How do we know there's a wind, when we can't see the
wind? In 1905 Einstein found a similar way to show the existence of
atoms, even though at the time we had no way to see atoms.
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A. If molecules really exist, what size are they?
Take something made of one single material and divide it in half. Take
one of the halves and divide it again into smaller pieces. Now divide one of those pieces. If you can keep dividing the
material into smaller and smaller pieces, you'll eventually get to the
individual atoms the material is made of. In many materials, groups of
atoms stick together to make somewhat larger natural units, known as molecules.
The fact that matter is made of atoms is no
longer news. Nowadays, we have
microscopes that let us see how atoms are arranged at the surfaces of materials,
and physicists routinely isolate individual atoms and molecules and experiment
with them one at a time. But 100
years ago, there were no such microscopes and no tools to isolate individual
molecules, so the evidence that atoms exist was much less direct.
Furthermore, in some experiments, matter behaved very differently from
the way people expected atoms to behave-so differently that some people
thought the experiments proved atoms weren't real.
Albert Einstein did believe that matter came in
smallest-possible units, and as he later said, he wanted "to find facts which
would guarantee as much as possible the existence of atoms of definite finite
size". He found what he was
looking for in a microscopic effect of the energy of heat.
By the early 19th century, physicists
had worked out some of the mathematical laws of heat, even though they had an
incomplete understanding of what heat actually is. Even before that time, people began to realize that certain facts about
heat would make sense if materials were made of small minimum-size units.
The basic idea was that an object's thermal energy is simply the energy
of its molecules in constant random motion; the greater the energy of the random
motion, the hotter the object.
Many real thermal phenomena were exactly what
this idea suggested they should be. On
the other hand, not all thermal processes seemed to match such
expectations. In particular, some materials behaved differently at very low
temperatures, more so as the temperature came closer to absolute zero
(-273.15°C). Some materials even showed different behavior at room
temperature. This indicated that something was wrong with the idea; what exactly was
wrong only became clear later. But
because of these problems a few scientists doubted entirely that matter existed
in basic units. Many others, who did
assume molecules were real, often just described the idea as a useful working
hypothesis.
Some of the most persuasive evidence that
molecules exist came from chemistry. Today
it's common knowledge that water is made from atoms of hydrogen and
oxygen. It had long been known that, to produce water from hydrogen and oxygen
gas without having any of either gas left over, you had to use twice as many
liters of hydrogen as oxygen. Similar
exact recipes were known for producing other substances. In the early 19th century, the physicist Amedeo Avogadro
realized these recipes implied something important: no
matter what types of gas you were working with, equal volumes of gas at the same
temperature and pressure are made of equal numbers of molecules.
Starting from this idea, plus the recipes for many different chemical
reactions, chemists were able to deduce something about the masses of each type
of molecule and the atoms that make up each type. They found that hydrogen atoms were the least massive of all the atoms,
carbon atoms were about twelve times as massive as hydrogen atoms, oxygen atoms
were sixteen times as massive as hydrogen atoms, and so on. Chemists could furthermore work out that molecules of hydrogen and oxygen
should be made of two atoms each, water molecules of two hydrogen atoms and one
oxygen atom each, and so on.
The one thing chemists and physicists could not work out from this was the
actual mass of any one kind of molecule. It
was one thing to know that a water molecule is about 18 times as massive as a
hydrogen atom; it was another entirely to know that a water molecule's mass is
about 30 yoctograms (30 x
10-24 grams).
What they could do, though, was work with standard quantities of any given
substance that were proportional to
the molecular masses. Since hydrogen
molecules were supposed to be made of two hydrogen atoms each, the standard
quantity of hydrogen was taken as two grams. And since water molecules were supposed to be 18 times as massive as
hydrogen atoms, the standard quantity of water was 18 grams. The standard quantity of a substance was called a "gram-molecule", or
"mole" for short. Defining a
mole this way meant that one mole of any substance would have the same number of
molecules as one mole of any other substance-whatever that number actually
was. If you knew that number-how
many molecules of something made one mole of it-you could figure out the mass
of just one of the molecules. People
tried various experiments to determine that number, but the early results were
not very precise.
This was the situation when Einstein began searching for
facts to establish the size of atoms. He
found a way that, if the earlier estimates were at least in the right
neighborhood, would let us determine molecular masses more precisely than ever
before. As we mentioned earlier,
this clue was in a microscopic effect of the energy of heat.
Einstein found that, if molecules really existed, then
small particles dispersed among the molecules of a fluid should also have a
random motion, very much like the thermal motion of gas molecules.
(.....continued)
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