This is the first Chapter of Richard P Feynman's Lectures on Physics. I have other Chapters as well But I cannot post them all together as it will be too big and cumbersome. I cannot promise this, but I will try to post the other topics as soon as possible. I have copied the illustrations in the end, they are numbered. You will have to scroll down everytime to see them. But don't worry as there are not many of them.

This Chapter deals with the Atomic Theory, an idea that has revolutionised physics. The fact that it has been written by Richard Feynman, the nobel laureate makes it even more interesting to read. So go on and have fun reading it.

Matter is made of atoms

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only

one sentence passed on to the next generations of creatures, what statement would

contain the most information in the fewest words? I believe it is the atomic

hypothesis (or the atomic fact, or whatever you wish to call it) that all things are

made of atoms—little particles that move around in perpetual motion, attracting

each other when they are a little distance apart, but repelling upon being squeezed

into one another. In that one sentence, you will see, there is an enormous amount

of information about the world, if just a little imagination and thinking are applied.

To illustrate the power of the atomic idea, suppose that we have a drop of

water a quarter of an inch on the side. If we look at it very closely we see nothing

but water—smooth, continuous water. Even if we magnify it with the best optical

microscope available—roughly two thousand times—then the water drop will be

roughly forty feet across, about as big as a large room, and if we looked rather

closely, we would still see relatively smooth water—but here and there small

football-shaped things swimming back and forth. Very interesting. These are

paramecia. You may stop at this point and get so curious about the paramecia

with their wiggling cilia and twisting bodies that you go no further, except perhaps

to magnify the paramecia still more and see inside. This, of course, is a subject

for biology, but for the present we pass on and look still more closely at the water

material itself, magnifying it two thousand times again. Now the drop of water

extends about fifteen miles across, and if we look very closely at it we see a kind

of teeming, something which no longer has a smooth appearance—it looks something

like a crowd at a football game as seen from a very great distance. In order

to see what this teeming is about, we will magnify it another two hundred and

fifty times and we will see something similar to what is shown in Fig. 1-1. This

is a picture of water magnified a billion times, but idealized in several ways.

In the first place, the particles are drawn in a simple manner with sharp edges,

which is inaccurate. Secondly, for simplicity, they are sketched almost schematically

in a two-dimensional arrangement, but of course they are moving around in

three dimensions. Notice that there are two kinds of "blobs" or circles to represent

the atoms of oxygen (black) and hydrogen (white), and that each oxygen has two

hydrogens tied to it. (Each little group of an oxygen with its two hydrogens is

called a molecule.) The picture is idealized further in that the real particles in

nature are continually jiggling and bouncing, turning and twisting around one

another. You will have to imagine this as a dynamic rather than a static picture.

Another thing that cannot be illustrated in a drawing is the fact that the particles

are "stuck together"—that they attract each other, this one pulled by that one,

etc. The whole group is "glued together," so to speak. On the other hand, the

particles do not squeeze through each other. If you try to squeeze two of them too

close together, they repel.

The atoms are 1 or 2 X 10-8 cm in radius. Now 10-8 cm is called an

angstrom (just as another name), so we say they are 1 or 2 angstroms (Å) in radius.

Another way to remember their size is this: if an apple is magnified to the size

of the earth, then the atoms in the apple are approximately the size of the original

apple.

Now imagine this great drop of water with all of these jiggling particles stuck

together and tagging along with each other. The water keeps its volume; it does

not fall apart, because of the attraction of the molecules for each other. If the

drop is on a slope, where it can move from one place to another, the water will

flow, but it does not just disappear—things do not just fly apart—because of

the molecular attraction. Now the jiggling motion is what we represent as heat:

when we increase the temperature, we increase the motion. If we heat the water,

the jiggling increases and the volume between the atoms increases, and if the

heating continues there comes a time when the pull between the molecules is not

enough to hold them together and they do fly apart and become separated from

one another. Of course, this is how we manufacture steam out of water—by

increasing the temperature; the particles fly apart because of the increased motion.

In Fig. 1-2 we have a picture of steam. This picture of steam fails in one

respect: at ordinary atmospheric pressure there might be only a few molecules in

a whole room, and there certainly would not be as many as three in this figure.

Most squares this size would contain none—but we accidentally have two and a

half or three in the picture (just so it would not be completely blank). Now in

the case of steam we see the characteristic molecules more clearly than in the case

of water. For simplicity, the molecules are drawn so that there is a 120° angle

between them. In actual fact the angle is 105°3', and the distance between the

center of a hydrogen and the center of the oxygen is 0.957 Å, so we know this

molecule very well.

Let us see what some of the properties of steam vapor or any other gas are.

The molecules, being separated from one another, will bounce against the walls.

Imagine a room with a number of tennis balls (a hundred or so) bouncing around

in perpetual motion. When they bombard the wall, this pushes the wall away.

(Of course we would have to push the wall back.) This means that the gas exerts

a jittery force which our coarse senses (not being ourselves magnified a billion

times) feels only as an average push. In order to confine a gas we must apply a

pressure. Figure 1-3 shows a standard vessel for holding gases (used in all

textbooks), a cylinder with a piston in it. Now, it makes no difference what the

shapes of water molecules are, so for simplicity we shall draw them as tennis

balls or little dots. These things are in perpetual motion in all directions. So many

of them are hitting the top piston all the time that to keep it from being patiently

knocked out of the tank by this continuous banging, we shall have to hold the

piston down by a certain force, which we call the pressure (really, the pressure

times the area is the force). Clearly, the force is proportional to the area, for if

we increase the area but keep the number of molecules per cubic centimeter the

same, we increase the number of collisions with the piston in the same proportion

as the area was increased.

Now let us put twice as many molecules in this tank, so as to double the density,

and let them have the same speed, i.e., the same temperature. Then, to a

close approximation, the number of collisions will be doubled, and since each will

be just as "energetic" as before, the pressure is proportional to the density. If we

consider the true nature of the forces between the atoms, we would expect a slight

decrease in pressure because of the attraction between the atoms, and a slight

increase because of the finite volume they occupy. Nevertheless, to an excellent

approximation, if the density is low enough that there are not many atoms, the

pressure is proportional to the density.

We can also see something else: If we increase the temperature without

changing the density of the gas, i.e., if we increase the speed of the atoms, what

is going to happen to the pressure? Well, the atoms hit harder because they are

moving faster, and in addition they hit more often, so the pressure increases.

You see how simple the ideas of atomic theory are.

Let us consider another situation. Suppose that the piston moves inward,

so that the atoms are slowly compressed into a smaller space. What happens when

an atom hits the moving piston? Evidently it picks up speed from the collision.

You can try it by bouncing a ping-pong ball from a forward-moving paddle, for

example, and you will find that it comes off with more speed than that with which

it struck. (Special example: if an atom happens to be standing still and the piston

hits it, it will certainly move.) So the atoms are "hotter" when they come away

from the piston than they were before they struck it. Therefore all the atoms which

are in the vessel will have picked up speed. This means that when we compress

a gas slowly, the temperature of the gas increases. So, under slow compression,

a gas will increase in temperature, and under slow expansion it will decrease in

temperature.

We now return to our drop of water and look in another direction. Suppose

that we decrease the temperature of our drop of water. Suppose that the jiggling

of the molecules of the atoms in the water is steadily decreasing. We know that

there are forces of attraction between the atoms, so that after a while they will

not be able to jiggle so well. What will happen at very low temperatures is indicated

in Fig. 1-4: the molecules lock into a new pattern which is ice. This

particular schematic diagram of ice is wrong because it is in two dimensions, but

it is right qualitatively. The interesting point is that the material has a definite

place for every atom, and you can easily appreciate that if somehow or other we

were to hold all the atoms at one end of the drop in a certain arrangement, each

atom in a certain place, then because of the structure of interconnections, which is

rigid, the other end miles away (at our magnified scale) will have a definite location.

So if we hold a needle of ice at one end, the other end resists our pushing it aside,

unlike the case of water, in which the structure is broken down because of the

increased jiggling so that the atoms all move around in different ways. The difference

between solids and liquids is, then, that in a solid the atoms are arranged in

some kind of an array, called a crystalline array, and they do not have a random

position at long distances; the position of the atoms on one side of the crystal

is determined by that of other atoms millions of atoms away on the other side of

the crystal. Figure 1-4 is an invented arrangement for ice, and although it contains

many of the correct features of ice, it is not the true arrangement. One of the

correct features is that there is a part of the symmetry that is hexagonal. You can

see that if we turn the picture around an axis by 120°, the picture returns to itself.

So there is a symmetry in the ice which accounts for the six-sided appearance of

snowflakes. Another thing we can see from Fig. 1-4 is why ice shrinks when it

melts. The particular crystal pattern of ice shown here has many "holes" in it,

as does the true ice structure. When the organization breaks down, these holes

can be occupied by molecules. Most simple substances, with the exception of

water and type metal, expand upon melting, because the atoms are closely packed

in the solid crystal and upon melting need more room to jiggle around, but an

open structure collapses, as in the case of water.

Now although ice has a "rigid" crystalline form, its temperature can change—

ice has heat. If we wish, we can change the amount of heat. What is the heat in

the case of ice? The atoms are not standing still. They are jiggling and vibrating.

So even though there is a definite order to the crystal—a definite structure—all

of the atoms are vibrating "in place." As we increase the temperature, they vibrate

with greater and greater amplitude, until they shake themselves out of place.

We call this melting. As we decrease the temperature, the vibration decreases

and decreases until, at absolute zero, there is a minimum amount of vibration

that the atoms can have, but not zero. This minimum amount of motion that atoms

can have is not enough to melt a substance, with one exception: helium. Helium

merely decreases the atomic motions as much as it can, but even at absolute zero

there is still enough motion to keep it from freezing. Helium, even at absolute

zero, does not freeze, unless the pressure is made so great as to make the atoms

squash together. If we increase the pressure, we can make it solidify.

Atomic processes

So much for the description of solids, liquids, and gases from the atomic

point of view. However, the atomic hypothesis also describes processes, and so we

shall now look at a number of processes from an atomic standpoint. The first

process that we shall look at is associated with the surface of the water. What

happens at the surface of the water? We shall now make the picture more complicated

—and more realistic—by imagining that the surface is in air. Figure 1-5

shows the surface of water in air. We see the water molecules as before, forming

a body of liquid water, but now we also see the surface of the water. Above the

surface we find a number of things: First of all there are water molecules, as in steam.

This is water vapor, which is always found above liquid water. (There is an

equilibrium between the steam vapor and the water which will be described later.)

In addition we find some other molecules—here two oxygen atoms stuck together

by themselves, forming an oxygen molecule, there two nitrogen atoms also stuck

together to make a nitrogen molecule. Air consists almost entirely of nitrogen,

oxygen, some water vapor, and lesser amounts of carbon dioxide, argon, and

other things. So above the water surface is the air, a gas, containing some water

vapor. Now what is happening in this picture? The molecules in the water are

always jiggling around. From time to time, one on the surface happens to be hit

a little harder than usual, and gets knocked away. It is hard to see that happening

in the picture because it is a still picture. But we can imagine that one molecule

near the surface has just been hit and is flying out, or perhaps another one has

been hit and is flying out. Thus, molecule by molecule, the water disappears—

it evaporates. But if we close the vessel above, after a while we shall find a large

number of molecules of water amongst the air molecules. From time to time, one

of these vapor molecules comes flying down to the water and gets stuck again.

So we see that what looks like a dead, uninteresting thing—a glass of water with

a cover, that has been sitting there for perhaps twenty years—really contains a

dynamic and interesting phenomenon which is going on all the time. To our eyes,

our crude eyes, nothing is changing, but if we could see it a billion times magnified,

we would see that from its own point of view it is always changing: molecules

are leaving the surface, molecules are coming back.

Why do we see no change? Because just as many molecules are leaving as

are coming back! In the long run "nothing happens." If we then take the top of

the vessel off and blow the moist air away, replacing it with dry air, then the

number of molecules leaving is just the same as it was before, because this depends

on the jiggling of the water, but the number coming back is greatly reduced because

there are so many fewer water molecules above the water. Therefore there

are more going out than coming in, and the water evaporates. Hence, if you wish

to evaporate water turn on the fan!

Here is something else: Which molecules leave? When a molecule leaves it

is due to an accidental, extra accumulation of a little bit more than ordinary

energy, which it needs if it is to break away from the attractions of its neighbors.

Therefore, since those that leave have more energy than the average, the ones that

are left have less average motion than they had before. So the liquid gradually cools if it evaporates.

Of course, when a molecule of vapor comes from the air to

the water below there is a sudden great attraction as the molecule approaches

the surface. This speeds up the incoming molecule and results in generation of

heat. So when they leave they take away heat; when they come back they generate

heat. Of course when there is no net evaporation the result is nothing—the water

is not changing temperature. If we blow on the water so as to maintain a continuous

preponderance in the number evaporating, then the water is cooled. Hence,

blow on soup to cool it!

Of course you should realize that the processes just described are more complicated

than we have indicated. Not only does the water go into the air, but also,

from time to time, one of the oxygen or nitrogen molecules will come in and "get

lost" in the mass of water molecules, and work its way into the water. Thus the

air dissolves in the water; oxygen and nitrogen molecules will work their way into

the water and the water will contain air. If we suddenly take the air away from the

vessel, then the air molecules will leave more rapidly than they come in, and in

doing so will make bubbles. This is very bad for divers, as you may know.

Now we go on to another process. In Fig. 1-6 we see, from an atomic point

of view, a solid dissolving in water. If we put a crystal of salt in the water, what

will happen? Salt is a solid, a crystal, an organized arrangement of "salt atoms."

Figure 1-7 is an illustration of the three-dimensional structure of common salt,

sodium chloride. Strictly speaking, the crystal is not made of atoms, but of what

we call ions. An ion is an atom which either has a few extra electrons or has lost

a few electrons. In a salt crystal we find chlorine ions (chlorine atoms with an

extra electron) and sodium ions (sodium atoms with one electron missing). The

ions all stick together by electrical attraction in the solid salt, but when we put

them in the water we find, because of the attractions of the negative oxygen and

positive hydrogen for the ions, that some of the ions jiggle loose. In Fig. 1-6

we see a chlorine ion getting loose, and other atoms floating in the water in the form

of ions. This picture was made with some care. Notice, for example, that the

hydrogen ends of the water molecules are more likely to be near the chlorine ion,

while near the sodium ion we are more likely to find the oxygen end, because the

sodium is positive and the oxygen end of the water is negative, and they attract

electrically. Can we tell from this picture whether the salt is dissolving in water or

crystallizing out of water? Of course we cannot tell, because while some of the

atoms are leaving the crystal other atoms are rejoining it. The process is a dynamic

one, just as in the case of evaporation, and it depends on whether there is more or

less salt in the water than the amount needed for equilibrium. By equilibrium we

mean that situation in which the rate at which atoms are leaving just matches the

rate at which they are coming back. If there is almost no salt in the water, more

atoms leave than return, and the salt dissolves. If, on the other hand, there are

too many "salt atoms," more return than leave, and the salt is crystallizing.

In passing, we mention that the concept of a molecule of a substance is only

approximate and exists only for a certain class of substances. It is clear in the

case of water that the three atoms are actually stuck together. It is not so clear

in the case of sodium chloride in the solid. There is just an arrangement of sodium

and chlorine ions in a cubic pattern. There is no natural way to group them as

"molecules of salt."

Returning to our discussion of solution and precipitation, if we increase the

temperature of the salt solution, then the rate at which atoms are taken away is

increased, and so is the rate at which atoms are brought back. It turns out to be

very difficult, in general, to predict which way it is going to go, whether more or

less of the solid will dissolve. Most substances dissolve more, but some substances

dissolve less, as the temperature increases.

Chemical reactions

In all of the processes which have been described so far, the atoms and the

ions have not changed partners, but of course there are circumstances in which

the atoms do change combinations, forming new molecules.

This is illustrated in a process in which the rearrangement of the atomic partners occurs is

what we call a chemical reaction. The other processes so far described are called

physical processes, but there is no sharp distinction between the two. (Nature

does not care what we call it, she just keeps on doing it.) This figure is supposed

to represent carbon burning in oxygen. In the case of oxygen, two oxygen atoms

stick together very strongly. (Why do not three or even four stick together? That

is one of the very peculiar characteristics of such atomic processes. Atoms are

very special: they like certain particular partners, certain particular directions, and

so on. It is the job of physics to analyze why each one wants what it wants. At

any rate, two oxygen atoms form, saturated and happy, a molecule.)

The carbon atoms are supposed to be in a solid crystal (which could be graphite

or diamond*). Now, for example, one of the oxygen molecules can come over to

the carbon, and each atom can pick up a carbon atom and go flying off in a new

combination—"carbon-oxygen"—which is a molecule of the gas called carbon

monoxide. It is given the chemical name CO. It is very simple: the letters "CO"

are practically a picture of that molecule. But carbon attracts oxygen much more

than oxygen attracts oxygen or carbon attracts carbon. Therefore in this process

the oxygen may arrive with only a little energy, but the oxygen and carbon will

snap together with a tremendous vengeance and commotion, and everything near

them will pick up the energy. A large amount of motion energy, kinetic energy,

is thus generated. This of course is burning; we are getting heat from the combination

of oxygen and carbon. The heat is ordinarily in the form of the molecular

motion of the hot gas, but in certain circumstances it can be so enormous that it

generates light. That is how one gets flames.

In addition, the carbon monoxide is not quite satisfied. It is possible for it

to attach another oxygen, so that we might have a much more complicated reaction

in which the oxygen is combining with the carbon, while at the same time there

happens to be a collision with a carbon monoxide molecule. One oxygen atom

could attach itself to the CO and ultimately form a molecule, composed of one

carbon and two oxygens, which is designated CO 2 and called carbon dioxide.

If we burn the carbon with very little oxygen in a very rapid reaction (for example,

in an automobile engine, where the explosion is so fast that there is not time for

it to make carbon dioxide) a considerable amount of carbon monoxide is formed.

In many such rearrangements, a very large amount of energy is released, forming

explosions, flames, etc., depending on the reactions. Chemists have studied these

arrangements of the atoms, and found that every substance is some type of arrangement

of atoms.

To illustrate this idea, let us consider another example. If we go into a field

of small violets, we know what "that smell" is. It is some kind of molecule, or

arrangement of atoms, that has worked its way into our noses. First of all, how

did it work its way in? That is rather easy. If the smell is some kind of molecule

in the air, jiggling around and being knocked every which way, it might have

accidentally worked its way into the nose. Certainly it has no particular desire to

get into our nose. It is merely one helpless part of a jostling crowd of molecules,

and in its aimless wanderings this particular chunk of matter happens to find

itself in the nose.

Now chemists can take special molecules like the odor of violets, and analyze

them and tell us the exact arrangement of the atoms in space. We know that the

carbon dioxide molecule is straight and symmetrical: O—C—O. (That can be determined

easily, too, by physical methods.) However, even for the vastly more complicated

arrangements of atoms that there are in chemistry, one can, by a long,

remarkable process of detective work, find the arrangements of the atoms. Figure

1-9 is a picture of the air in the neighborhood of a violet; again we find nitrogen

and oxygen in the air, and water vapor. (Why is there water vapor? Because the

violet is wet. All plants transpire.) However, we also see a "monster" composed

of carbon atoms, hydrogen atoms, and oxygen atoms, which have picked a certain

particular pattern in which to be arranged. It is a much more complicated arrange-

ment than that of carbon dioxide; in fact, it is an enormously complicated arrangement.

Unfortunately, we cannot picture all that is really known about it chemically,

because the precise arrangement of all the atoms is actually known in three

dimensions, while our picture is in only two dimensions. The six carbons which

form a ring do not form a flat ring, but a kind of "puckered" ring. All of the

angles and distances are known. So a chemical formula is merely a picture of such

a molecule. When the chemist writes such a thing on the blackboard, he is trying

to "draw," roughly speaking, in two dimensions. For example, we see a "ring"

of six carbons, and a "chain" of carbons hanging on the end, with an oxygen

second from the end, three hydrogens tied to that carbon, two carbons and three

hydrogens sticking up here, etc.

 

How does the chemist find what the arrangement is? He mixes bottles full

of stuff together, and if it turns red, it tells him that it consists of one hydrogen and

two carbons tied on here; if it turns blue, on the other hand, that is not the way

it is at all. This is one of the most fantastic pieces of detective work that has ever

been done—organic chemistry. To discover the arrangement of the atoms in these

enormously complicated arrays the chemist looks at what happens when he mixes

two different substances together. The physicist could never quite believe that the

chemist knew what he was talking about when he described the arrangement of

the atoms. For about twenty years it has been possible, in some cases, to look at

such molecules (not quite as complicated as this one, but some which contain

parts of it) by a physical method, and it has been possible to locate every atom,

not by looking at colors, but by measuring where they are. And lo and behold!,

the chemists are almost always correct.

It turns out, in fact, that in the odor of violets there are three slightly different

molecules, which differ only in the arrangement of the hydrogen atoms.

One problem of chemistry is to name a substance, so that we will know what

it is. Find a name for this shape! Not only must the name tell the shape, but it

must also tell that here is an oxygen atom, there a hydrogen—exactly what and

where each atom is. So we can appreciate that the chemical names must be complex

in order to be complete. You see that the name of this thing in the more complete

form that will tell you the structure of it is 4-(2, 2, 3, 6 tetramethyl-5-

cyclohexanyl)-3-buten-2-one, and that tells you that this is the arrangement. We

can appreciate the difficulties that the chemists have, and also appreciate the reason

for such long names. It is not that they wish to be obscure, but they have an

extremely difficult problem in trying to describe the molecules in words!

How do we know that there are atoms? By one of the tricks mentioned earlier:

we make the hypothesis that there are atoms, and one after the other results come

out the way we predict, as they ought to if things are made of atoms. There is

also somewhat more direct evidence, a good example of which is the following:

The atoms are so small that you cannot see them with a light microscope—in

fact, not even with an electron microscope. (With a light microscope you can only

see things which are much bigger.) Now if the atoms are always in motion, say in

water, and we put a big ball of something in the water, a ball much bigger than the

atoms, the ball will jiggle around—much as in a push ball game, where a great

big ball is pushed around by a lot of people. The people are pushing in various

directions, and the ball moves around the field in an irregular fashion. So, in the

same way, the "large ball" will move because of the inequalities of the collisions

on one side to the other, from one moment to the next. Therefore, if we look at

very tiny particles (colloids) in water through an excellent microscope, we see

a perpetual jiggling of the particles, which is the result of the bombardment of the

atoms. This is called the Brownian motion.

We can see further evidence for atoms in the structure of crystals. In many

cases the structures deduced by x-ray analysis agree in their spatial "shapes" with

the forms actually exhibited by crystals as they occur in nature. The angles between

the various "faces" of a crystal agree, within seconds of arc, with angles

deduced on the assumption that a crystal is made of many "layers" of atoms.

Everything is made of atoms. That is the key hypothesis. The most important

hypothesis in all of biology, for example, is that everything that animals do, atoms

do. In other words, there is nothing that living things do that cannot be understood

from the point of view that they are made of atoms acting according to the laws

of physics. This was not known from the beginning: it took some experimenting

and theorizing to suggest this hypothesis, but now it is accepted, and it is the most

useful theory for producing new ideas in the field of biology.

If a piece of steel or a piece of salt, consisting of atoms one next to the other,

can have such interesting properties; if water—which is nothing but these little

blobs, mile upon mile of the same thing over the earth—can form waves and foam,

and make rushing noises and strange patterns as it runs over cement; if all of

this, all the life of a stream of water, can be nothing but a pile of atoms, how much

more is possible? If instead of arranging the atoms in some definite pattern,

again and again repeated, on and on, or even forming little lumps of complexity

like the odor of violets, we make an arrangement which is always different from

place to place, with different kinds of atoms arranged in many ways, continually

changing, not repeating, how much more marvelously is it possible that this thing

might behave? Is it possible that that "thing" walking back and forth in front of

you, talking to you, is a great glob of these atoms in a very complex arrangement,

such that the sheer complexity of it staggers the imagination as to what it can do?

When we say we are a pile of atoms, we do not mean we are merely a pile of atoms,

because a pile of atoms which is not repeated from one to the other might well

have the possibilities which you see before you in the mirror.

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