem. I understand that TMG(trimethylglycine) is Betaine, and the HCL supplement is Betaine HCL. How much betaine does TMG contain?  Are there other things related to it---like Hydrochloride? How much betaine is in a betaine HCL 10 grain capsule?  What are the equivalencies between the two?

Jon Hutchins, a physicist, replies:

     According to the Merck index, betaine has a FW = 117.15, and the HCl compound has a FW = 36.5 higher, or 153.65, so 117g of betaine or 154g of betaine.HCl contain about the same amount of stuff. The grain is about 64.8 milligrams.

Shirley, a parent, asks:

     I need to find out what you would mix with baby oil to color it...I have a project that I need to use oil to preserve the object...Now I need to have a way to color it, but with what? If I use food coloring it beads up, if I use oil based paint, a settlement settles to the bottom, not staying mixed, & becomes cloudy, unless I used the wrong proportions.

Dennis Dykema, professor of art, replies:

     Your question is a bit of a puzzler. I can understand why food coloring wouldn't work as it is a dye in a water based liquid. Of course it will bead up in an oil based liquid. Other colorants like oil based paints achieve their color by the dispersion of finely ground solid pigments. These, as you've noted tend to settle because they are heavier than the oil, and occlude the clarity of oil because of their opacity.
        I remain a bit puzzled by your question, but suspect that you might have the best luck if you seek out someone who specializes in fiberglass fabrication. Such a manufacturer might be able to steer you to the dyes which are used to color the two-part resins which are the basis for fiberglass. You may remember 30 years ago or so, that craft stores sold kits which could be used to make clusters of plastic grapes or plums. These kits included dyes which were mixed into the resin along with the catalytic hardener. I think that sort of things has gone out of style, (thankfully), but I'm sure some major craft suppliers might be able to provide you with these dyes.

Andrea, a high school student, asks:

     I'm a sophomore in an honors chemistry class. I was doing some lab work on the molar volume of hydrogen gas for a project. My partner and I had a lot of trouble completing the lab work, but we finished it except for a section on the Ideal Gas Laws. We were wondering if there was a chance that gases may not be ideal at low temperatures or high pressures. I think that they might be but I'm not quite sure and she also had no idea! I was wondering if you could help explain this to me?

Steve Tonsfeldt, a physicist, replies:

     You are 100% correct in your suspicion that the ideal gas law breaks down for low temperatures and/or high pressures. Let's go back to the three assumptions for the ideal gas model.
     1. The gas is assumed to be composed of individual particles (atoms or molecules) whose actual dimensions are small in comparison to the distances between them. (Note that this assumption gets progressively worse as pressure increases or temperature decreases - the atoms or molecules get closer together.)
     2. These particles are in constant motion and therefore have kinetic energy.
     3. Neither attractive nor repulsive forces exist between the particles. (This one is violated big-time at low temperatures because many gases liquify, which means that the attractive force between the atoms or molecules wins out over the random or thermal energy. Also, at high pressures for any gas, there will be enough repulsive collisions between the atoms or molecules that will modify the pressure.)
     Physicists and chemists describe the deviation from ideal behavior in tables or graphs of the compressibilty or compression factor Z, which is defined as PV/nRT (= 1.00 for ideal gas) and usually plot Z versus P, the pressure that is measured experimentally. The net result to remember is that the product PV does not have the same value for all gases, nor is the pressure dependence the same for different gases, because the interatomic or intermolecular forces will be slightly different. Nevertheless, the ideal gas law is a good first approximation if the conditions are not too extreme.

Heather, a high school student, asks:

     If I'm looking at a plant and see that it's green, I know that I see it as green because it contains chlorophyll, a pigment that is green because it absorbs all wavelengths of the visible light spectrum except green, which it doesn't absorb well--am I right? Well, what is it that causes chlorophyll not to absorb green light? And if I see all other colors because they absorb every color in the visible light spectrum except that which I see, what is it that enables them to absorb those particular colors? In other words, why are things good at observing certain wavelengths of light while reflecting and transmitting others?

Joe Traylor, a physicist, replies:

     First of all, the color you see is a combination of MANY colors. The eye is an "integrating device." That is, it combines its response to all the wavelengths of light into one sum response called color. Thus, the green from the plant really has MANY colors which your eye interprets as "green."
     Now, about the absorption. This is really not as difficult as you might think. Imagine an atom not as electrons circling a nucleus, but rather as electrons in particular energy levels, each different level having a slightly different configuration or some other feature. All atoms will stay in the "ground state," the lowest energy state, unless something causes them to be excited to a higher energy state. Light is one of the things that can cause them to jump to a higher energy state. When that happens, the light photons are absorbed, with all their energy going into raising the energy of the electrons. You say, but when the electrons drop back to the ground state, won't they just give off the same light again? Not necessarily. Think of it this way: suppose the light that came in caused the electron to jump from state "0" all the way to state "5" in one jump. When the electron dropped back down, it might do it in steps: 5 to 3, 3 to 2, then 2 to 1, as an example. Result: different light emitted than absorbed. By the way, the dropping down sequence often gives off infrared (not visible) rather than visible light, so you don't see it with your eyes.
     Lastly, why green? Very interesting question. Plants have been made to absorb all across the visible spectrum so that they can use all the light, not just the green center of the spectrum. Thus, they absorb red and blue pretty well, and OK but less well in the green. Result: you see more reflected green that other colors. This way, the plants can grow even in subdued light that doesn't have much green! It's a benefit to us who try to grow plants indoors with artificial, house lights that are strong in the reds and weaker in the greens and blues. In the Fall, the same "green" plant turns red, not because it has added the red, but because the green chlorophyll has gone away. It was "red" all the time! The particular colors are determined by the atoms that make up the molecules of the material as well as the way the atoms are arranged on the particular molecules and the way the molecules bond to one another. It's all rather wonderful for me and an exciting way to think of the way nature is maximized to work together.

Bill Newsome, from Charlotte N.C., asks:

   I work with a lot of steamers and boilers in the food equipment repair business and I have tried to find out the answer to this question for a long time. For every pound of pressure in a boiler..How many degrees of temperature rise is there for every PSI of pressure?

Steve Tonsfeldt, a physicist, replies:

For lower pressures, such as up to 20, 30 psi on the gauge, the Handbook of Chemistry and Physics has essentially 2.5 Fahrenheit degrees rise for the boiling point of water for every 1 psi increase in pressure.

Ryan, a high school student, asks:

     I'm confused. Sound is a form of energy , I think, but it must travel through matter to diffuse. It exists as a wave like light does, but sound energy cannot "diffuse" unless accompanied by matter. Aren't there small particles in sound waves like photons in light waves? Also if I clap my hands in a vacuum, will the sound energy go through the vacuum and into any matter nearby? Or does the sound have to be made inside the matter?

Joe Traylor, a physicist, replies:

     You are on track but have one error in your thinking. Yes, sound and light both possess energy, but there is one very significant difference: sound is expressed in the motion of particles. It REQUIRES particles. That is, the motion of the particles IS sound. Yes, it is quantized, and the quantum is called the phonon by analogy with the quantum of light, the photon. (Phonon is pronounced "foh-non" and rhymes with photon.) So, sound is a disturbance of the positions of particles. Sound propagates by molecules colliding with each other or by one molecule pulling on its neighbor in solid materials. Light on the other hand is a disturbance of the electric field, not the positions of atoms or molecules. Thus, light can propagate in a vacuum where there is no matter. Electric fields don't require the presence of matter. Sound can only exist in matter (any kind, solid, liquid, or gas) and therefore cannot propagate in a vacuum. One more way to say it: sound is mechanical, and light is electrical.
     Lastly, you asked about clapping in a vacuum. Good trick if you could do it, but don't try. Our bodies don't behave well in vacuum! But suppose you could. Yes, energy would still go away from your hands, but in the form of heat, not sound. Furthermore, the heat would be expressed in infrared light waves! No sound, but rather light! The same thing happens when you clap you hands in air, but because to sound is so loud, you hear it and never think about the infrared that went away as well.
    I'm impressed that you are thinking about these things! Keep it up. The atomist view of matter and the energy view of waves are very important. Congrats on wrestling with such significant ideas.

Matthew Russo, a college student, asks: 

     What is the ionization of rain water as well as it's polarity? Also (this is what this is all about)...If rain water does not have a neutral ionization can a material or field with the reciprocal ionization repel or even disperse the rain water?

Jon Hutchins, a chemist, replies:

   Water is a polar molecule, but has no net charge. It contains ions such as hydronium ion and hydroxide ion, also ions formed from dissolved atmospheric gases, such as carbon dioxide and sulfur dioxide. However, the charges on all the ions will cancel out. Water droplets could be given an electrostatic charge (using electrodes) and made to move towards an oppositely charged electrode. This is the principle behind the electrostatic precipitator, used to remove tiny dust particles from power plant smoke.

Stewart Henderson, a college student, asks:

    I have been given a project involving analysis of low alloy steel. I have run AAS on these samples. I am however struggling to find a decent gravimeteric method to use to compliment this. Could you suggest some methods of determining the composition gravimetrically?

Jon Hutchins, a chemist, replies:

     You don't say what metal you wish to analyze gravimetrically. Nickel can be done as the red dimethylglyoxime complex. I'm sure other methods exist for different metals. I would suggest consulting a standard analytical reference text, such as Kohltoff's book, which should be available in any college library.

J. Nicol, a parent, asks:

Would you please comment on the following.

1) Cup of water brought to boiling point in a microwave oven
2) Water reheated a few minutes later in the microwave oven
3) Water did not appear to boil during 2) above although the microwave on time during this period exceeded 100 seconds.
4) Assumed microwave damaged by condensation during 1) above
5) Carefully retracted the cup at arms lenght
6) Upon reaching the cooler air outside the mwave cavity, the cup of water in its entirity flashed into steam.

Question:- What is the approximate maximum temperature that water can achieve when heated in the above manner at normal  atmospheric sea level pressure ?

Steve Tonsfeldt, a physicist, replies:

     You had a very close call with your microwave experiment! So-called "superheated" fluids are dangerously explosive and are sometimes avoided by the chemists' use of boiling beads, little glass beads they put in their beakers.
     Are you familiar with the fact that liquids are rather strange in that they can be both superheated above their boiling temperatures and supercooled below their freezing temperatures and still remain liquid? For example, according to the physics, clouds shouldn't form under the temperature conditions that are known to exist in the air. But they do form and so there must be a mechanism. It turns out that dust, soot, sea salt particles or other foreign matter provides nucleation sites or condensation surfaces for the water to attach to. Those instant heat packets that are sold are a supercooled solution that quickly freezes, liberating heat, when you disturb it by clicking a corner tab, making a nucleation site. 
     In the superheating of liquids the vapor pressure inside the very small initial cavity that forms is artificially low because it is surrounded on all sides by liquid and so any cavity that does form tends to collapse. This allows an unstirred liquid to be superheated above the "normal" boiling point. For smooth boiling to occur we again need nucleation sites such as small pieces of sharp-sided glass or bubbles of air. Perhaps like me you have seen a small stream of bubbles rising from scratch marks in the bottom of a pan of water on the stove that you are going to heat to a boil.
     I would suspect that your cup has a very smooth surface and that your initial heating of the water to a boil drove out all the initial air bubbles in the water so that there were essentially no nucleation sites. As with the heating pouches, any bumping can cause spontaneous nucleation of bubbles big enough to survive and the vaporization proceeds explosively. I have heard that water under carefully controlled conditions can be heated to 200 degrees Celsius, 100 degrees above the normal boiling point. 
     I am glad that you were not harmed and that you were curious enough to ask about why it happened. I hope this has helpe
d and please get back to me if I can be of further help.

Ben Myers, a college student, asks:

     As I understand it, we have three kinds of cones in our eyes that respond with small electrical discharges when they're hit with specific wavelengths of light--red, green and blue. Can we consciously (or unconsciously for that matter) tell the difference between an actual purple (pure, made up of only one wavelength of light) and a mixed purple (with two wavelengths that interact as in some Impressionist art where we get little dots of primary colors)? It would be interesting to see a close up of the waveforms (simulated, since it's not actually a wave or a particle) and compare them. I wonder if the two waveforms add exactly to equal that of the single waveform of purple? Perhaps it is that we don't actually have three kinds of cones --- just a smooth frequency response over the range of visible light? Makes you wonder about other things, too. Could we mix the right frequencies of infrared light to get something visible? Thanks for your help.

Bob Ferguson, a psychologist, replies:

     Ben--this is a really interesting question; I've had fun thinking about it. You've got several questions embedded in what you wrote, so I'll try to get to them all.
         First, it really does seem to be the case that we have 3 types of cone receptors in the normal human retina. Each type is sensitive to a range of wavelengths, but shows maximum sensitivity at either 420nm, 534nm or 564nm. These are often called the "blue", "green" and "red" cones, respectively, but it would be better to think of them as being most sensitive to short, medium and long wavelengths. There are lots of good, solid data to confirm these 3 types of cones, but I won't bore you with that here. What's more interesting is how they work to produce the experience of color.
     You are absolutely right that it's possible to create 2 identical appearing color patches, one from monochromatic light and one from a combination of two or three wavelengths. For example, a patch of nearly monochromatic yellow can be shown side by side with a patch that has no yellow at all, instead it's a combination of red and green light (yes, red & green), and if you get the balance of red & green just right, the 2 resulting patches will appear the same to the human observer. (BTW, such pairs are called metamers.) Why? Because the wavelength of the monochromatic yellow light is close enough to the "red" and "green" cones that it simulates both of them to fire. In fact, that's how the visual system normally codes for yellow: red + green cones firing. So, if instead we simultaneously stimulate the red cones with red light & the green cones w/ green light, we get the impression of yellow. As far as the visual system is concerned, IT'S THE SAME THING!!! [Somebody should make a TV commercial using that line. ;-) ]
     That's also how TV screens work. They produce tiny dots of red, green and blue light which are so small that they seem to blend together to a viewer seated at a normal distance. Note that the wavelengths don't really combine--they remain separate & distinct. By varying the brightness of the red, green & blue dots on an area, the screen produces all of the colors that the camera sees.
     Here's the simplest way to think about all this--wavelength is a physical dimension of light that can be measured by technology. Color is a purely subjective experience in the head of an observer. The two are certainly related, but not the same thing. So, if a light came on in the forest, but no one was there to see it, there would be no color.

Anthoy de Lorenzi, a parent, asks:

     Looking for cleaner faster transportation in the future, has any scientist used reverse polarity as a new concept for a car or train? The way magnets repel from each other you would think there was a way to make a floating car with no friction that would not use gas. For example, what if there were big enough magnets under a special car or train and other magnets in the road or track? Is this feasible?

Shawn Stone, a physicist, replies:

     You ask a very good question. Scientists have been using the repulsion of magnets for many years now. Japan has put magnetically levitated trains to use for 25 years without any accidents. Since there is no rail friction, the trains can travel at a very high rate of speed (up to 200 mi/h). This still takes energy however to get them going and keep them going (we still have to slow the train down and deal with air resistance etc.) The energy savings of magnetically levitated trains is significant using 60% less fuel per passenger than an automobile and 70% less than an air plane. Florida, Texas, and California are constructing Mag-Lev rail lines as we speak. As for cars, we are a long way from that I believe.  I hope this answers your question.

Crystal M., a high school student, asks:

     I was wondering how Avagadro's number was calculated and who calculated it (because I know it wasn't Avagadro).

Jon Hutchins, a chemist, replies:

     According to my old P. Chem book, Robert Brown (Brownian movement fame) calculated it in 1827. The modern derivation I have runs to 3 pages, and involves calculus. I don't have time to digest it and send a simplified proof, but I can send you a Fax of the derivation, if you send me a Fax number (hutchins@bvu.edu). Click here for more details on the History of Avagadro's Number.

Shawn Stone, a physicist, also replies:

     Thank you for your question. It is a good one and I had to look it up myself. In 1865 the Austrian chemist Johann Joseph Loschmidt used Maxwell's kinetic theory of gases and Avogadro's principle (gases of equal volume contain equal numbers of molecules) to arrive at 6.X10^23 particles. Since it followed from Avogadro's principle it was called Avogadro's constant.

Buddy Smith, a college student, asks:

     Dumping large amounts of raw sewage into rivers or lakes often leads to massive fish kills, although sewage itself is not toxic to fish. Similar fish kills also occur in shallow lakes that become covered in ice during the winter.  What kills the fish? How might you reduce fish mortality after the accidental release of raw sewage into a small pond containing large bass?

James Hampton, a biologist, replies:

     Glad to read of your interest in fishkills. As I understand it, the two phenomena, sewage kills and winter kills are related by oxygen content. Fish absorb oxygen through their gills from the water. The oxygen in the water is only a small fraction of what is found in the atmosphere and it is the contact of atmosphere and water that maintains the oxygen content of water. In winter, the ice covers the lake eliminating the contact between air and water, diminishing the oxygen content of the water. This is why the Department of Natural Resources wants to put an aerator in Storm Lake (in the town where I live), to keep the ice open and give contact between water and atmosphere. Large sewage dumps pose a similar problem since the sewage contains a large number of oxygen consuming bacteria. The bacteria use up the oxygen and the fish suffocate in a manner of speaking. Similar effects occur in some lakes in the fall as the decomposing algae serve as food for oxygen consuming bacteria, again diminishing the oxygen available to fish. Some kind of aerator would help with a fish kill in any of these cases (similar to what most people do in their fish tanks--you could use a fish tank to simulate some of these conditions) but the best thing is just to avoid the sewage spill in the first place.
     One last comment, some sewage dumps kill the fish outright because of the content of the sewage itself. Don't forget fish are breathing that stuff, but only when the sewage is at a very high concentration.

Liz N., a high school student, asks:

     The question is: In a lab, we put about a tsp. of CaCl subscript 2 and half a tsp. of NaHCO sub. 3 and 10ml. of phenol red, which is a pH indicator. When all three were mixed in a sealed plastic bag, a foamy yellow substance formed, the bag became warm, and it filled with carbon dioxide. After the reaction finished, the foam died down and a yellow liqiudy substance was left. My question is, what was the substance that was formed? My teacher doesn't know (this is a biology class) but says it was probably NaCl, Ca(CH) sub. 2, or CaCO sub. 3. She thinks it is probably not the second one. I know that the phenol red indicates pHs between 6.8 to 8, and it changed from red to yellow in the experiment. So basically, we mixed three substances which gave off carbon dioxide, heat, and a new substance, which is what? Please answer this as soon as possible! It is very important. Thank you!!

Jon Hutchins, a chemist, replies:

     I am assuming the phenol red is in water, otherwise this gets more complicated. The final yellow color tells you that the final solution is acidic. This is due to the excess calcium chloride, which can react in water to form Ca(OH)Cl + HCl. The HCl reacts with the basic sodium bicarbonate to liberate carbon dioxide and form sodium chloride. So your final mixture contains NaCl, carbon dioxide, and something like Ca(OH)Cl. 

Dave Williams, a teacher, asks:

     What does the insulation R-value (R-factor) stand for?  How can I use this information to calculate how much heat is lost from a Hot Water Heater over a period of time?  I would like to calcuate how much energy a 4500 W water heater uses in one day to keep the water at 147 F as compared to 120 F and how much less it would take to use a timer to turn on the water heater at 4:00 AM, turn it off at 8:00 AM, and back on again at 3:00 PM for supper, etc. to show my students that is less energy to get a programmable thermostat instead of leaving the heater on all day.

Steve Tonsfeldt, a physicist, replies:

    Hello Dave! The R-value for insulation is the English system unit for thermal "resistance" to heat flow. It is the reciprocal of the heat flow (in Btu) through 1 square foot of the layer per hour per degree Fahrenheit of temperature differential. In other words:
    heat flow rate (in Btu/h) = area A (in sq. ft) x delta T (temperature differential in Fahrenheit degrees) / R (in sq. ft deg. F/ Btu/h). 
     In order to do your calculation comparing energy used to keep the water at 147 deg. F vs. 120 deg. F, you will have to estimate the room temperature so you can calculate delta T for both cases and also estimate the insulation area A and the R-value of the insulation.
     For your calculations involving use of a timer to turn the heater on and off, you would need to use calculus to integrate the heat flow rate equations because temperature will depend on time. Please contact me if you need any help in setting up the equations. Perhaps the important point to make with your students is that the heat flow rate into the room is all waste heat and that it is proportional to T(hot water)-T(room) and that it is obvious that reducing T(hot water) by shutting off the heater reduces the amount of waste heat.  
Hope this has been of some help!

Scott, a middle school student, asks:

    Would it be possible to use ocean water when running steam turbines to create electricity? If so, could the heating of the water be adapted to condense the salt from the water, leaving fresh water which could then be used for irrigation or something else? Why is it so difficult to take the salt out of ocean water so that the fresh water can be used for other things?

Steve Tonsfeldt, a physicist, replies:

    Hello Scott! You have some very good questions about use of the ocean as an energy source. For any heat engine to work, you must have a high temperature input reservoir at temp. T-hot and a low temperature exhaust reservoir at T-cold, so you would probably have to use a deeper, colder water region and a warmer, shallower water region as your heat reservoirs. The next problem would be to find a working fluid appropriate for your heat engine. Ideally it would be some substance that would vaporize at the temperature of the warm water and condense at the temperature of the cold water. Scientists have considered possibilities like this, but the main drawback to getting energy from the ocean temperature differences is that the efficiency of the heat engine would be very low because of the small temperature differences available. Talk to your science teacher for help in making the calculation, but for the most efficient heat engine possible, the Carnot engine, efficiency = T-hot - T-cold divided by T-hot, where the temperatures are absolute temperatures in Kelvins.
    Your question on the process of distilling fresh water out of sea water is also a good one. Unfortunately it is very expensive in terms of energy at 540 calories per gram of water. Various desalinization plants around the globe have found it more efficient to use osmosis techniques for separating out fresh water. Ask your chemistry teacher for details on how osmosis works - it is a fascinating phenomenon!
  Hope this has been of some help. 

Kirsty MacArthur, a middle school student, asks:

     When is there the highest level of oestrogen in the menstrual cycle?

Jerry Poff, a biologist, replies:

     In order to answer the question we have to assume the menstrual cycle is 28 days long. That is not necessarily the case but it is an average length. If we make that assumption the estrogen(oestrogen) level is the highest on the 12th day after menstruation begins and a day or two before ovulation.  Thanks for the question!

Jeff Smith, a high school student, asks: 

     Is there any way to tri-sect an angle?

Tim McDaniel, a mathematician, replies:

     As you know, to "tri-sect" an angle is to divide it into three precisely equal parts (i.e., into three angles whose sum is equal to the original angle itself.) Can it be done?
         Mathematicians have proven that there is no way to tri-sect an angle by construction. "By construction" means you're allowed to use something to write with (pen or pencil), an unmarked straight edge, and a compass. Notice I did not say, "No one has yet figured out how to tri-sect an angle by construction"; instead, it has been proven that it cannot be done by construction!
         However, you can tri-sect an angle using a computer and appropriate program. You can also tri-sect an angle without a computer by hand using an implement known as an "Archimedean Spiral." Notice that in each of these cases you are violating the constraints associated with "by construction" that I discussed above.
          Thank you for the great question! Keep them coming!

Dali, a college student, asks:

     I want to make a medium similar to the Rembrandt medium. This includes boiling linseed oil with an oxidizing metal of low melting point which used to be lead.  This made the oil dry faster. Can I use another metal instead of toxic lead?

Dennis Dykema, an artist, replies:

     I'm not sure I can be of much help here. Many years ago I mixed up this medium, and I remember it as a dreary and time-consuming affair for a small amount of a really great medium. Knowing the toxic features of lead, I'd never do it again.
     A look at the periodic table should suggest some possibilities, but with my limited knowledge of that table, I'd suspect that there aren't any metals with the properties needed for this medium. Aluminum melts at a much higher temperature, and gold and silver are too expensive, (among other things). Zinc is the only possibility I can think of, though even that may have too high a melting point. Sorry I can't be of more help.
     I'll add this though, with the thought that you might be willing to try a substitute. NOTE: you can stop reading here if you're a purist, and go out a buy a very good ventilation system for when you're cooking the lead based brew.
     Otherwise try Liquin, a product by Windsor and Newton. It works well in making a paint with nice brushable qualities, it accelerates drying time, and retains a reasonable flexibility of the paint surface. I go further by mixing Liquin, Stand Oil, and Damar Varnish in a !:!:! ratio.

Kim Griffith, a high school student, asks:

     Can a solid freeze? How? What are some examples? How does this change happen? Do the particles change in any way?

Steve Tonsfeldt, a physicist, replies:

     Hello Kim! For the purpose of chemistry and its characteristic energies, the atoms are the building blocks that are unchanged in any physical change such as freezing. Usually we use the term freezing to describe the process of going from the liquid state to the solid state, from where the atoms or molecules are free to slip and slide around, to where the atoms or molecules are "locked in" to specific geometrical arrangements, such as in a crystal. But, depending on pressure and temperature, different solid structures are possible for the same atoms. Perhaps this is what you had in mind when you asked whether a solid could freeze. For example, water ice can exist in a large number of solid phases, depending on temperature and pressure. Likewise pure carbon can exist as graphite (like your pencil "lead") in a low pressure and temperature environment such as the surface of the Earth and as diamond under conditions of higher temperature and pressure deeper inside the Earth. I hope that this helps answer the questions you have posed!

Heidi asks:

     Can you tell me as much as you know about the BRADFORD METHOD? It's used for protein determination and for protein quantification. I specially want to know in which cases it's not possible to use this method.

Jon Hutchins, a chemist, replies:

     Regarding the Bradford method: I think you would need a water soluble protein. Otherwise you could do a total nitrogen determination by the Kjeldahl method. You need reagents (see Bio-Rad supply company) and a color measuring device (eg: a Spec 20 spectrophotometer) operating at 595nm. A procedure is given on p.20 of Experimental Approaches in Biochemistry and Molecular Biology by Zeidan and Dashek. Publishers Wm. C. Brown (1996). Good luck!

Dana Beeman, a middle school student, asks:

     What can you tell me about the different chemicals in bleach? I couldn't find much at the  library.

Jon Hutchins, a chemist, replies:

     Bleach is basically a water solution of sodium hypochlorite (Na+ ClO-). Hope this helps.

Jared Minnick, a high school student, asks:

      I have been looking like crazy to find a definition of a "heavy metal". I have looked at numerous inorganic and other chemistry books, dictionaries, encyclopedias etc. and the closest I could come was "a metal that has a high molecular weight".  This is not in depth enough for my needs. What separates a heavy metal from other metals? Are their specific differences other than weight? Thanks.

Tim Ehler, a chemist, replies:

     By definition, heavy metals are considered heavy because of their higher molecular weight. The heavy metals, those primarily near the bottom of the periodic table, exert their action primarily by inactivating enzymes; enzymes catalyze reactions by binding a reactant molecule at an active site. Most enzymes have amino acids with sulfhydryl (-SH) groups. Heavy metal ions have the tendency to tie up these groups rendering the enzymes inactive. One specific example is that of mercury, formerly known as "quicksilver", poisoning. Mercury ions will react with the sulfhydryl groups of an enzyme causing a change in the enzyme's physical shape. This change in shape will destroy the enzyme's active site rendering it inactive. Fortunately, there are antidotes for mercury poisoning.

     Heavy metals are also perhaps the most common of all water pollutants. The most frequently encountered heavy metal elements are those of lead (Pb) and mercury (Hg). Some less common elements include cadmium, chromium, nickel, and copper. Most often, it is inadequate disposal of wastes from mining or industrial activities that causes these metals to find their way into water supplies.

Karen, a parent, asks:

     We tried an experiment with 2 jars of water each containing the same quantity of rock candy. One jar sat on the table, unstirred, and the other was heated. Of course the heated one showed a quickend dissolving of the solid. Why? Is it because the hot water molecules are bombarding the solid more frequently, rather like more surface area exposed? Is it because the heat breaks the bonds between the molecules? I'd like the question answered with regard to the molecular activity so an 8-year-old can grasp it.

Shawn Stone, a physicist, replies:

     Rock candy is a large crystal of sugar. The molecules of sugar are loosely held together by a type of molecular bond called an ionic bond. When the water is heated this gets the molecules of water to start jiggling around much faster and harder than cold water. These water molecules now are moving fast and carry a lot of energy with them (this is known as heat). When they run into the rock candy, they have enough energy to knock some sugar molecules loose (more molecules than the cold water). Also, this happens at an increased rate since the molecules of water are moving around faster.

Carlos, an Italian pharmacist, asks:

     Hi. I'm writing from Italy. I am a pharmacist and today I had to prepare a water solution of citric acid 10%. The only two compounds were water and citric acid.  We have some books to help us in this situation and looking up citric acid I found that in diluted water solution citric acid transforms itself into ossalic acid by fermentation.   I would like to know
             1- If this is true? and, if true,
             2- Under which concentration does this happen?
             3- How fast is this process?
             4- What are the conditions that help or disturb this process?
Thanks for the help.

Jon Hutchins, a chemist, replies:

     I think you are talking about conversion of citric acid to oxalic acid. Fermentation requires some living organism (microbe). If this is not present (sterile solution) citric acid should be stable. After all, it is present in many fruit juices. Oxalic acid, incidentally, is toxic, so fermentation is to be avoided. The reason fermentation of dilute solutions may be a problem is pH. Lowering pH by using stronger solutions probably slows down fermentation.

Sara, an 8th grade student, asks:

     What is the meaning of 'rate' in  physical science?  

Steve Tonsfeldt, a physicist, replies:

     Rate involves two changes. Usually changes that occur as time passes are easier to understand. One example would be speed, which is the rate at which distance changes as time changes, and is therefore defined as the change in distance divided by the change in time. However, rates or changes can occur when variables other than time change, such as the concentration of one substance in a solution changing because of the addition of another substance of varying amount. Or one could talk about the change in average height for the countries in Europe as one goes from North to South there. There are many examples that one can come up with. The main point to remember when someone talks about "rate" is that one thing is changing because something else is changing. Hope this has been of some help!

Ashlee, a parent, asks:

    Is light from a fire matter?

Shawn Stone, a physicist, replies:

    Thanks for your question Ashlee, it is a very good one.
    What defines something as matter is the property of mass (how much stuff they are made of). We can tell that everyday objects have mass because we can touch them and see them. They are quantifiable to us and so we have no question that they have matter (mass). For light, things become a little bit harder to measure. We do know that light can be considered to be made of particles called photons. However, we do not have an instrument that can measure the mass of a photon directly. This is where things get a little bit complicated. It was Einstein who discovered an equation that helps matters a little, E=mc^2. This is a relation that states that energy is mass multiplied by the speed of light [c] squared. It effectively finds that matter is energy and energy is matter. You know that from sitting next to a fire that you feel warm much like the Earth is warmed by the sun. This light carries energy, and must contain some mass (matter) according to E=mc^2, but we have not been able to experimentally verify (measure) this yet.
     I hope this was not too complicated. If you have any other questions, please do not hesitate to ask.

Tami, a college student, asks:

    Why do you think people view psychologists as being different from scientists?

Bob Ferguson, a psychologist, replies:

    First, what evidence do you have that they do? Personal experience? Common Sense? Anecdotes? As I see it, contemporary psychology is centered around the notion that these are not reliable sources of information if we really want to understand human behavior. Instead, we need to do systematic observation under controlled conditions (can you say "experiment"?) where alternative hypotheses can be ruled out. And therein lies part of the problem, as well as part of the answer to your question. Many of the most interesting & important questions about the human condition are not especially amenable to controlled experimentation (for example: What went wrong at Columbine?). This leaves the door wide open for all kinds of speculation, much of which can never be tested, but is very popular on talk shows and in popular bookstores. Combine this with the fact that anyone who is willing to write or talk about human behavior is often regarded as a 'psychologist', & I think the outlines of an answer to your question begin to emerge.

Finally, one last factor probably also plays a role--a phenomenon from social psychology called the 'availability heuristic', which simply says that we often base our judgements about people or events on those instances which are most 'available' to us--i.e., the ones that are most memorable. And who are the most memorable 'psychologists'? Freud, Jung, Joyce Brothers, Dr. Ruth, and Bob Newhart (at least for those of us old enough to remember his TV show). Most of these are not even psychologists, and none are typical of the profession, yet they define psychology for much of the population.

So, IF it's true that psychologists are viewed differently from other scientists (and that's a testable question), these may be some of the explanations.

Corinna asks:

    Do you think that stabilized oxygen can be used in place of iodine or chlorine to purify water?  Is it safe used in conjunction with a .01 micron water filter?

Jon Hutchins, a chemist, replies:

    Ozone (O3) is widely used to disinfect water, especially in Russia, I believe. It is made by an ozone generator which requires electricity and air, but no other chemicals. I would not describe ozone as stabilized oxygen, actually it is destabilized. Some oxygen releasing agents (oxidizing agents) may well be useable for disinfecting, but I don't know the specifics. Obviously the byproducts would need to be non toxic. 

Louise McCarney, a college student, asks:

   Why does blowing on a lighted candle, if blowing hard enough,  put it out?  What is the flame and what are the conditions necessary to sustain the flame?  How does blowing on the flame alter these conditions so that the flame is no longer sustained?

Steve Tonsfeldt, a physicist, replies:

    The question about why blowing hard toward a candle will put it out is a very good one! Most people are already thinking about eating the birthday cake under the candles. Candles have a lot of chemistry and physics in their operation. Michael Faraday gave a whole series of lectures entitled "The Chemical History of a Candle" in 1848 in the famous Christmas lectures at the Royal Institution in England. If you are interested in the topic, it is covered in a book in the Scientific American Library series called "Fire" by John Lyons, W.H. Freeman Pub. As for the question, recall that a candle is solid and needs to melt (which takes energy) and that capillarity takes the liquid up the wick to the point where the liquid is vaporized (which again takes energy) and this vapor is burned in the flame. You can prove this by blowing out the candle and quickly hold a lighted match not to the wick, but above the wick. The candle will relight! So the heat from the flame is necessary to do these conversions and also to provide the activation energy for the combustion reaction itself. If you blow gently , it will burn brighter because you are feeding in more oxygen, like a bellows at a furnace, but if you blow too hard I think you blow the heated air away from the wick and the temperature drops below the combustion temperature. Hope this helps! It's a very good question about a fascinating phenomenon.

Laura Mangan, a high school student, asks:

    My I am doing a paper on beer for chemistry and I need the chemical compound for it, and I can not find it.  I also am showing the difference between beer and non-alcholic beer and having no luck.

Jon Hutchins, a chemist, replies:

    Beer contains a huge variety of compounds, derived from grain, from yeast, and from hops. I suggest looking at a science encyclopedia if you need further details. The major constituent is water, with about 4-5% ethyl alcohol. This last material is mostly removed in non-alcoholic beer.

Marisa Szeps, a grade school student, asks:

    My science project has to do with attracting and repeling forces due to electrical charges. I inflated two balloons and attached them to string. I hung both from a door jam. I rubbed each of them ten times against my hair. They should have attracted but I could only get them to repel. Why? Why? What influences the electrical charges and can you suggest a way to make it work?

Steve Tonsfeldt, a physicist, replies:

    Marisa, your balloons acted properly by repelling each other because since you prepared them the same way, they had to be of the same charge, and like charges repel. I think they were both negatively charged. To see why, let's start with this. Materials are made of atoms and atoms are usually neutral - they have as many electrons as protons. However the outer electrons are held less tightly and are most easily shed. The process is not entirely understood, but different materials (different atoms) have different attractions for these outer electrons. For example, if you lay a piece of Saran wrap on a metal bowl, it will cling, because electrons are transferred from the plastic wrap to the more-grabbing metal. Rubbing really only effects things in increasing the area in contact and not much else. Anyway, by comparing different materials placed in contact, a so-called triboelectric sequence can be generated. The following list is taken from Physics, by Eugene Hecht, 1994, Brooks/Cole Publishing:

asbestos, rabbit fur, glass, mica, wool, quartz, cat fur, lead, silk, human skin or aluminum, cotton, wood, amber, copper or brass, rubber, sulfur, celluloid, India rubber

    Of any two materials from the list placed in contact, the first becomes positively charged and one listed anywhere after it becomes negatively charged. Since human skin and the furs(human hair also?) are before rubber it looks like they become positively charged and your rubber balloons become negatively charged. In order to get attraction you need to rub one balloon with sulfur or celluloid to make it positive, so that it will then attract your negative balloon. Give it a try and good luck!

Fran Knobel, a parent, asks:

     My son recived an "E" on his science fair project. His teacher said, "Your project was more of a survey than a scientific project. You did not have an independent/dependent variable." Please explain these variables. His project was "Which Greens Do Kids Prefer"--Spinach, Broccoli or Green beans." 25 girls and 25 boys, both between the ages of 6 and 12, were asked.

Bob Ferguson, a psychologist, replies:

     I''m not familiar with the requirements that your son's teacher specified for this project, so I cannot comment on the grade, but perhaps I can clarify a couple of the terms & ideas you asked about. First, some definitions:
   Independent Variable: This is a factor that is under the researcher's control and that is systematically varied or manipulated to determine its effects. To truly qualify as an independent variable, the researcher must control the amount and timing of the independent variable as it is applied to each person in the experiment. Clearly, neither sex nor age qualifies since your son had no control over how those were assigned to the individual people.
   Extraneous Variable: This is a factor which might influence the outcome of the experiment, but that is not the focus of this particular study. Extraneous variables are the potentially contaminating factors which, if not controlled properly, can make the interpretation of a research project virtually impossible.
   Dependent Variable: This is a factor that is systematically measured, at times and in ways determined by the researcher, in order to assess the effects of the independent variable. In other words, this is what you look at to see if the experiment worked. If I understand your son's project correctly, the participants' food preference responses would qualify as a dependent variable.
    Now, let me make an assumption: when the teacher said that this was not a "scientific project", I assume that she/he was referring to a "scientific experiment". If so, then I agree--technically speaking, this was not a true experiment. Why not? To avoid a long & really boring answer, let me just say that the essence of a true experiment is to achieve enough control over all three of the types of variables I listed above so that cause-effect questions can be asked (i.e., did the independent variable cause the dependent variable to change?") Other types of studies (observational research) can tell us WHAT happened, but not WHY.
     Now--back to your son's study. If he found that either sex or age was systematically related to their veggie preferences, what would that tell us? Would we know why the differences occurred? No. For example, there are lots of differences between boys & girls other than sex which might account for the different preferences.
     So--instead of being a formal experiment, this project seems to be an example of descriptive research, and there is a long & distingushed history of this type of research in both the behavioral and natural sciences. Sometimes, the degree of control needed to qualify for a true experiment just isn't possible (astronomy is a good example of an entire discipline built on observational research). There is nothing inherently wrong w/ observational or correlational research--it's just important to keep in mind the limitations of such work. If you have a cause-effect type question, then an experiment is needed.   Hope this helps.

Ben Meyers, a college student, asks:

I'm thinking about tracking systems for the theatre, that is using an array of antennae to measure the level of a radio signal coming from an RF transmitter, then compairing and triangulating to get the location. I think i'd need three antenna for a 2D space and 4 for a 3D space.
     I've been looking for information on the web for a while and I cannot seem to find much about how the atmosphere impedes radio transmission. Maybe I have not looked hard enough. What do I have to worry about other than the inverse sqare law? What does air do to RF transmission? What about big bags of bone and water?
     PS.  I mean high VHF and UHF.

Joe Traylor, a physicist, replies:

     Yes, there are atmospheric effects, but they are not likely to be a problem for you in theater. Relections from walls, steel superstructure, etc, may be more of a problem, but even then may be accounted for during your calibration exercise. The difficulty is that, due to reflections and the resulting interference caused by them, that the signal strength from a transmitter can vary *greatly* as the person moves from spot to spot on stage. This is why typical auditorium wireless PA systems usually use two antennas instead of one; when one receives a weak signal, the second may receive a stronger one. The weakened signal can occur just because the speaker turns his/her head.
       Triangulation is the basis of GPS, the global positioning systems, so you're on the right track.
    As I recall, you are at ISU. No doubt the ISU library has a bunch on this. I suggest you check it out. Check out the ARRL Handbook and look under vhf and uhf, and on the web,
www.arrl.org. Search the technical area.

Don Hall asks:

Does sodium have a frequency? Can it be manipulated by ultrasound? 33mHz? Can sodium be mutated into another form? chlorites? This is a project to rid brine content of drilling water.

Jon Hutchins, a chemist, replies:

Sodium ion can be removed from water by ion exchange, reverse osmosis, distillation, possibly by complexation. Changing another sodium salt (eg a chloride) to a chlorite really does nothing to the sodium, only the anion. I'm unsure about the ultrasound question.

Sara McKean, a high school student, asks:

In what stage of pregnancy is the gender of the baby determined?

James Hampton, a biologist, replies:

     The gender of a human baby is determined at the moment of conception. Human sex determination is based on the complement of sex chromosomes. Females have two copies of the X chromosome in addition to 44 non-sex determining chromosomes (autosomes). Males on the other hand have only one X chromosome and have a Y chromosome that includes genes to make them male. When eggs and sperm are produced, collectively called gametes, they receive only one of the sex chromosomes. Since women have only X chromosomes that is all that eggs can have. However, males have both X and Y so half of sperm contain the X chromosome and half contain the Y. If the egg is fertilized by a sperm containing the X chromosome, then the baby will be a girl and this is determined from the moment of fertilization. On the other hand if a sperm carrying a Y chromosome gets to the egg first, then the zygote and resulting baby is male.

     This method of sex determination is not universal. There are almost as many methods of determining sex as there are possibilities. Some species, like many birds, have females that are heterogemetic W & Z chromosomes while the males are homogametic ZZ. Some creatures like crocodiles have sex determination based on the temperature of the egg while it is incubated, one sex coming from cool eggs and the other from warmer eggs. There are many shellfish that start out life as one sex and change to the other as they mature. Finally, there are some fish that can be either male or female depending on the environment in which they find themselves.

Shannon Hill, a middle school student, asks:

I am doing a science project to see if adding horse manure to a compost pile will speed up the process of the decomposition of the material within the pile. My project is all set up and going, but I am unsure how to go about measuring decomposition in a scientific way. There are two piles, each with soil, egg shells, potatoe and apple peelings, and a coffee filter. One of the piles has the added horse manure. Please help. Thanks.

Chad Scholes, a biologist, replies:

There isn't a simple way to measure decomposition. I will mention several things that may be useful to you for your experiment.

Decomposition is dependent upon living things feeding on the material. Compost piles typically have many types of organisms that are associated with them. Macroscopic organisms such as earthworms, millipedes, mites, and other invertebrates are important initially in breaking down the large pieces of material into smaller ones. When the pieces are smaller then fungi, protozoans, and bacteria will do most of the work. Therefore, observations of the organisms associated with the decomposing material can indicate the rate of decomposition.

As organic material decomposes, the structure, texture, and color of it often changes. Frequent observations and pictures will help you document the rate of decomposition. One easy way to measure this might be to measure the height of the pile of material, assuming that you do not disturb it.

Decomposition usually results in the production of many gases. Two of the gases that will be produced are carbon dioxide and methane. If you have your compost piles in a type of container you could cap them and measure gas production (possibly with a balloon) as an indicator of rate of decomposition. One of the problems with capping your compost piles is that the organisms doing the decomposing need lots of oxygen to do a good job. Some organisms can decompose without oxygen, but it is usually slower and much smellier.

Compost piles are usually fertilized and inoculated with organisms to help begin decomposition. Which of these do you think your horse manure will do?


Jean Bogart, a middle school student, asks:

The question is: I am an 8th grader who is fascinated by artificial intelligence. For my science project this year, I'm considering coding a very crude, simple chatterbot. Anyway, do you know what language would be best to program in (preferably an easy version of BASIC if possible?), how I could get started, and where I could find some source code to use as a template? (Or will I have to start from scratch?)
And if this is too difficult to be attempted, I apologize for wasting your time. I actually designed a similar program last year--without any adult help--and the results were less than encouraging. However, I did manage to create a very simple conversational program using an old Apple IIe and a whole lot of code in BASIC.
My research led me to this page (I believe you teach courses in artificial intelligence, or something of that kind). I hope you can answer my question, since this has been my dream project for quite some time.
Thanks! :)

Ken Schweller, a computer scientist, replies:

Thanks for writing Jean. You came to the right place. My hobby is constructing conversational bots and I have created them in many languages, including BASIC. One of my bots who goes by the name of 'MrChat' is especially notorious. He has appeared in two books already.

hwired.gif (13777 bytes) Outline of "High Wired: On the Design, Use, and Theory of Educational MOOs"
University of Michigan Press, 1997.  Contains a chapter by Ken.
bots.gif (5721 bytes) Andrew Leonard's book Bots devotes a chapter or so to Collegetown's MrChat programmed by Ken Schweller

MrChat will be appearing by himself in a full chapter interview in a new book out Fall 1999. You can learn to program a bot like MrChat by visiting the CollegeTown Virtual Community at Buena Vista University and applying for membership.   Once you log onto CollegeTown you can proceed to Ken's Office to talk to MrChat or to the TV Studio where you can ask to have your own bot which you can then program. This bot is created using a special object oriented programming language called MOO code.   If you log onto CollegeTown contact Ken (me) for further details. Press here for further instructions on programming a conversational bot and here for details about the Loebner Contest, an annual contest pitting bot against bot to see which appears most intelligent. Caution:  None of these bots has come anywhere close to passing Turing's Test which challenges a user to pick which of two conversationalists is a bot and which a human simply on the basis of keyboard output. All conversational bots use simple pattern matching, key words, and random responses to create the illusion of intelligence but they understand little or nothing about what they are saying.


Ajit Dubhashi, an electrical engineer, asks:

I am an electrical engineer so perhaps my question is really stupid.  I need to have a surface completely free of silicone.  We suspect that the surface has a thin film of this on it  which causes poblems.  Is there a simple quick test that can be performed on the surface such as 'add a drop of alcohol, add a drop of XYZ and look for change in colour etc' ?   We have tried using UV light that causes the material to flouresce but this is difficult for thin films.  Thanks for your help.

Jon Hutchins, a chemist, replies:

Probably the standard way would be infrared analysis, using some surface technique involving bouncing IR across the surface, and seeing what wavelengths are absorbed. I don't know of any simple chemical test (silicones are pretty unreactive), however, a physical test involving wettability might work.  Sorry, don't know the details. Finding a very good clean solvent to remove the oily silicone layer is, of course, important. Good luck!


Joanne H. Davis, a teacher, asks: The question is: We are currently building series circuits. The light source we are using is a LED. The energy source is two "d" cell batteries connected in series. When we hook in one LED it works fine. However, when another LED is added, the batteries will not carry the load. Why does it take so much voltage to run a LED?

Joe Traylor, a physicist, replies: You've asked a good question that has a subtle answer. It is not that the battery can't "carry the load" but rather the LED itself causes a voltage drop that is more than half of the battery's voltage. Therefore, two of them in series require more voltage than a 1.5 Volt cell can deliver. Voltage is a funny concept. A good way to think of it is the ability to cause current to flow. Thus, a 3 V battery can push current twice as strongly as a 1.5 V cell. Now, LED's are like a tall hill. It takes a minimum push (voltage) to get up the hill, called a threshold voltage. The particular value depends on the materials used to make of the LED, but typically they are between 0.6 and 0.9 V. Less than that threshold, and no current flows. More than that, and yes, it flows and lights the LED. Put two of them in series and EACH requires that much of a threshold voltage. A typical 1.5 V cell will likely not have enough push to do them both, but one D-cell should be able to light one LED. But you say, you've already tried two batteries. Now you may have a second phenomenon going on. Were the batteries new? (I mean, brand new from the store.) As carbon batteries get old --both in age and in use-- the internal resistance of the battery increases dramatically. Alkalines not as bad, and lithiums less yet, but all do it to a degree. If you measure the voltage of the battery with a voltmeter, it will probably read 1.5 V. But, in a working circuit with current flowing, the resistance of the battery itself eats up much of the energy, and the effective voltage available to the rest of the circuit may be much lower than 1.5 V. (This is the reason car batteries don't work well in cold weather; the internal resistance increase as temperature decreases.) Suggestion: to confirm what I've said, try two NEW batteries in series with two LEDs. The voltages of the two batteries will add and make a total of about 3 V and should light both LEDs. Good luck! Second suggestion: Try one battery and two LEDs, but this time wire the LEDs in parallel. If both light, your battery has enough ummph to carry the load.


Kara Ellis, a teacher, asks: Can you explain, in third grade terms, the process of the Earth revolving and rotating around the Sun? My students are having some difficulty with the concept that the Earth revolves, the Moon orbits around the Earth, and the Earth and moon together orbit the Sun. Can you help us out?

Mark Biermann, a physicist, replies: The motions of the moons about planets and of the planets about the sun is one of the most fundamental questions in all of science. It is not surprising that your students are having some trouble with the whole concept because aspects of this question have been challenging scientists for thousands of years, and many questions still remain. When you ask about the "process" of the Earth revolving and rotating there are two basic aspects of the question that must be dealt with: what is happening and why it is happening. Let's look at the "what" part first. Our solar system consists of all the objects that orbit, or revolve, about the sun. The sun is a star and is incredibly large compared to the other objects in our solar system. The primary objects in the solar system, besides the sun, are the planets and the moons that orbit the planets. Not all of the planets have moons, and some planets have many moons. It turns out that the earth has one moon. Venus, which is about the same size as the earth, has no moons, and Mars, which is much smaller than the earth, has two moons. This is just the way things are in our solar system. One can picture all of the planets lying in one plane that passes through the sun. That is, if you were to set the sun on a table (you would need a big table), all of the planets would pretty much lie on the same table top. Being one of the planets, the earth travels in an orbit about the sun on the same table top as all of the other planets. The path that the earth follows as it revolves, its orbit, has the shape of a slightly flattened circle, called an ellipse. The earth's orbit is very close to a circle, but is not quite a circle. The earth moves along this oval path all of the time and repeats one full circle each year. So, it takes 365 and a quarter days for the earth to get back to the same place in its orbit. In the same way that the earth orbits about the sun, our moon orbits about the earth. The orbit of the moon is an ellipse, an oval that is not quite a circle. If we go back to thinking about the table top, the path of the moon does not quite lie on the same table top as the path of the earth. For half of the moon's orbit it is above the table top, and half of the time it is below the table top. Note, however, that this tilt is actually quite small. Since the moon orbits about the earth, it follows the earth along in the earth's orbit. The moon always stays centered on the earth and since the earth is moving, the moon must follow along with it. The moon only takes about 29 days to complete one full orbit about the earth. Thus, while the length of a year is based on the time for the earth to orbit the sun, the length of a month is about the length of time it takes to moon to orbit the earth. The motion of the earth about the sun, and of the moon about the earth goes on constantly. At certain times, the moon can get between the sun and the earth. The moon is about 400 times closer to the earth than the sun and so it is never in danger of getting lost to the sun. However, when things line up just right, the moon can block our view of the sun from earth. We call this a solar eclipse, since the moon is blocking, or eclipsing, the sun. If the earth gets between the sun and the moon, which happens fairly often, we get a lunar eclipse, since the earth blocks the sun from the moon. While all of this is going on, the earth continues to spin on its own axis like a top. However, the top is slightly tilted. Go back to the table top idea. The earth is revolving, or orbiting, on the table top. However, it is not spinning straight up from the table top. Like many spinning tops, the earth leans a little bit to one side as it spins. The spinning of the earth is what gives us day and night. When the side of the earth someone is on is facing the sun, that person has day. When the person is facing away from the sun, that person has night. If the earth were pointing straight up from the table top as it spins all the people on the earth would have the same length of day and night. That is all people would have 12 hours of day and 12 hours of night in every 24 hour day, because 24 hours is how long it takes the earth to complete one spin. Because of the tilt in the earth's spin, only the people on the equator have 12 hours of day and 12 hours of night all of the time. All the other people on the earth have longer days during the summer and shorter days during the winter. Well, this has gotten quite long. But before I quit I should say a little about why the sun and the earth and the moon move the way that they do. The whole solar system is held together by a force called gravity. Gravity is one of only 4 basic forces that we know about. Gravity exists between any two objects that are made of matter. It is always a force that wants to pull the objects together. So, it is gravity that holds you to the surface of the earth and it is gravity that holds the moon to the earth and the earth to the sun. Many other details can be discussed, such as why things formed as they did in the solar system and why the orbits have the shapes that they do. These are rather complicated so I won't go into them now. However, if you want me to do so, let me know and I will be happy to try. I hope this at least starts to answer your question. It is a great question and I hope you keep on thinking about it.


Kim Ringeisen, a parent, asks: Which is heavier, cold water or hot water ? If hot water is heavier, why does cold water lay lower than the hot water layer in the oceans? I believe that hot water is heavier due to its expansion - it has more mass, but sinks because it is more dense - is this true?

Mark Biermann, a physicist, replies: You have posed a very good question. Water is a unique substance in the way it changes with changes in temperature. Most liquids follow a simple pattern: as the temperature of the liquid increases, the liquid expands. The other way of saying this is that as the liquid cools, it contracts. As the liquid contracts, it becomes more dense. That is to say, more mass gets packed into a smaller volume of space. So, a cube of a liquid with dimensions of one inch on a side will contain more mass if it is more dense than another liquid. The more dense liquid will thus have more mass per volume, and, hence, more weight per volume. This will cause it to sink below a liquid that is less dense. For most liquids, then, the rule is simple. The colder the liquid, the more dense it is. Thus, the coldest part of the liquid is always at the bottom. But then there's water. Over a wide range of temperatures, water acts like most other liquids. From 100 degrees Celsius (212 degrees F) to 4 degrees C (39.2 degrees F), water will contract as the temperature drops and expand as the temperature rises. However, from 4 degrees C to 0 degrees C (32 degrees F) water does just the opposite. As the temperature of water drops from 4 degrees C to 0 degrees C, water actually expands. So, water is most dense at 4 degrees C and water at this temperature will always sink below water at any other temperature. The interesting behavior of water from 0 degrees C to 4 degrees C is why water always freezes at the surface. Water freezes at 0 degrees C (32 degrees F). Say we have a lake and that fall is going into winter. The air temperature is cold enough that the water in the lake starts to cool. Water near the surface drops from about 55 degrees F (13 degrees C) to about 46 degrees F. The cooler, denser water sinks below the warmer water below it. But now the surface water cools even more. It drops below that all important temperature of 39.2 degrees F. Now, as the water cools further, it becomes less dense. Instead of sinking, it floats at the surface of the lake. When the temperature of the surface water reaches 32 degrees F, it freezes and we get ice on the surface of the lake. The sort of "backwards" behavior of the water just above the freezing point makes this possible. I hope this answers your questions. Water is certainly a wonderful substance. It's what makes the earth unique among the known bodies in the universe.


Cory Loes, a college student, asks: If black is the lack of all colors, and when a person uses bleach, bleach is suppossed to abstract all colours, then why does an object turn white, instead of black? White is all the colors on the spectrum. Maybe I am wrong, but just wondering.

Mark Biermann, a physicist, replies: You have gotten into a subject that has caused much confusion over the years and for good reason. It can be a confusing topic. The key to minimizing the confusion is to keep in mind a clear distinction between two closely related, but very different, parts of this problem: color and pigment. Color is best defined based on light itself which provides us with the information that the brain needs in order to perceive color. White is in fact the color that you get when all of the colors of the visible spectrum of light are combined together. So, white light is the light produced by the sun and other sources that produce a continuous spectrum of light that includes all of the visible colors. Now for the other part of this problem: pigment. Pigment is a dye or something similar. It is added to cloth or paper or paint or whatever to produce different colors. How does it produce different colors? Let's take the example of a piece of red cloth. When white light falls on a piece of red cloth the molecules of pigment in the cloth act in such a way as to absorb all of the colors of light EXCEPT red. The red light is reflected off of the cloth and travels to the eye of an oberver. For this reason, the observer sees the cloth as being red, because only red light reaches the observer's eye from the cloth. And this is pretty much the way things go for all different colors. The pigments in the materials selectively absorb some colors and reflect other colors. The color we see for a given material depends on what combination of colors of light have been absorbed or reflected. Now think about paints. I remember mixing different colors of paint together to see what color I'd end up with. By mixing different colors of paint, I was producing different combinations of pigments that absorbed and reflected different colors of light. Different combinations of pigments produced different colors of paint. However, one combination always produced the same result. When I combined all of the paints together I always got black (or maybe a really dark brown). This makes sense when we think in terms of what pigments do. Pigments selectively absorb certain colors of light. If we combine more and more pigments together, more and more colors of light get absorbed as a general trend. When all of the pigments get combined we are getting the maximum absorption possible. All of the different colors of light are getting absorbed and so, of course, the resulting paint looks black. In summary, a combination of ALL the pigments leads to ALL of the colors of light being aborbed so that NONE of the colors get reflected to your eye and you get black paint. Note that things actually get rather complicated when dealing with pigments, but the general idea of the above argument holds true. Now how does bleach fit into all of this? We use bleach to make clothing look nice and white. To get something to look white, we want it to reflect as much of the white light that shines on it as possible. Hence, we want as little absorption as possible. What bleach does, then, is to remove as much PIGMENT from the material as possible. The absence of pigment allows for all of the colors of light to be reflected from the material and so it looks white. So bleach does not remove "color" from cloth. It removes pigment from cloth. While combining all of the colors of visible light together does give you white light, combining many different pigments together does just the opposite. If we want something to look white we need to remove those pigments. That is what bleach is for.


Ben Meyers, a high school student, asks: I have a question about your book. (Physics of stereo/quad sound) In section 6.5 you talk about column speaker systems in which multiple loudspeakers reinforce each other to produce a more directed wave. This happens because at certain angles away from directly in fromt of the column the waves cancel with each other and in front of the column the two waves line up crest to crest and trough to trough. That's the part I don't understand. Why do you get 4 times the intensity directly in front of the column instead of just summing the intensities of the two lou dspeakers? And is the energy that is directed away from the normal and then canceled out ju st wasted? If it is... that's a bummer. Someone told me something about it being in my trig/algebra class this year (some double angle identity thing) but i don't remember. thanks.

Joe Traylor, a physicist, replies: Thanks for reading my book! It's flattering to any author to have people read their work and ask questions. Your question relates to how two (or more) waves interfere. You are right: the AMPLITUDES of the waves just add or subtract. Thus, the resulting amplitude of the total wave is just the sum of the amplitudes of the individual parts. However, the intensity of the wave is what our ears respond to, and that depends on the SQUARE of the amplitude. That means that if two waves of equal amplitude are perfectly in phase, the total amplitude is twice as great but the intensity is FOUR times as great, since 2 squared is 4. When two speakers both give off sound, there will be some places where the intensity is four times as great as one speaker would make. (Or, if there are 10 speakers, there will be some spots where the intensity is 100 times as great as from one!) In other places the waves will cancel each other giving zero amplitude and zero intensity. (If you're interested, check out pages 12-14, 121-123 in the book.) The result is that you can combine several speakers in a single cabinet to produce a pattern of sound that is very intense in some directions and almost negligble in others. This effect is used to focus sound on an audience, rather than sending it up or back where there are no people. You asked about the energy. Don't worry; no energy is lost. If you calcualted the total energy produced, you would find it to be the same as the total of each single speaker. The intense regions have high energy and the quieter ones low energy, but the total over all directions is the same. So, you could think of the focussing effect as focussing energy as well as focussing sound. Fascinating topic! Glad you asked!


Leia, a grade school student asks: Why is the middle of the earth so very hot that it melts rocks?

Joe Traylor, a physicist, replies: A very good question! The center of the earth is so hot because of the enormous pressure that the outer parts of the earth exert on it. You are familiar with the effects of gravity holding you down to the earth, making things fall toward the earth when dropped, etc. Most people don't think about the fact that the earth itself is held together by gravity! That means that the matter on the outer parts of the earth is really pushing down on the insides, and that push causes high heat. The same is true for every planet. A real life example of this: when a car drives on ice, sometimes the weight of the car causes enough pressure to cause the ice to melt-- at least enough to make a slick layer of water on top fo the rest of the ice. Makes driving in icy conditions even worse. By the way, bet you didn't know: the very center of the earth is actually solid, not liquid! Yes, most of the core is liquid, but at the very middle it's thought to be solid again. The reason is the same: the enormous pressure. In the very center, the pressure is so high that even at the high temperatures, the materials are pressed together to be solid!


Garrett McLeish, a college student, asks: If a beam of light shines on a sphere whose diameter is equal to the diameter of the light beam, is the total surface of the sphere equally shadowed as it is lit? Is there an exact border where a shadow (dark) and light meet? Are any reactions taking place at this border as well?

Mark Biermann, a physicist, replies: If a sphere is centered within a beam of light that has the same diameter as the sphere, then one half of the sphere would be illuminated and one half of the sphere would be in the dark. The side facing the beam of light would, of course, be the well-lit side, and the side, or hemisphere, away from the beam of light would be the dark side. As to how exact the division between light and shadow would be, one has to consider a number of factors. The most important are surface roughness on the sphere and the wavelength of the light. If the surface of the sphere is quite rough then you would see a rather fuzzy line between light and shadow. When dealing with light, distances shorter than a wavelength of light, which is quite short, cannot be distinguished. Hence, even if the sphere were "perfectly smooth" the division between light and dark wouldn't be more "exact" than to within a wavelength of light. But since a wavelength of light is a fraction of a millionth of a meter, being within a wavelength of light is still pretty good. Finally, I am not certain what you mean by "reactions" that may be taking place at the "border." Nothing particularly unique or interesting would necessarily occur on the light/dark border. Of course, anytime light interacts with matter, something happens. Whether it is scattering, reflection, refraction, dispersion, or absorption, the light and the matter interact in many complex and interesting ways. The fact that these processes may be occuring near the edge of a shadow is largely irrelevant, however. I hope I got at what you wanted to know. Let me know if I goofed anything up and I will see what I can do.


R. Martin Muldoon, a parent, asks:
My 6 year old daughter asked me the following: 'When I spin a glass of ice water, why doesn't the ice spin with (proportionally) the glass itself?'

Joe Traylor, a physicist, replies:
When you swing a baseball bat, the end swings along with the middle only because the two parts are rigidly attached to each other. That is, the molecules in the bat have strong bonding to one another. In the case of a glass of ice-in-water, the ice is very poorly bond to the surrounding water, and the water is very poorly bound to the walls of the glass. Therefore, when you rotate the glass, the water hardly follows, and thus, the ice even less. There is a little bit of bonding at the walls, but precious little, so that the water is little influenced by the motion of the walls.
An interesting project for your daughter: FREEZE the whole glass --that is, increase the bonding-- and then the contents rotate along with the glass!
Mark Biermann, a physicist, also replies:
 
In some ways the better question is "Why does the ice spin at all?" The ice does spin because the water in which it is floating is spinning. But then, "Why does the water spin?" Just because you make the glass start to spin, why does the water also begin to spin? The water begins to spin because of friction between the water and the inside surface of the glass. We don't often think about water having friction, but it does. All fluids, air, water, orange juice, etc. have greater or lesser amounts of friction as they slide over some surface. This property of the fluid is referred to as its viscosity. The more viscous is a fluid, the more friction it will tend to experience as it slides over a surface. Hence, honey is much more viscous than water.
So, it is the friction between the glass and the water that makes the water begin to spin. As the water spins, so does the ice. The water does not spin as rapidly as the glass because the viscosity of water is fairly low and so you get a lot of "slippage" as the spin that you impart to the glass is then imparted to the water. If you did the same experiment with honey, the honey would do a good job of spinning right with the glass. As it is, the water picks up some of the "spinning" of the glass via friction, but also lags behind because the frictional force between the water and the glass is not all that great. Since the ice floats in the water and moves with the water, it also lags behind the spin of the glass.


Jodi Rhoades, a high school student, asks:
What are low temperature and high temperature plasmas?

Mark Biermann, a physicist, replies:
Typically we think of matter as existing in one of three states. Those states are solid, liquid and gas. We have a pretty good intuitive sense of what is meant by solid, liquid or gas. In reality, there are actually four states of matter. The fourth state of matter is a plasma. In order to understand what a plasma is, we must first remember that matter is made up of atoms, and atoms consist of negatively-charged electrons surrounding a positively-charged nucleus. Under the right conditions, some of the electrons that usually are held to a single atom can break free. Under just the right conditions, one or more electrons can be broken free from all of the atoms in a sample of matter. The resulting substance consists of electrically-charged particles. There are the negative electrons and the positive ions. The positive ions consist of the atomic nuclei and the remaining electrons still bound to that nucleus. Such a collection of ionized particles, with equal amounts of postive and negiative charge, is called a plasma.
Plasmas typically exist in gases that have been ionized. Plasmas exist in stars and in many types of lasers. The most common mechanism for causing the electrons to break free, that is, for causing the plasma to form, is the absorption of heat by atoms when matter is raised to very high temperatures. The energy of the heat allows the electrons to break free. Hence, most plasmas are high temperature plasmas, forming and remaining in existence so long as the matter is held at a very high temperature. The existence of low temperature plasmas is also possible. A plasma will form whenever enough energy is supplied to a sample of matter to cause the atoms to break into separate postively and negatively charged ions. If this energy is supplied without the need to raise the temperature to very high levels, one obtains a "low temperture plasma." An electrical dischage through a normal gas will produce a plasma under the correct conditions.
Of course I am completely off base with this answer if you wanted to know about the plasma in blood, but since you asked a physicist this question, I am guessing that I approached this the right way.


Heather, a high school student, asks:
If a tornado goes over an ocean would it pick up water? And if it does, is it still called a tornado?

Joe Traylor, a physicist, replies:
Tornadoes seldom happen over oceans. The conditions that cause them don't happen over oceans (you get hurricanes instead). However, tornadoes do happen over lakes, usually by starting out over land and then moving over water that happens to be in the path. Yes, they do pick up water, and yes, they are still called tornadoes when they do.
One more point. Hurricanes and tornadoes are really very similar. If you look at a satellite map of a hurricane, you notice a giant spiral of clouds, often hundreds miles of miles in diameter. The wind speeds may be upwards of 100 mph. Torandoes are almost identical except in scale: they are only a few miles in diameter. Because they are tighter, they have higher winds, upwards of 500 mph.


Shogo, a middle school student, asks:
Are there any active volcanoes on the planet Mars? And is it possible to melt the polar ice caps on the North and South Poles?

Mark Biermann, a physicist, replies:
There are no active volcanoes on Mars. According to astronomers and geologists, the volcanoes on Mars have not been active for at least 200 million earth years.
Melting the polar ice caps on Mars is pretty much impossible. To do this we would need a stunningly large amount of energy to heat up the surface and atmosphere of Mars. Then we need to hold this heat in an atmosphere that is 100 times thinner than that of earth. In essense, it is a practical impossibility to melt the polar ice caps on Mars. Probably the only way to melt the ice caps would be to greatly increase the output from the sun. More heat from the sun would warm Mars enough to do the melting. The sun will in fact go through a stage in which it will give off more energy. Astronomers believe that in several billion years, the sun will swell into a massive red giant star. At this stage the sun will grow in size and give off tremendous amounts of energy. This should melt the ice caps of Mars quite easily. One problem though. The melting of the ice caps will be followed fairly rapidly by the incineration of the entire planet. Mars will be nothing more than a cinder at the edge of a massive red giant star.
Ken Schweller, a computer scientist, adds:

By the way, when Professor Biermann speaks up melting an 'ice cap' you musn't assume that the ice is necessarily made up of water as we usually assume when we talk casually about 'ice'. The polar caps may be made up, for example, of carbon-dioxide 'ice'. See a previous posting on this list about 'Water on Mars' for more details.


Mike Drajewicz, a middle school student, asks:
I am working on a Mars Base project for grade 9 and have designed a system that will require me to create an oxygen base by heating potassium chlorate and manganese dioxide and then diluting the resulting pure oxygen with the existing mars atmosphere. My question is - will the human lung be able to purge itself of the carbon dioxide it produces if the atmosphere in my Mars base is one fifth oxygen and four fifths carbon dioxide? Will I have to use an inert gas such as nitrogen to dilute my atmosphere as we see on earth?
Thanks very much for helping out.

John Hutchins, a chemist, replies:
80% carbon dioxide is not tolerated by humans. Even elevated levels cause drowsiness. So the answer is "no", you would need another inert gas.


Shogo, a middle school student, asks:
How can humans change the atmosphere of Mars so it is breathable for humans and plant life?

Mark Biermann, a physicist, replies:
The answer is that we cannot. This is for two reasons. First the make up of the Martian atmosphere is inconsistent with plant and animal life, as we know it. The atmosphere of Mars is 95 percent carbon dioxide, about 3 percent nitrogen and about 2 percent argon. We would have to find some way to generate huge amounts of oxygen on Mars. Even if this could be done we would have a second and even more fundamental problem. A planet holds onto its atmosphere in the same way it holds onto objects on its surface, that is, through gravity. The gravitational force of the Earth on atoms and molecules in our atmopshere is what holds our atmosphere in place. The more massive an object, the greater the gravitational force it can exert. Mars has a mass that is less that 11 percent of the Earth's. That is, if the mass of the Earth were 10 kilograms, the mass of Mars would be a little over 1 kilogram. Because Mars has so little mass, it cannot hold onto an atmosphere very well. The relatively small mass of Mars, combined with the fact that Mars produces very small amounts of the gasses needed to form an atmosphere, lead to Mars having a very thin atmosphere. The atmosphere of Mars is 100 times thinner than that of the Earth. Mars just can't hold onto a dense atmosphere, and a dense atmosphere is what plant and animal life need.
Bottom line: Even if we could manage to generate large amounts of oxygen on Mars, all of our work would be for nothing. The gasses we added to the Martian atmosphere would just go floating out into space, leaving us right back where we started from.


Dan Rheingans, a high school student, asks:
As I pondered the condition of amnesia one night I came across an interesting question that I could not find the answer to. If a person obtains the state of total memory loss, i.e. can't even remember things that just happened let alone memories of the distant past, how is it that they are still able to speak any language? Isn't language something we learn, and when we use it aren't we pulling it from our collective memory, even though we do as much thousands upon thousands of times a day? I would appreciate any answer you can give. Thanks.

Bob Ferguson, a psychologist, replies:
 
This is an interesting question because it highlights a misconception that lots of people have about amnesia. I suspect that most folks are familiar with it as a plot device in the afternoon soaps
  • (writer #1: "What should we do for tomorrow's episode?"
  • writer #2: "Let's have our star get hit on the head & suffer amnesia--that should give us something to write about for a few more days").

Actually, there are 2 types of amnesia: antergrade & retrograde. The former is associated with Alzheiemer's disease, certain other brain dysfunctions, and certain types of rare neurosurgical procedures. It involves normal memory for old (pre-trauma) events but a lot of difficulty in remembering stuff that happened recently. For example, a newspaper may be re-read several times a day, with each reading a "new" experience.

Retrograde amnesia is the type you referred to in your question--difficulty in remembering old stuff. And you are exactly right; all old memories are clearly not lost. The amnesic still typically understands language normally, can drive a car, walk, operate a TV or VCR, etc, and all of these involve memory. So, what is lost is retrograde amnesia? It's what is known as autobiographical memory--stuff about our personal lives, like our name, address, marital status, occupation, and so on. And that lead's memory researchers to suspect that, since autobiographical memories can be lost independently, they may represent a separate type of memory system, perhaps stored differently from our other long-term memories.
Hope this helps.


Joseph, in middle school, asks:
Where did the face on Mars come from?

Mark Biermann, a physicist, replies:
The face on Mars came from the same place as the Man in the Moon: Coincidence. The "face on Mars" is a collection of geologic formations that, when the sun hits them just right and we view them from just the right angle, take on the appearance of a human face. But that is all it is. A collection of rocks and hills and valleys that by coincidence happen to look like a face under just the right conditions. The same applies to the fact that to some people the face of the moon looks like a person's face. Similarly with the Old Man of the Mountain in New Hampshire. I have seen this rock formation and from the right angle it really looks like a face in profile. But when we moved on up that valley in northern New Hampshire it became clear that all I was looking at was a stone cliff. From different angles it just looked like a bunch of rocks.
Bottom line: sometimes a coincidence is just a coincidence. The "face on Mars" is a good example of this.


Melissa Fahr, a college student, asks:
While teaching today, I read an answer with a square root in it as radical 2. This answer led to a discussion with my cooperating teacher about the term radical. He has always thought as a radical as the sign around the number, the fish- hook thing as he calls it. If that is the case, then a cube root would also be a radical. We discussed it back and forth and never came up with a really good answer for our problem. So my question to you is, is the fishook like sign called a radical and if it is not, what is the name of it??

Tim McDaniel, a mathematician, replies:
Hi Melissa. Have you been getting enough sleep?
Short answer: The fishhook-like dealie is either called a "radical" OR a "radical sign". The fishhook-like dealie with a little "3" on the hook is either called a "compound radical" OR a "compound radical sign".
Long answer: I went to the Webster's Unabridged Dictionary for this one. "Radical" comes from Latin "radicalus - having roots" and "radix - root". I thought that was kind of cool. Anyway, "Radical" is both an adjective and a noun.
ADJECTIVE: The "Radical Sign" is the fishhook thingie itself. The "Radical Quantity" is the number inside the radical sign. The "Radical Sign" is considered a prefix to the "Radical Quantity". I used to think of the radical quantity as being *inside* the radical sign, but now I know that's wrong; the radical sign is simply considered to come *before* (i.e., precede) the radical quantity. So thinking of the radical as the sign *around* the number is not quite right (sorry). Therefore, you should probably have read it "radical sign two" but, English being English, we customarily get lazy and sloppy and drop the noun "sign" stuff and just read it "radical two".
NOUN: "Radical" has two definitions. (1) Any quantity from which the root is to be extracted; I'm guessing this is derived from the sloppy/lazy dropping of "Quantity" from the adjective/noun pairing "Radical Quantity". (2) The radical sign; similarly, I'm guessing this is derived from the sloppy/lazy dropping of "Sign" from the adjective/noun pairing "Radical Sign".
Uh, what was your question again? Oh yeah. The fishhook dealie is a "radical sign" (radical as an adjective) but due to what I'm guessing is sloppy/lazy use of the language, it's now ok to also refer to this fishhook dealie as a "radical" (a noun).
Finally, the cube root dealie (fishhook with a little 3 on the hook) is known as either: (1) a "compound radical sign", where "compound" is an adverb modifying the adjective "radical" which in turn modifies the noun "sign" (see number 1 above); OR (2) a "compound radical", where "compound" is an adjective to the noun "radical (see number 2 above).
There you go! Thank you; drive through please....


Andrew, a middle school student, asks:
How do scientists know that the asteroid they found with the bacteria on it is from Mars?

Mark Biermann, a physicist, replies:
The short answer is that they don't KNOW that the meteorite is from Mars or that it contains bacteria. What scientists studying the meteorite have is a large amount of indirect evidence that the meteorite is from Mars and that it may contain the evidence of life.
The evidence that is rock is from Mars is geologic is origin. In 1976 two spacecraft from Earth, the Viking probes, landed on Mars. They studied the rocks on the surface of Mars and we learned a lot about the make up of rocks on Mars from the Viking spacecraft. It turns out that the meteorite found in Antarctica matches the unique chemistry of rocks on Mars, as measured by Viking, very well. This strong match between Martian rocks and the meteorite is what leads scientists to believe that the meteorite is from Mars. It should be noted that 11 other meteorites have also been matched to the unique Martian chemistry found by Viking.
The evidence for life is also indirect. The meteorite contains a unique pattern of organic molecules. Organic molecules are carbon containing compounds that are required for life. Also in the Mars rock are several unusual mineral phases that are known products of primitive living things here on Earth. Finally, scientists found structures that could be the fossilized remains of ancient lifeforms. These structures are microscopic. The fact that all three of these things were found close together tends to support the idea that life did exist on Mars in the distant past. As it now stands, scientists continue to study this Mars rock in order to confirm or deny that life actually did exist on Mars. The book certainly is not closed on this meteorite, and additional work is being carried out to try to determine if there really was life on Mars.


Dan Rheingans, a high school student, asks:
How is it that the equation a^n + b^n = c^n is one which mathematicians cannot validate? We use it very commonly with triangles in The Pathagorean Therom and accept it as truth, as all evidence would lead us to belive, but fail to find out why? Any answer would be appreciated, thanks.
P.S. If the equation is indeed supposed to be written
x^n + y^n = z^n, I apologize, I wasn't sure.

Tim McDaniel, a mathematician, replies:
 
Hello Dan. What a good question!
OK, first of all it doesn't matter a whit if you use "a, b, c" or "x, y, z"; after all, they're just stupid letters.
The most commonly-asked question is whether or not there are any *integer* solutions to the equation "a^n + b^n = c^n" where a, b, c, and n are positive *integers*, with n greater than 2. (Real number solutions are trivial; it's a ton tougher if "a, b, and c" must be integers.) For n=2, this is trivial; for example, let a=3 and b=4 and c=5 and notice that "3^2 + 4^2 = 5^2" . "5, 12, and 13" work too. But what about for n>2; e.g., what about if you *cube* (n=3) instead of *square* (n=2) each term? "Fermat's Last Theorem" states that there are *no* integer solutions (i.e., that there are no integer values of a, b, and c that work in the equation "a^n + b^n = c^n" where n>2). Unfortunately, Fermat didn't bother to actually prove this to be true!
Pierre de Fermat was one of the greatest mathematicians of all time. His work on number theory (like this stuff!) was ground-breaking, and his stuff on infinitesimals (way-way-WAY-tiny numbers) paved the way for Newton and Leibniz to develop Calculus. (So as a professor who teaches Calc, I guess I partially owe my job to Fermat.) Fermat was also quite a mischievous character; he frequently stated "theorems" then left them dangling for other math nerds to try to prove, even though he sometimes knew that a proof was impossible! Fermat wrote this particular theorem in mid-1600's in the margins of a book, stated that he had a simple proof but didn't have enough room to write it down. Legend has it that Fermat then went and get himself killed in a dual the next day, but I've always thought that sounded too cool to actually be true. But there sure is a lot of romance that has built up around this particular theorem.
Fermat's Last Theorem has definitely been shown to be true for all n less than 125,000, and for many other special values. But tons of folks (including me!) tried and tried to develop a general (for ALL integers n>2) proof of Fermat's Last Theorem. Everyone failed until about five years ago, when a guy named Andrew Wiles at Princeton announced he'd come up with one. The proof is way, WAY complicated, and is currently being reviewed by mathematicians before being pronounced as "The Real Deal". But in my opinion it looks like Wiles may have actually done it!
Isn't this cool? Remember, Dan, that studying math in college is more than just studying numbers and how to manipulate them to get answers; it's also about ideas, logic, theory, proving stuff, and history. Mathematics sits pretty much dead-dog in the middle of the crossroads between "liberal arts" and "professional" studies. That's one of the things that makes math so awesome!


Jason and Xavier, two middle school students, ask:
What side of Mars will be closest to earth on January the 1st 1998?

Mark Biermann, a physicist, replies:
I am not quite sure how to respond to your question. Since both the Earth and Mars are rotating on their axes, in addition to traveling in their orbits, the relative positions of each body changes during the course of a day. The length of a Martian "day" is slightly longer than the length of an Earth day and the length of a Martian "year" is much longer than the length of an Earth year (almost double). Putting all of this together gets kind of complicated. If you need to know if a certain feature of the Martion surface will be facing earth at some point during the day of January 1st, 1998, I am afraid I can't help you there. You may need to check into some more specialized resources for that kind of an answer. If you have access to the World Wide Web, I recommend that you check out the NASA homepage to see if it can help out. The address for the NASA homepage is
http://spacelink.msfc.nasa.gov/home.index.html
Sorry I couldn't be more help. Good luck with your investigations.


Several middle school students have asked us:
Is there any water on Mars? Was there ever any water there? Do the polar ice caps of Mars actually contain frozen water?

Ken Schweller, a computer scientist, replies:
I am no expert but on this subject but I consulted several sources on the Internet to try to find out if there is/was water on Mars.. The gist of what I found is that liquid water probably flowed on the surface of Mars in the distant past (in the first billion years). The evidence for this is from the existence of river beds, tributary systems (evidence for rainfall), muddy craters, and collapsed terrain with outflow channels. This suggests that at one time the atmosphere of Mars was much more dense. Today the only water left, if there is any, is probably locked underground as permafrost, so it is not likely that the polar ice caps of Mars actually contain frozen water.
I got my answer from the following two internet sources. You should look into these for the full details.
Adam Matlock, a college student, asks:
I was driving back to school from home one day, and it was foggy out. However, the fog was much worse around the farms and in the middle of nowhere than around the cities/towns/villages/huts. I was wondering why that was... why is it less dense when there are things around? Same for snow, too. Why is there a better chance for a "white-out" and seemingly more snow in the country than around "stuff"?

Mark Biermann, a physicist, replies:
 
Fog is at once rather simple and rather complicated. It is simple in that the reason fog devlops is relatively straightforward. The air around us contains water in a vapor, or gaseous, state. The air can hold only so much water vapor and the amount of water vapor it can hold depends very strongly on temperature. If the air temperature gets too low, some of the water vapor liquifies, or condenses, into liquid water. The temperature at which water vapor starts to condense is called the dewpoint. When the liquid water first starts to form, it is often as tiny drops of water that can float quite easily. These tiny drops of water taken together are fog.
Things get complicated when we try to pin down the exact weather conditions under which fog will form. The atmosphere is a complex place and many effects work together to cause the conditions that we see around us. There are many possible explanations for what you saw the other day. One very pausible one is this: populated areas tend to generate heat, thus increasing the air temperature in town. If the air temperature is very close to the dewpoint, the extra heat provided in populated areas could keep the air temperature above the dewpoint in town (no fog). Since there is no extra heat source "in the middle of nowhere" the temperature drops below the dewpoint more quickly than it does in town and fog forms more quickly also. Of course, many other factors could also be at play here, but there are too many possiblities to cover them all.
As far as white outs go, the key is wind. Out in the country there is nothing to block the wind and so the snow gets picked up and blown around. This wind-carried snow causes the white out. In town, the wind tends to be much less, and much less constant. Hence, the strong, steady winds that are the hallmark of white out conditions don't exist all that well in town. It is worth noting that a sudden descrease in the wind speed under white out conditions means that a lot of snow that was flying along horizontally, suddenly drops out of the air and onto the ground. That is why Lakeside, a town on the eastern, or downwind, side of Storm Lake in north western Iowa where I live, got dumped on this past winter. Wind whipped across the lake, unabated, and carried snow with it. When this snow-laden wind hit the trees and homes of Lakeside, the snow was dumped out on the area in the form of 10 to 15 foot drifts. In short, Lakeside was acting like a gigantic snow fence.


Jacky Chan, in high school, asks:
We have been looking for a picture of a Mars Base. Can you help us on this?

Ken Schweller, a computer scientist, replies:
Many students have written to us asking various questions about Mars and what it would be like to try and live there. There are many excellent sites on the Internet that talk about exploring Mars. Here are a few we hope you will find useful in answering your questions. The second reference in particular may have some pictures of interest to you.




Adam, a college student, asks:
After a keg of beer has been tapped but only partially drank, how should the remainder of the beer be stored to keep it fresh (not get flat)? Should we remove the tapper but keep the pressure in the keg, remove the tapper and all pressure, or leave the tapper on? This question has been pondered by me and many other college students.

Jon Hutchins, a chemist, replies:
Keep it cool, and keep the pressure on (I'm not sure it matters how you do this). The carbon dioxide lowers the pH which helps prevent spoilage. Also pressure stops bacteria etc from entering the beer. Keeping stray microorganisms out, or inactive, is the key.


The students in Mrs. Medlyn's grade school class ask:
How do we know that Hale-Bopp will return or that it ever passed by us before?

Mark Biermann, a physicist, replies:
We are able to learn quite a bit about comets because, when it comes to things in outer space, comets are often pretty close to earth. Hale-Bopp in particular does get fairly close to the earth and so we can study it using telescopes and other instruments. We have even studied it using the Hubble Space Telescope.
In order to know if the comet has passed near earth before and if it will do so again, we must know the path that the comet follows across space. We can know what path the comet follows through space by first knowing what forces act on the comet to make it move in space as it does. The most important force acting on the comet that determines its path through space is gravity. We are familiar with gravity because it is the force that holds us to the surface of the earth. But gravity does much more than just that. Gravity is a force that acts between any objects that have mass. Gravity is always an attractive force. Hence, gravity pulls us toward the earth, and it pulls the earth toward us. Gravity provides an attractive force between the sun and all of the planets. This gravitational force is what keeps planets like the earth in their orbits about the sun.
Because the comet Hale-Bopp consists of matter and has mass it also experiences a gravitational force from the sun. Like the planets, Hale-Bopp is attracted to the sun strongly enough that it is in an orbit around the sun. But the orbit of Hale-Bopp is quite a bit different than the orbit of the planets. The nine planets that orbit our sun have orbits that are similar in many ways. The orbits of the planets are all pretty close to being circles. The orbit of Venus is the most circular and the orbit of Pluto is the least circular. The actual shape of the orbits of the planets is an ellipse. An ellipse is sort of the squashed-down circle. Some ellipses are so close to being circles that it is very hard to notice that they aren't actually circles. The orbits of Venus and Earth are like that. Other ellipses are quite flat, like an egg shape. Well the orbit of Hale-Bopp is more like an egg than a circle. But it is an orbit. Hale-Bopp follows an oval orbit around the sun.
The planet's orbits are also similar in that they all lie in the same plane. That is, if you set the sun on a table, all of the planets would follow paths that would pretty much keep them on the surface of the table. Hale-Bopp has an orbit that would make it go down into the table, loop over the top of the sun and then drop ack down into the table. So, most of the time the comet is a long way below the sun, much farther from the sun than the farthest planet. But every once in a while, the comet moves close to the sun in its orbit. When is does that, it moves up from below the earth, passes over the sun and then moves back down again. It is at this point that we can see it.
One final point about the orbit of Hale-Bopp is that it takes a long time for the comet to complete one full loop. It takes the earth 1 year to circle the sun. It takes Pluto, the most distant planet from the sun, about 248 years to circle the sun. It takes Hale-Bopp thousands of years to circle the sun.
It is interesting that the orbit of Hale-Bopp actually changes when it comes in close to the sun. While the gravitation of the sun is the main factor in determining the orbit of the comet, other gravitational forces can also affect it. Early last year, the comet passed close by the planet Jupiter. Jupiter is the largest planet and so it provides a strong force of gravity. Hale-Bopp got close enough to Jupiter that the gravity of Jupiter actually changed the shape of Hale-Bopp's orbit. While Jupiter was not able to break the comet out of its orbit around the sun, it did change the orbit. Based on the forces of gravity and the sizes of Hale-Bopp, the sun and Jupiter, we know that before Hale-Bopp went close to Jupiter last year it had an orbit that made it circle the sun once every 4206 years. So, it would have passed by the earth about 4206 years ago. However, the gravity of Jupiter changed that orbit. Now it will take Hale-Bopp only 2380 years to circle the sun. So, while it has been 4206 years since Hale-Bopp last passed by the earth, it will be back again in only 2380 years. (I still wouldn't wait up if I were you.)
In summary, we know when Hale-Bopp passes by the earth because we know the shape of its orbit. And we know the shape of its orbit because we understand the effect of the force of gravity on planets and comets.


Jason Masuch, a middle school student, asks:
What is the atmosphere of Mars like?

Mark Biermann, a physicist, replies:
 
The atmosphere of Mars is quite different from that of the earth. First of all, an atmosphere is held to a planet just like a person is, by gravity. The gravitational force of the earth on you or me holds us to the surface of the planet and doesn't allow us to float off into space. In the same way, the gravity of the earth holds onto the atoms and molecules in our atmosphere and doesn't allow them to float off into space. Mars is much smaller than the earth, about half as big in diameter, and so its gravitational pull is much weaker than that of the earth. Because its gravity is so weak, Mars can't hold onto its atmosphere very well. Molecules in the atmosphere of Mars can float off into space quite easily compared to those in the earth's atmosphere. The end result is that the atmosphere of Mars is quite thin compared to that of the earth. The atmosphere of Mars is about 100 times thinner, or less dense, than that of earth.
The make up of the atmosphere of Mars is also much different than that of the earth. The atmosphere of earth is about 76 percent nitrogen and about 23 percent oxygen. The other 1 percent of the atmosphere consists of many gases such as carbon dioxide, hydrogen and helium. Mars on the other hand has an atmosphere that is 95 percent carbon dioxide, 2 to 3 percent nitrogen and about 2 percent argon. So, even if the atmosphere of Mars were not so thin, we still wouldn't be able to breathe up there.


Mike, in grade school, asks:
What does "hawking radiation" have to do with pair production and the schwartzchild radius of a black hole?

Mark Biermann, a physicist, replies:
What an impressive question. I'm still getting over the fact that you have even heard of these terms, let alone want to know what they are all about. First of all, let's make sure on a definition or two. The Schwarzschild radius is sort of the defining measurement for a black hole. Every object has a Schwarzschild radius. It is the radius to which the object needs to be compressed in order for it to become a black hole. If an object is compressed to within its Schwarzschild radius, then its gravitational pull is strong enough that not even light can escape and, by definition, the object is a black hole. The mass of an object determines its Schwarzschild radius. An object the mass of the earth would have to be compressed to the size of a grape to be a black hole. In summary, the Schwarzschild radius sort of defines the boundary of a black hole. A sphere centered on a black hole and with a radius equal to the Schwarzschild radius is often called the event horizon. I will use the terms event horizon and Schwarzschild radius interchangeably.
Now let's talk about pair production. According to modern physics, mass and energy are pretty much equivalent. Mass can be turned into energy and energy can be turned into mass. Mass and energy are related by Einstein's formula: Energy equals mass times the speed of light squared. A key point to keep in mind is that the total amount of mass and energy stays constant.
In certain situations, energy can combine in such a way that particles of matter are suddenly created. The particles of matter appear in pairs. This process by which energy is converted into mass is called pair production. The pairs always consist of a particle and its "antiparticle." An antiparticle consists of antimatter. For example, the antiparticle to an electron is a positron. Because of the requirement that the total amount of mass and energy is constant, if pair production is to take place, energy must be used up from somewhere.
Now let's say that this requirement that the total amount of energy and mass stay constant can be violated. This is a basic law of physics, but in theoretical physics, many physicists believe that pair production is happening all of the time and that no energy is used up in order to make the two particles. Of course this violates the idea that energy and mass taken together must stay constant. But the law isn't really violated if the two particles then destroy each other so quickly that their existence could never be measured. So, many physicists believe that pairs of particles are appearing out of nothing, and then disappearing before we can measure that they exist. Because we can't measure them we don't violate any laws. (I said this was quite a question. I realize that this answer is getting quite strange, but, as they say, you asked for it.)
Which brings us back to black holes. Some physicists were thinking, "These pairs that appear spontaneously are destroyed when they come back together and annihilate each other completely. What would happen if one of the particles in the pair got pulled away from the other before the destruction could take place?" We would have magic particles appearing in space. Many physicists believe that this does in fact happen near a black hole. A pair of particles appears spontaneously. Before they come together and wipe each other out, one of the two particles moves across the event horizon of the black hole and is swept away into the black hole. No particle annihilation can occur and we just get a particle out of nothing.
Or did we. Even around a black hole the piper must be paid. The energy required to make that new particle ultimately came from somewhere. That "somewhere" is believed to be the balck hole. The black hole actually gives off some energy in this manner. So, not all energy sucked into a black hole stays there. Some of it manages to escape in this incredibly strange manner. The black hole slowly gives off energy in this manner. This energy is called Hawking Radiation, after Stephen Hawking, a mathematician. In Hawking's theory all black holes eventually lose all other their energy through Hawking radiation.
Well that's the best I can do. I hope I came close to answering your question. Most of this theory is quite speculative and it is very difficult to test experimentally. If you have more specific questions about some aspect of this, (who wouldn't) please feel free to ask them. Good luck with a really tough topic.


Bert, a college student, asks:
What are the some detailed advantages to fusion? Why is the fusion challenge worth funding? How close are we to commercializing the process?

Mark Biermann, a physicist, replies:
 
When you ask about the "detailed advantages" to fusion, I will assume you mean the advantages of controlled nuclear fusion as compared to other energy sources. For example, let's first compare nuclear fusion to fossil fuels such as coal, and oil. Use fossil fuels as an energy source essentially means that one burns these fuels as a means of producing heat. The problems with fossil fuels are many. They produce pollutants that are released into the enviroment. Some pollutants are very easy to measure, such as sulfur dioxide or other chemicals. Other possible pollutants have more controversial effects, such as the carbon dioxide that is released and could be contributing to global warming. Fossil fuels also have the major disadvantage of being a finite resource. That is, we only have so much coal and oil and when we run out, we run out.
Fusion has a number of advantages compared to fossil fuels. A properly designed nuclear fusion reactor would release few pollutants. A nuclear fusion reaction does not rely on combustion, or burning, as do fossil fuels, and so the would be no release of carbon dioxide, and, consequently, no concerns about global warming difficulties. Also, the fuel supply for nuclear fusion is essentially sea water. The amount of fusion energy available in a cube of sea water one kilometer on a side is equivalent to the energy in all the known fossil fuel reserves. A cube one kilometer on a side is quite small compared to the size of even a single ocean, let alone all of the oceans on earth. The bottom line is that the fuel source for nuclear fusion is essentially inexhaustible.
What are the advantages of nuclear fusion compared to nuclear fission? Fission is a fundamentally different process. The two big disadvantages of nuclear fission is that it can be difficult to control and that is produces large amounts of high level nuclear waste. Nuclear fusion is a fundamentally different process. While nuclear fission involves breaking large nuclei into smaller nuclei, fusion is based on joining smaller nuclei into larger nuclei. Because of the fusion process, virtually no high level nuclear waste is produced. This eliminates to need to find a place to store this highly radioactive waste material. Also, fusion is quite easy to control. It does not function as a chain reaction, as fission does, and so the dangers of "run away" reactors are not present.
Why is the fusion challenge worth the investment? Some of the above explanation should help to answer this question. The bottom line is that if nuclear fusion can be brought on line in a viable fashion, we would have an energy source that is virtually inexhaustible and that has a minimal environmental impact. It is an over statement to say that nuclear fusion would be completely waste or pollution free. But it would be about as close as we could possibly get. The payoff from controlled nuclear fusion would be incredible.
When will nuclear fusion be commercially viable? There is quite a bit of disagreement on this point. Estimates vary widely. Probably the best estimates are that it could not be sooner than about 50 to 60 years, just to overcome the engineering and financial challenges. Others say it could be much longer than that. The primary factor in determining how soon it will be is funding for the research. An easy answer to this question is that if funding for nuclear fusion research is cut off the answer to when it will be commercially viable is easy. In that case the answer is never. Hopefully that won't end up being the long term answer.


Bob Orlando Gedzano, a high school student, asks:
How do you prove fire is not alive? My little brother asked me this, and I couldn't come up with a decent answer, even though it is obviously not living.

Jack Mellen, an animal ecologist, replies:
This is one of the classic rhetorical questions of biology. Biology teachers ask this question in an attempt to get students to consider the general properties of life. Although the manner in which biologists state these properties changes over time, the following properties are the central features that characterize life. We can show differences between fire and life by considering which of these properties fire lacks.
  1. Organisms are very highly organized. One basic feature of life is that it can organize matter into larger and more complex molecules. Fire does not do this. Incidently, this is not a contradiction to the laws of thermodynamics. Life does this work only because outside energy is available to organisms. For most ecosystems the ultimate outside source of energy is sunlight.
  2. Organisms reproduce their own kind, and only life can produce life. Although fire begets fire once it is started, fire can be started through a variety of methods which are independent of fire itself.
  3. Organisms utilize energy to perform a wide variety of tasks. The reactions involved in energy metabolism of organisms are catalyzed by enzymes. Thus, energy is harvested in a very regulated manner. Fire does consume fuel, but fire does not depend upon complex chemicals such as proteins to facilitate the oxidation of its fuel.
  4. Organisms respond to their internal and external environment. Fire also responds to ambient conditions, growing or shrinking with the availability of fuel and oxygen. What makes the responsiveness of organisms particularly fascinating is that living things respond to the environment in ways that allow them to regulate their internal environment, which is to say that organisms manifest homeostasis. Fire cannot do that, either.
  5. A heritable program composed of DNA structures the pattern of an organism's growth. The structure of fire has no heritable basis.
  6. Changes can occur in the heritable program of an organism, these changes may be propagated from generation to generation within populations of organisms. The differential survival of organisms with different variations of heritable programs leads to genetic changes in the population that are recognized as evolution. Fire can't evolve.



Ben Meyers, a high school student, asks:
We are studying wave physics right now and we learned that a light wave will curve around a corner as it goes through a slit that has a width which is somehow related to the wave's length. Why does it curve?
We found an entry by Mark Biermann referring to diffraction. It answered Robbie Schweller's question about sound vs. light diffraction. Mr. Biermann mentioned that Robbie would have to wait for another time to answer the question as to why. Could you explain that now? We are really confused/curious about the reasons for diffraction; especially when applied to light. What does it interact with to make it change directions?

Mark Biermann, a physicist, replies:
First of all, you are in good company if you are confused/curious about diffraction. Diffraction is one of the most complex phenomena associated with waves. As a matter of fact, certain aspects of diffraction are still an area of current research in optics and optical physics. Many of the details of diffraction are still not understood by anyone, including scientists and engineers.
A good way to think about diffraction is to first think about a related effect called interference. You have probably heard about interference in one context or another, but in talking about waves it has a very specific meaning. Interference occurs when two distinct waves overlap in time and space. These two waves then interact in a way dictated by the form of the waves. If the peaks of two waves overlap, the waves reinforce each other and the resulting wave is much stronger at that point. This reinforcement is called constructive interference. If the peak of a wave overlaps the trough of another wave, the two waves tend to cancel each other, leading to destructive interference. If one is dealing with light waves, interference can be oberved by placing a screen, such as a piece of white paper, in the area where the two light waves are overlapping. A pattern of bright areas, resulting from constructive interference, and dark areas, resulting from destructive interference, will appear on the screen. The form of this pattern of bright and dark areas depends directly on the waves that are interfering with each other and is called an interference pattern. The bright areas and dark areas are sometimes called fringes because of their shape.
In many ways, diffraction is just a very specific type of interference. Diffraction occurs when a wave interferes with itself. It is at this point that the details of diffraction start to get a little bit difficult. The entire concept of a wave interfering with itself may seem a little bit odd, but that is what happens in diffraction. Picture a slit cut in a piece of metal. A light wave falling on the slit fills the entire width of the slit. Light at the top of the slit is part of the same beam of light as the light at the bottom of the slit, but those two parts of the light wave are distinct from each other. Just as two distinct waves of light can interfere with each other, two distinct parts of the same light wave can also interfere with each other. Light from the top of the slit interferes with light from the bottom of the slit whenever light from these two distinct parts of the beam are allowed to overlap. For example, if a screen is placed on the side of the metal slit opposite the light source, we can see a pattern of light and dark lines on the screen. The pattern arises because light from distinct parts of the slit, such as the top and the bottom, is overlapping on the screen. The interference that occurs due to this overlap is referred to as diffraction and the resulting interference pattern is called a diffraction pattern.
Light within a single beam of light can interfere in many different and complex ways. For example, diffraction leads to regions of constructive and destructive interference. Regions that we would expect to be bright are not and regions that should be dark are well lit. Because of this interference, light gets redirected along new paths. This is what is meant when one talks about diffraction "bending" the light wave. What we refer to as bending is just the result of destructive interference removing light from an area where we would expect it and redirecting the light into a new area. The bending of the light wave is one result of the complex diffraction pattern arising due to the interference of the light wave with itself.
We're almost done. A long answer is going to have to be a little longer because there is still an important point that must be cleared up. At this point you may be wondering, "If diffraction occurs when the light wave interferes with itself, why don't we see strange diffraction patterns all of the time?" That is, why is it that we don't actually see all of these things that I have been describing in such excruciating detail? The answer lies in the nature of light itself. Effects such as interference and diffraction arise due to the wave nature of light, or any wave for that matter. When two waves, or two parts of one wave, overlap, interference and diffraction patterns arise. The form of the pattern depends on the specific form of the waves involved and if the waves change the pattern will change. Well suppose that the waves that are interfering or diffracting change about 100 million times each second. Each time a change occurs, the pattern of interference changes along with it. Since the changes are so rapid, the individual patterns are essentially impossible to observe. What we observe is the average over the millions of patterns that are arising pretty much randomly over each second. In the interference or diffraction pattern of the light the bright and dark regions get washed out, and the distinct shape of the pattern is lost. What we see is the normal pattern of brightness and shadow that we encounter in our everyday lives.
It turns out that most light that we deal with does exactly what I just described. The form of the light wave changes randomly on the order of 100 million times per second. These random changes are a result of the manner in which the light is produced. Light is produced by billions of individual atoms each producing individual photons of light that when put together give us a beam of light. The individual atoms are unrelated to each other and so the individual photons are not well related. The result is a light wave that changes randomly on a basic level. The light wave is not well behaved and any interference arising due to this light just gets washed out due to the random variations in the wave. Such light is referred to as incoherent light due to these random changes. While most light is incoherent, it is possible to minimize these random changes. If we can make all of the atoms producing the light act together, then all of the individual photons will be related to each other and the overall light wave will no longer have as many random changes. The light wave would then be well behaved and interference and diffraction arising from this wave would not change rapidly and would not be washed out. Such a well behaved light wave is referred to as coherent light. Coherent light is produced by a laser and by a few other light sources. When light from a laser passes through a metal slit, or when two laser beams are allowed to overlap, all of the diffraction and interference effects that I have described are clearly observable. So, in order to see diffraction in light, you need to use a coherent light source.
I hope this answered some of your questions about why diffraction occurs. Let me know if you have anymore questions.


Samantha Sinclair, a college student, asks:
Please can you help me with this assignment as I am well and truley STUCK!!
"Think of simple chemical tests for distinguishing between su gar,salt, starch for food thickening, citric acid, Harpic toilet cleaner and bicarbonate of soda. All of which are white powders. Describe how to carry them out in as sensible way to feel confident about which substance/ion is being tested for. How can a positive and negative result be determined What should be expected from each substance?"

Jon Hutchins, a chemist, replies:
Since this is being given as an exercise, I don't think I should give away the answer completely. However, here are some clues which may lead you to do a little experimentation by yourself. (1) Which of these give a blue color with iodine (need solutions)? (2)Can you test for pH (with pH test paper, or even litmus paper?). Which are acidic, which basic, which neutral? (3) Which will burn with charring? (4) Silver nitrate solution gives a white precipitate with chloride. (5) Which will liberate a gas when acid is added? Good luck with the rest!


Andy Offenburger, a college student, asks:
Do you believe humans will ever discover a truly 'indivisible piece of matter,' that is, the most basic building block for all matter? And, if so, how could we define it when we will never know if our discoveries are limited by our abilities?

Joe Traylor, a physicist, replies:
Andy, I would have to say, "Yes and No." "Yes", because at any one moment our present understanding is all we have. When we thought there were four fundamental forces, we thought there were several fundamental particles, and went and looked and found them all. Now that we have been able to understand three of the forces as stemming from one more fundamental source, the number of fundamental particles is considerably smaller, because the older "fundamental" particles are now understood to be composed of the "more fundamental" particles such as quarks. If we ever are able to include gravity in the universal-force model, then the particles will decrease again. The particles come from and confirm the model. If the "ultimate model" has one particle, then Yes, there will be only one.
But I would also say, "No," because the view of models and particles is transitory and dynamic. When you are telling your grandchildren about how it was when you were in college, you'll all probably chuckle at the primitive ideas folks had back in the '90's. (PS. This is more real than it sounds: in the 1890's, the Univ. of Chicago catalog said in the physics section that just about everything had been learned about physics and we were just refining the details!)


Eddie, a grade school student, asks:
When is the best time to see halebopp the comet?

Mark Biermann, a physicist, replies:
The best time to view an astronomical object depends on many factors. For viewing the comet Hale-Bopp we have to be concerned about when it will be brightest, when it will be well above the horizon, and what other bright objects may also be in the sky. It turns out that these three considerations work out very well for the comet Hale-Bopp.
The comet will be brightest from late March into early April, according to all of the best estimates by astronomers. It will reach its greatest height above the horizon during the first ten days of April. Finally, the comet can obviously only be seen when the sun is down. However, it will also be better to view it when the moon is not very bright either, that is, when the moon is a crescent or below the horizon completely. If you put all of these things together, the best time period in which to view the comet is a two week time period beginning about March 25th and continuing until about April 7th. During this time the moon will not be up in the evenings so the comet will not have to compete with the moon. The best time to see the comet on any given evening during this time period is about 1 hour and 15 minutes to 1 hour and 30 minutes after sunset. That is, note when the sun goes down and look for the comet about 1 hour and fifteen minutes later. One final comment about where to look. During the two week time period I just mentioned, the comet will be between 1/4 and 1/3 of the way from the horizon to the highest point on the sky, that is, the point straight overhead. It will be in the northwest sky, slightly more west than north. So, look to the northwest, about a 1/4 of the way up the sky and you should be able to see it.
Note: The brightness of comets is tough to predict, so Hale-Bopp may get really bright or it may not do much. Hopefully, it will get very bright and be very easy to see. Also, you can also see the comet before and after the two weeks mentioned, it just might not be as nice.


Tony Scheidel, a high school student, asks:
Will compressed trioxane burn once it has become wet?

Jon Hutchins, a chemist, replies:
1,3,5-Trioxane is listed in the Aldrich catalog as a flammable solid. It is also an ether, which means it may form dangerous peroxides. As to how much water will make it non-flammable, I really don't know. I do strongly recommend reading the MSDS safety sheet on this compound before using.


Gianluigi Giannoni, a teacher, asks:
What is the meaning of the quantic number "s"(spin)?

Mark Biermann, a physicist, replies:
The quantum number S is used to describe a quantity known as electron spin. Electron spin is a difficult quantity to comprehend in that it is a fundamentally quantum-mechanical quantity. Quantum mechanics is used to describe microscopic systems, such as atoms, molecules, nuclei, and basic particles, such as protons, neutrons and electrons. Microscopic systems don't, in general, act much like things do in the everyday, or macroscopic world. However, we tend to try to understand these microscopic systems by analogy with everyday systems that we have some intuition and insight about. When it comes to electron spin, this method of understanding by analogy just doesn't work very well because there is no such thing as macroscopic, or large-scale, spin. Spin is microscopic and is only described by quantum mechanics.
A number of things can be noted about electron spin. Electrons seem to have an intrinsic, or built in, angular momentum and a built in magnetic dipole moment. That is, independent of any orbital motion of the electron, the electron acts as if it possesses angular momentum and its own magnetic field. One way of picturing this idea of a built in angular momentum and magnetic dipole moment is to picture the electron as spinning on its axis, kind of like the earth spinning on its axis. The spinning of the electron leads to angular momentum and a magnetic dipole moment. Note that there are a number of difficulties with picturing the electron as actually spinning on its axis. However, it is one way of getting some insight into a fundamentally quantum mechanical quantity.
A couple of final points. Electron spin can have only two values that are often referred to as "up" and "down." The electron spin quantum number can have values of 1/2 and -1/2, corresponding to up and down orientations. Also, the results related to electron spin come naturally out of quantum mechanics if the effects of relativity are also accounted for. So, electron spin is intimately connected with the theory of relativity. Finally, there are other types of spin in microscopic systems. Nuclear spin also exists, but it is described by a different quantum number.


Kendra Kelley, a grade school student, asks:
How can you tell a female Guinea Pig from a male? Also what are the signs a female gives when she is pregnant? Does a female Guinea Pig have to be in heat to mate?

Jerry Poff, a biologist, replies:
Guinea pigs have an estrous cycle that is 16.5 days long. Usually ovulation(release of eggs from the ovaries) occurs during estrus(heat) & it is only during estrus when the female is receptive to the male. She could care less about the male during the rest of the time. Estrus in the guinea pig lasts for about 12 hrs. As you can see nature has coordinated coitus and ovulation very well-both occur during estrus(heat).
As far as I know there is no way to tell male from female other than examining the external genitalia. As you would expect,the male has a penis and the female has a vulva. Very difficult to explain how to examine - one has to be shown! Sorry!


Mrs. Medlyn's 5th grade Scientists ask:
If light has no mass then what draws it into a black hole?

Joe Traylor, a physicist, replies:
What a great question! The answer is not so hard to say, but it is quite hard to master. Remember Einstein's famous formula, E=mc**2 ? Well, there are lots of ways to interpret that formula; let me give you one. It says that mass and energy are really the same thing. That is, if you have something on the left side of an equation and something else on the right, doesn't the equals sign really mean "are the same thing"? If that is true, then anything with energy will show some properties similar to those of mass. Not in "heaviness," of course, but rather in interaction with a gravitational field. Now, light has very little interaction with gravity, so it takes a very large gravitational field to make much effect. You're right; a black hole has a HUGE gravitational field. Thus, even light is attacted to it.
(Note: there are lots more technical ways to answer this question, many much more rigorous than the above. My answer is just a start.)


Nathan Kelly, a high school student, asks:
I have an extra credit project. I was wanting to know how Avegradro came up with his nuber 6.02 x 10^23. This is an extra credit problem for Physical Science. I have to have it in before someone else does so if you could get me a reponse as soon as you can I would really be thankful.

Jon Hutchins, a chemist, replies:
Avogadro, it seems, did not actually figure out the number, it is just named after him. What he did do is to state the hypothesis that equal volumes of gases at the same temperature and pressure have the same number of particles {Avogadro's Hypothesis, 1811). It wasn't until 1865 that a German physicist, Loschmidt, worked out the number theoretically. To learn more about all this, I suggest reading Isaac Asimov's book, "On Chemistry". Good luck with your extra credit!

Charlie Slagle, a chemist, replies:
Avogadro did experiments to show that equal volumes of gases, under the same conditions, contained equal numbers of atome (molecules). This fact was then combined with the differential equation solution of the Ideal Gas Law (a combination of Boyle's and Charles' Laws) to find the integration constant which turned out to be the Ideal Gas Law Constant. It was then discovered that if the atomic weights were expressed in grams, one mole contained 6.023exp23 atoms.


Nathan Kelley, a high school student, asks:
I am in a computational science class and our group is doing a project on dimensions of subwoofer boxes. We are looking for any formulas that we could use to figure out the dimensions that you would need to build your own sub box. We would appreciate any help that you could give us.

Joe Traylor, a physicist and computer scientist, replies:
Essentially there are two kinds of subwoofer enclosures: ported and non-ported. "Ported" enclosures have a hole (usually with a pipe sticking back inside the enclosure) and non-ported ones are sealed. Let's talk about each.
Non-ported enclosures are more common. The goal for a non-ported enclosure is to ABSORB the rear directed sound. That's right; don't let the sound out of the box, because if you do, it will interfere with the sound directly coming off the front of the woofer. Some of the interference will be in-phase and cause the bass at that frequency to be increased in volume, while other frequencies will be out of phase and cancel or reduce the intensity at that frequency. In either case, you get messy bass, not uniform across frequencies. Thus, many bass units are filled with fiberglass, batting, or some material that absorbs the rear-directed sound inside the box. If you're thinking that that means you lose 1/2 of your total sound energy, you're absolutely right. But, good sound is what we want, not loud sound.
Ported enclosures are harder to build. They are used to try to take some of the rear-directed sound and delay it a little before intentionally allowing it to escape the box. When it does come out, it is again in phase with the front-sound and increases the bass at particular frequencies where bass roll-off may begin to be a problem. Ported systems usually go to lower freqencies. Dimensions here are critical, and if you're really dead set on building one of these, I'd suggest you (1) call the Bose people in Massachusetts and ask them for any amateur-level descriptive material on ported enclosures and (2) look for popular electronics magazines that feature sound equipment, or (3) look in the library under speakers. There were lots of designs published about 20-30 years ago.


Mat McEntee,a high school student, asks:
We are doing a project for a computer science class. We are doing the project on the trajectory of an arrow. Our problem is that when sighting in a bow at ground level, then going hunting out of a tree stand the arrow won't hit in the same spot. We need a formula for trajectory based on height and distance.

Mark Biermann, a physicist, replies:
Calculating the path that an object will follow is in general a very difficult problem. Especially for something like an arrow, many variables have to be accounted for. Things that can affect the flight include: the degree to which the shaft of the arrow flexes or remains rigid; the type of arrowhead on the shaft; the fletching, or feathers on the arrow, that is, are the feathers properly mounted?, are they balanced?, do they cause the arrow to spin as it flies?; the existence of a cross-wind, a tail-wind, or a head-wind. If all of these variables must be accounted for it is virtually impossible to state a "general formula for trajectory based on height and distance."
It is possible to make a simplifying assumption that does allow us to state a general result for the trajectory. As with all assumptions it has the disadvantage of ignoring possibly important phenomenon. But the assumption also allows us to treat the problem in a fairly simple manner. This assumption is to treat the arrow as if it undergoes projectile motion. In many situations, projectile motion is a good approximation to the motion objects actually experience. In projectile motion, two main simplifications are made. First the object is considered to be a particle. That is, we assume that the shape of the object doesn't matter. Obviously this is a big assumption, especially for an arrow, but it is an assumption that must be made if we want a general result. Second, we assume that the only force that acts on the arrow after it leaves the bow is the force of gravity. Hence, the only force acting on the arrow is straight down. Of course this is also a big assumption since we are now ignoring the effects of wind and of air in general.
If we can in fact use projectile motion, then the path of the arrow can be described straightforwardly. The arrow will experience no acceleration in the horizontal direction and the only vertical acceleration it will experience will be due to gravity. The path of the arrow can be described using two equations. One equation gives the horizontal position of the arrow and the other gives its vertical position. The two equations are

    x = x0 + v0x(t)

    y = y0 + v0y(t) - (1/2)g(t*t)

where

    x is the horizontal position
    y is the vertical position
    t is the time after the arrow is released or fired from the bow
    x0 is the initial horizontal position
    v0x is the initial speed in the horizontal direction
    y0 is the initial vertical position
    v0y is the initial speed in the vertical direction
    g is the accelceration on the arrow due to gravity

So, in order to use these equations you need the initial position of the arrow and the inital speed of the arrow. The value of the acceleration due to gravity depends on the units you are using. For instance, if you are using distance in meters and time in seconds, g is equal to 9.8 m/s/s. If distance is in feet and time is in seconds, g is equal to 32 f/s/s.
Remember, this result is only an approximation and leaves out things like wind resistance. However, in many situations it is quite helpful and I hope it helps you out


Jonathan Germain, a high school student, asks:
Im looking for a chart or set of charts of solubilities of salts in water varying with temperature. I have alredy tried the handbook of Physics and Chemistry (77th edition). Thanks..

Jon Hutchins, Professor of Chemistry, replies:
Hello Jonathan! Regarding your question about the solubilities of salts at different temperatures, I can think of two sources in our library that might be helpful: a 2 volume book by Seidell, and the International Critical Tables. If you would like more specific references to these two reference works I can look them up, or if you have a need for specific data, I would be glad to see what I can find. Good luck!
email hutchins@bvu.edu



Gus Morrow, a parent, asks:
I am often involved in a debate over evolution. Is there any DNA evidence that proves a relationship between man and ape?

Jack Mellen, an animal ecologist, replies:
An example of such evidence can be found in a 1987 article by Li, Tanimura, and Sharp entitled "An evaluation of the molecular clock hypothesis using mammalian DNA sequences." Journal of Molecular Evolution 24:330-342.
Whether or not this "proves" anything begs the greater question of whether or not science deals in "proof."


Judy Andrews, a teacher, asks:
I have asked this question before and failed to see the answer. I'll try again and do my best to check from time to time to see if I get an answer. A first grader in my class once asked me "If a space ship could travel toward the sun,and not burn up as it got closer to the sun would the sun begin to 'pull' the space craft closer to it. Does the sun have the ability to 'pull' objects toward itself?"

Once again a question has been asked that has so stimulated our group of scientists that *two* of our physicists have again jumped at the chance to reply. Joe Traylor leads off:
Yes, the sun pulls everything towards it! That is the very reason that the earth continues to orbit the sun rather than just flying off into space. Think of it this way: Suppose you had a ball on a string and whirled it about your head. The ball would go in circle because the string pulled on it (and you pulled on the string). If you cut the string, the ball would leave it's circular path and fly off straight ahead in whatever direction it was traveling and the instant the string was cut. The sun pulls on the earth with gravity. The gravity is acting like the string, causing earth to go in a cirle around the sun.
Now, about your spaceship. Yes, it would fall towards the sun. It's not moving in a circle, so would fall, speeding up more and more as it "fell." In fact, its weight --the pull of the sun on it-- would get more and more as it approached the sun, since the pull of gravity increases (dramatically!) as the distance between you and the pulling object, the sun, gets smaller. When the ship had gone 1/2 the way there, its weight would be 4 times greater!
You say, "Wait a mimnute, I thought it would be "weightless!"" Weightless is just a feeling when nothing is pushing up on us. When you jump off a high ledge, you feel weightless while you fall. You know that you really weigh just as much as before, but it sure feels different while falling. Thus, the spaceship has weight while it falls, and its weight gets greater and greater.
Lastly, this is all really about the big subject of gravity. Gravity is the pull one object exerts on every other, just because they both have mass. So, the sun which has lots of mass is always pulling on every other obeject around, you, me, the oceans (that's why we have tides, because of the gravitational pull of the sun and the moon), the air, etc. The amount of pull (how strong it is) depends on how much mass the two objects have and the distance between them. You feel much more pull from the earth than the sun only because we are so close to the earth.
An interesting fact just for the fun of it: of the four "fundamental" forces --nuclear strong force, nuclear weak force, electric field forces, and gravity-- the one you asked about, gravity, is the *least* understood. Although Isaac newton described it mathematically several hundred years ago, we still do not know WHY its there. It's a property of matter to attract all other matter, but no one knows why!
Mark Biermann has this to say:
Yes, the sun can pull objects toward it. The source of this pull is the force of gravity. Gravity is one of the basic forces in the universe and is responsible for many events that we experience everyday. Gravitational force exists between any two objects that have mass. So, if an object contains matter, it will exert a gravitational force on another object and the second object will exert a gravitational force on the first object. We experience this when we don't float out into space from the surface of the earth. Gravitational force exists between us and the earth, holding us firmly to the surface of the earth. I should note that the gravitational force is always attractive, so the earth always pulls us down and never pushes us away. Also, the gravitational force is larger the more mass there is involved and the closer the objects are together.
So let's apply this to the spaceship and the sun. Both the sun and the spaceship have mass and so there is a graviational force between them. The force is attractive so the sun pulls the spaceship toward it. Since the sun is enormously massive, the force would be quite strong. Also, the closer the spaceship got to the sun, the stronger the force would be. Bottom line: unless you really want to get pulled into the sun by a very strong gravitational force, it would be best to keep your distance.


Josh Jensen, a high school student, asks:
I was trying to find which chromosomes cause Severe Combined Immunodeficiency (SCID). I know there is an X-linked form, and at least an autosomal recessive form as well. I tried looking at OMIM, but that was way over my head.

Jerry Poff, a biologist, replies:
The term severe combined immunodeficiency disease(SCID) is given to a diverse group of disorders characterized by defective development or function of T & B lympocytes( a type of white blood cell). This results in severe impairment of B cell function(production of antibodies) & T cell function( destroying virally infected cells).
The transmission of these immunodeficiences may be X-linked recessive or autosomal recessive. The more common autosomal recessive form of SCID is as a result of an error in a gene on chromosome 2. Another less common form is transmitted by an error in a gene on chromosome 9. Both of these genes are important to the formation of enzymes necessary for the normal function of lympocytes. The enzymes are deficient as a result of the altered gene.


Evan Burmeister, a high school student, asks:
I know that for every force there is an equal and opposite force. But say a book is sitting on a table. The book is pushing down, because of gravity. But how can you say the table pushes back on the book? If the book was gone wouldn't the table jump up into the air? Also, does temperature effect the speed of sound in the air? And would sound move faster in air or in a solid?

This is such an interesting question that *two* of our physicists have elected to tackle it! The first, Joe Traylor, replies:
Evan: Good question! People have struggled with action-reaction forces for centuries. You're on the right track.
First, you already seem to realize that forces come in pairs. Maybe you had not thought about the fact that ALL forces come in pairs (at least). That is, "force" is really an interaction term, and you always need at least two players. So, "weight" is the pull of gravity down on the book, but in fact the book is pulling up on the Earth just as strongly.
So, how do we know the table pushes back? Two ways to know, neither of which may thrill you. First way: if the table didn't push upwards the book would fall due to gravity. You admit that the book has weight, is being pulled by the Earth. Thus, if nothing stopped it, the book would fall. But the table DOES stop it, so the table must be pushing upward, equal and opposite to the book.
Secondly, you said all forces came in pairs. Thus, if the book and table interact they exert equal and oppositie forces on one another. Book down, table up. (Told you you wouldn't like the answer! Logic is seldom fun to argue with!)
Lastly, would the table push up (jump up?) with no book on it? No, because forces always come in pairs. No book pushing down, then no table pushing up. Table, yes; push, no.
Another thing, does temperature effect the speed of sound in the air?
Sure does. The speed depends on the speed of the molecules in the gas (air). Heat 'em up, and they are moving faster, thus sound moves faster.
One more. Would sound move faster in air or in a solid?
Trickey question, since it depends on which solid. however, a general rule: sound moves fastest when the bonds between molecules is strongest. Thus, faster in a solid where they are tightly bound than in a gas where they are (very) loosely bound.
The reason it's a trick question is a very hot, light weight gas such as hot helium might actually have a higher speed of sound than a very heavy-atomed, soft (weakly bound) material such as lead.
 
Our second physicist, Mark Biermann, also responds:
Newton's third law often leads to confusion, but it is really just a formal way of stating what all of us take for granted about the way in which the world works. First of all we have to remember that the two forces in an "equal and opposite" set of forces always act on TWO DIFFERENT OBJECTS. So, the example you have given of the book and the table is a good one. The book pushes down on the table, and yes, the table does push up on the book. If the table were not pushing up on the book, what would keep the book from falling? Take away the force of the table on the book and the only force on the book is the force of gravity and the book would be falling. Obviously the book does not fall when it rests on the table and there is a force of the table on the book, equal and opposite to the force of the book on the table, giving us a good example of a force pair.
It is worthwhile to clarify a couple of points. First, the two forces in a force pair are not in a cause and effect relationship. One force does not "cause" the other force. Hence, the terms action and reaction can be misleading. Also, the table doesn't jump because when the book is removed the force pair no longer exists. When the force of the book on the table is removed, by removing the book, the force of the table on the book also ceases to exist. Finally, the table would not jump unless a force were exerted on it in the upward direction. There is nothing mentioned in this discussion that could provide such an upward force on the table.
One more example might help with this whole force pair question. Say someone punches a wall, fist first, and regretfully breaks his hand. Obviously the person's fist exerts a force on the wall, possibly even cracking or denting the wall. But a force exerted on the wall will not harm the person. Only a force acting ON THE FIST will damage the fist. Where did this force come from? It is simply the force of the wall on the person's fist. The force has to be there, by Newton's Third Law. The force of the fist on the wall has an equal and opposite force that also acts. It is the force of the wall on the fist. It is the force on the fist that does the damage to the person's hand.
Now about sound. Your two questions are actually closely related. Sound is a wave and the "thing" that travels in a wave is energy. Most waves require some material, a medium, to carry the energy of the wave. When a sound wave travels from a person speaking to a person listening, energy is transfered from the speaker to the listener via the material between the two people. Usually the material is air, but sometimes it is water or steel or something else. The energy of the wave is actually transfered by vibrations within the material. The individual molecules of air, or whatever the medium happens to be, are caused to vibrate by the sound wave. As the molocules vibrate, they collide with neighboring molecules. These collisions are what allow the wave to travel from one point to another. Air molecules don't actually travel from the speaker to the listener. Instead the energy of the wave travels across the room by the many collisions that occur between the vibrating air molecules. As the vibrations and collisions travel across the room, the energy and the sound wave travel across the room.
The type of medium can affect the way sound waves travel. If the atoms or molecules of the medium are close together, they will tend to collide with each other very easily. The more easily they collide with each other, the better a sound wave will travel through the material. So, sound will tend to travel with lower losses and greater speed through a material in which molecular collisions occur easily and often.
You can try this out by using a steel door frame. Place your ear on the door frame and then tap lightly on the door frame far from your ear. You can hear the tapping much more clearly and loudly through the door frame, a dense solid, than through the air around the frame, a much less dense gas. Please be clear that density is not the only property that effects the speed of sound in a material. Actually a number of things work together in a fairly complex manner to determine the speed of sound. Density is just one of the key players in the overall process, and since this answer is already quite long, I don't really have time to go into all of the details. If you are interested in the details, let us know with a follow up question. KEY POINT TO REMEMBER: the better the molecules collide together, the faster sound will tend to travel in that material.
Apply our key point to your two specific examples. Temperature does effect the speed of sound in air (and water for that matter). As air warms up the molecules tend to move around much more quickly. Hence, they tend to collide more often. More collisions lead to a higher speed of sound in warmer air. The speed of sound in air at 0 degrees C is 331 m/s while the speed in air at 20 degrees C is 343 m/s. In comparing the speed happen much more easily and efficiently in a solid than in air. For this reason, the speed of sound is much greater in a solid than in air. For example, the speed of sound in aluminium is 6420 m/s, about 20 times greater than the speed of sound in air.


Julia Walter, a high school student, asks:
I never really understood Einstein's formula: Energy is equal to Mass times the Speed of Light squared. The Speed of Light is constant and that means when you increase the energy of an object its mass increases too. But how can an object increase its mass if no further atoms are added? I read somewhere that energy converts somehow to mass, but I can just not picture how this works. Thank you!

Mark Biermann, a physicist, replies:
The equation with which you have difficulty is the source of much misunderstanding and confusion. The best way to understand that formula is to try to put it into the context, or background, from which it arises. This formula is one of the key results of Albert Einstein's theory of Special Relativity. (He also developed a theory of General Relativity, but any discussion of that will have to wait for another time.) The ideas of special relativity were developed early in the 20th century and so in many respects they represent a fairly new set of concepts. Einstein was interested in studying the relationships between different quantities that can be measured and the laws of physics themselves. Many fascinating and, frankly, strange results came out of this study. Some of the most famous are that time slows down as one travels at higher speeds, that lengths shorten at higher speeds and that objects can't travel at the speed of light or above.
Einstein also discovered the result in which you are particularly interested. What he found is that mass can be thought of as just another form of energy. Energy is an amazing concept to begin with. It can take on many different forms and can be transferred by many means. We have energy of motion, arising simply because an object is moving so fast. We have potential, or stored energy, such as the energy in a stretched spring or rubber band. There is electrical energy and heat energy. There is stored chemical energy, as in a battery or in dynamite. All of these various forms of energy transform into other forms of energy all of the time. It turns out that mass is just another of these many forms of energy. Just as chemical energy is changed into electrical energy in a toy car, and electrical energy is changed into chemical energy when a battery is recharged, so mass can be transformed into heat energy and energy of motion and radiant energy, such as that in light, can be transformed into the form of energy we call mass. When it comes right down to it, the strong distinction that we tend to make between matter and energy has less to do with physics and more to do with the language that we tend to use.
The formula you asked about gives the specific relationship for the amount of energy stored as mass in some object. Basically the equation says that if mass is transformed completely into energy, then the amount of energy that is produced is given by the mass times the speed of light squared. In some ways, matter is a really great battery. Lots of energy is stored in the matter. If it can be relaesed, then we have a great energy source. The key to this is that in general it is very difficult to cause mass to transform into other forms of energy. That is, in general, mass is pretty stable stuff. In certain situations the transformation of mass into energy does occur, with amazing results. Examples of mass converting to energy are the fusion reactions that occur in the sun, atomic bombs and nuclear reactors. All of these processes use the conversion of mass into energy in order to work.
I hope this helps to answer your question. If you have related questions or if some point still is not clear, please ask a follow-up question and we will try to help as best we can.


Gaurav, a middle school student, asks:
I have a very simple question. Why doesn't the shadow of a bird flying in the sky appear on earth? I would be grateful if you can send me the answer. Thanks

Mark Biermann, a physicist, replies:
The reason we don't see the shadow of a bird on the ground is because of size and because of how large things appear to be. When it comes to shadows, how large something appears to be is as important as how large it actually is. The best known example of this is a solar eclipse. In a total solar eclipse, the sun is actually completely blocked by the moon. That is, if you are in the total eclipse area, you are in the complete shadow of the moon. But it is known that the sun is much, much, much bigger than the moon. How can the moon block the entire sun? Because the moon is much closer to the earth than is the sun and so from the earth the moon "appears" to be almost exactly the same size as the sun. So in the right situation, even something quite small can block something much larger.

There is another point that is important too. There are two parts to any shadow. In one part of the shadow, the light source is completely blocked. It is fairly limited in size and is called the umbra. In the much larger part of the shadow the light source is only partially blocked. This part of the shadow is called the penumbra. The effect of the penumbra is so small that it is often not even noticed when one is out in the sun. The penumbra of a tree provides little shade. One must be in the umbra to actually feel like one is in the shade, that is, in the tree's shadow.

[Photo of Shadows]

So how does this apply to bird shadows. If the apparent size of the bird were big enough, the bird would block the sun and a shadow would appear on the ground. The only shadow one would notice is the umbra, the small part of the shadow in which the sun is completely blocked. Often a low- flying airplane will actually be big enough to block the entire sun and cast a distinct shadow on the ground as it flies overhead. Birds, however, are so small that only the penumbra reaches the ground and we never really notice a shadow. The umbra is just too small and the penumbra is just not strong enough to be noticed. So while part of the bird's shadow does reach the ground, it isn't the part that can be noticed. I have included a simple drawing that helps to illustrate this point. In one case, a larger object such as an airplane, casts its umbra onto the ground and we see a shadow. For the bird, only the penumbra reaches the ground.


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