Astronomy

Having accepted atomism, it is necessary to account for the differences between solid, liquid, and gaseous states. Matter in any of these states consists of molecules. Ice, water, and steam represent three states of the same compound of hydrogen and oxygen. Mercury, an element not a compound, can be solid, liquid, or gaseous. Usually a solid passes through a liquid state before becoming gaseous: however, it is possible, at certain temperatures and pressures, for solids to pass directly to the gaseous state or from gas to solid.

It has been seen that the result of heating a body (increase in temperature) is to increase the energy of motion (kinetic energy) of the molecules of which it consists. In the solid state the molecules are thought to be bound together by certain forces so that we have a condition of stability and, to a degree, orderly and permanent arrangement. For the present we need not be concerned with the details of shape and arrangement of the molecules. Perhaps it is sufficient to imagine a box full of egg-shaped rubber balls bound together by thin rubber bands. If the balls are hollow and contain a mechanism which will make them vibrate, we will have a vibrating mass, the individuals of which are limited in their movements. If the effect of the internal mechanisms could be controlled so that the agitation could be varied, we would be able to demonstrate in a crude manner the ” solid” at various temperatures.

When the temperature was increased to the proper value, the elastic bands would break and the individuals would be freed. They would then begin to bounce and collide haphazardly and would try to escape from the room. This would be a crude picture of a gas.

A crystal could be pictured the same as any other solid, but the molecules would be arranged in a more orderly manner.

If a room contains many elastic balls bouncing here and there, we have a picture of a gas. Suppose that a layer or two settles to the floor, but still is in an agitated state. This may be considered a crude model of a liquid above which is its vapor.

By rubbing two solids together their temperature is increased by an amount equal to the work done in overcoming friction. It may be considered that the molecules in the surface layers have been excited into more violent movement resulting in greater average kinetic energy, hence, in higher temperature.

Absolute zero is that lowest possible temperature at which the molecules of matter cease to vibrate. This logically follows from the kinetic theory of heat and of matter. Absolute zero is at about 4590 F. below the ordinary Fahrenheit zero or 4910 F. below the freezing point of water. On the Centigrade scale it is about 2730 C. below the Centigrade zero which is at the freezing point of water.

It is well known that a liquid is cooled by evaporation. If we consider that a liquid consists of molecules moving haphazardly (within certain limits) due to collisions with each other, some of these molecules will have sufficient speed to escape the attractions of their neighbors. These, then, find themselves in the space above the liquid and are now a part of the vapor above the liquid. Inasmuch as the only molecules which escape are those having a great enough velocity in a direction away from the surface of the liquid, it is obvious that the liquid is losing only those molecules which at the time of escape have much more than average kinetic energy. Such losses result in a lower average velocity of the molecules left in the liquid and therefore the temperature of the liquid decreases.

Inasmuch as the molecules of matter do not cease to vibrate or to move about until absolute zero is reached, it is obvious that there is much kinetic energy in bodies at ordinary temperatures. A piece of ice is cold to us, but it is relatively hot compared with liquid air and even more so compared with absolute zero. Here we must eliminate our sense of temperature and look at Nature without this prejudice. There is enough total kinetic molecular energy in a piece of ice the size of a baseball to raise a ton weight more than 30 feet vertically. If we could find a means of extracting the total kinetic energy of the molecules of a piece of ice of this size each second, we would have the equivalent of a motor of about two horse-power. It should be noted that the foregoing involves only molecular energy and not so-called chemical and atomic energy.

Other Applications of Atomism

The great success of the atomistic principle as it is involved in the kinetic theory of matter is one of the wonders of the modern scientific age. It is to be expected that it has found other applications equally fascinating and promising. It is now being pressed further into the service of explaining the structure of matter. Molecules are not only divided into atoms, but the latter are now known to consist of still smaller particles. The reality of the electron is thoroughly established. It takes 1800 electrons to equal in mass that of an atom of hydrogen which has the smallest mass among the atoms of elements.

When Maxwell (1873) propounded the electromagnetic theory of light (radiation), his achievement was epochal. The exact manner in which the radiant energy traversed space was not known, and the next epochal event was the founding by Planck (1900) of the quantum theory. Here we have the atomistic principle applied to energy instead of being confined to the material of the universe as it had been. In other words, in the quantum theory we have the atomistic idea applied to physical processes. We now have the atom of matter, the atom (electron) of electricity, and the atom (quantum) of action (a product of energy and time). Planck assumed the emission of radiation (from the sun, a lamp filament, etc.) to occur discontinuously. He conceived elements of energy of equal magnitude analogous to the equality of electrons, or atoms of a given element. Radiation or radiant energy is emitted of various wavelengths or frequencies which must be taken into account in laws of radiation. By inventing the quantum of action Planck was able to derive a law of radiation which explained the experimental data hitherto not understood. The elementary quantum of action is equal to the elementary quantum of energy multiplied by the frequency of the radiation. Thus again, we find science in a state which required a creative mathematical physicist to iron out inconsistencies, to put the finishing touches on existing theories, and to explain much of the accumulated data.

Now the physicist uses quanta as commonly as he does electrons and atoms and molecules. Bodies are built of molecules, the molecules of atoms, and the atoms of electrons (and protons) . Here we see the atomistic principle applied to ” material” (matter) and then to electricity (What shall we call it?). Finally, a physical process - the radiation emitted by the electrons - is divided into quanta. With such pictures of the universe being constructed we may cease to be surprised at anything, but our interest and admiration will grow. Will we ever get to the final foundation? Will mind be finally explained by the physicist?

These are mere glimpses of the electron theory and the quantum theory introduced to complete this portion of the picture for the present. They are so important, so modern, and 50 far-reaching that they are treated later in more detail.

It is interesting to view the particles of gas more intimately.

The velocity of a molecule of gas depends upon its mass. At the temperature of melting ice, hydrogen molecules have an average velocity of about one mile per second. Oxygen molecules being about sixteen times heavier travel about one fourth as fast as hydrogen molecules. These velocities are of the order of magnitude of projectiles fired from guns. It is fascinating to think of the nitrogen and oxygen molecules of the air about us moving between collisions with the velocities of bullets. They are striking our faces with these velocities and it is obvious that we should be thankful for their very small mechanical energy. We cannot conceive the smallness of the mass of a hydrogen molecule. Its mass is related to that of a baseball about as the mass of the baseball is to that of the Earth. There are about 102.5 molecules of hydrogen per ounce of the gas, or 10 million billion billion molecules or 10 trillion trillion molecules per ounce. The reader may take his choice of these numbers, but it is likely that the baseball comparison of relative mass gives a better idea of the size than the foregoing numbers. The diameter of the hydrogen molecule is less than ten billionths of an inch (8.5 X 10-9 inch). Particles must be a thousand times larger to be visible under the most powerful microscope.

Perhaps some idea of the number of molecules in an ounce of hydrogen gas might be obtained if we set out to count them.

There are about two billion persons on Earth. Suppose each was able to count 100 molecules per minute continuously. It would take the entire population of the Earth one hundred million years to count the molecules in an ounce of hydrogen gas. The mass of the Earth is again inconceivably greater than the mass of hydrogen weighing an ounce at the Earth’s surface, so it is seen that the number of molecules in the Earth alone is quite beyond comprehension. Similarly the greatest known distances in the stellar universe are inconceivably large. The human being is puny indeed and his mind can never comprehend the picture in its entirety. Nevertheless, we may enjoy knowing that there will always be awesome magnitudes to contemplate when we desire to exercise our imagination. There would be a maximum of about 7 billion molecules in a single row of them five feet long and it would take a person a lifetime to count the number in this short row of molecules in “single file.”

The Statistical Method

In dealing with molecules and other minute particles of matter which are shooting about as in the case of a gas confined in a vessel, we cannot arrive at any definite conclusion without studying averages. A single molecule, if we take averages, collides billions of times per second. If we direct our mind’s eye upon anyone molecule of a gas, we will find that its path is hap-hazard, unpredictable, and quite accidental. The same is true of the course of life of any human being. However, the insurance companies by observing a large number of persons can make sufficiently accurate predictions upon which to base a sound business. Anyone of us may die the next moment, or fall out of a window tomorrow, or collide with a street-car the next day. When an individual will marry, how many children he will have, or how much money he will acquire, only the future can tell us. No one can predict what will happen in a particular case, but from adequate records of a sufficient number of cases a safe prediction can be made based upon the” law of averages.” Many applications daily are now made of the results of statistics and science has successfully utilized the statistical method in various ways.

Maxwell (1841-1879) was the next great mathematical physicist after Newton to greatly change the course of scientific thought. Although he has greater scientific achievements to his credit, he placed the kinetic theory of gases on a firm foundation from which it has not been shaken, by developing the statistical method. He applied natural laws to the individual molecules, but without attempting to follow an individual he gave his attention to totality. It has been seen that the number of molecules in even a small quantity of matter is very great; therefore, we can have faith in the law of averages.

It is certain that the movements of molecules of a gas depend upon less complicated factors than the lives and activities of human beings. All molecules of the same element or gas have equal masses, with slight exceptions of no consequence at this time. The kinetic energy of anyone is determined by its mass and velocity. The mean velocity of the molecule, based upon the study of the combined effect of the billions of molecules, is a very definite and constant value for any given set of conditions. In fact, about all we must convince ourselves of in order to have faith in the statistical method as applied to gases, is that the rate of collision of molecules is constant for a given pressure, volume, temperature and gas.

Perhaps it will aid the reader to have faith if we revert momentarily to the number of molecules. A minute sphere two thousandths of an inch in diameter is about as small an object as we can see with the unaided eye at a distance of one foot. If this sphere were filled with gas at atmospheric pressure and of ordinary temperature, it would contain about 2000 billion molecules. Expressed in another way this number is equivalent to two million-million. Counting at the rate of 100 per minute for the usual working hours throughout a year, it takes a person a lifetime to count a billion. At this rate it would take 2000 persons their entire lifetime to count the molecules in that minute sphere two thousandths of an inch in diameter. Insurance can be safely based on the statistics of a number of persons, relatively few compared with the number of molecules in a sphere invisible to the unaided eye. Considering this fact along with the more complex vagaries of human beings as compared with those of molecules, it is seen that we can have utmost faith in the constancy of the results of the statisical method as applied to molecules of matter. Maxwell established these facts beyond question.

Brownian Movements

If we suspend in air an object easily visible to the unaided eye, it will be subjected to collisions from all directions, of molecules of the gases in the atmosphere. But we do not see it move here and there because it is being bumped from all directions. The number of molecules colliding with it per second is inconceivably large. Even in the smallest part of a second necessary for our consciousness to note a movement of this small suspended object, it would receive billions of impacts. The force upon it would be equal in all directions owing to the application of the law of averages so that even if it had no mass, it would not be moved appreciably.However, if we reduce the size of this suspended object, we should be able to arrive at a point where there is not a sufficient number of collisions from all directions for the effect to be equalized on all sides. In other words, the particle would be subjected to different forces from various sides and we would expect it to be bumped here and there in a haphazard fashion. Brown (1773-1858), a botanist, while examining under a microscope some liquids containing particles of pollen about one thousandth of an inch in diameter, noticed that these particles moved irregularly. He also noticed that the movements were more conspicuous for the smaller particles. Brown did not explain this, but, scientist that he was, he recorded his keen observations.With the establishment of any new principles and generalizations which are shown to be sound, many of the observed facts of past records are explained. Brown’s observations were to await the kinetic theory of matter before true light could be shed upon them. Hence, about fifty years later the Brownian movements were shown to be due to the impacts of molecules of the liquid in which the pollen particles were suspended. The same kind of movements have since been demonstrated in gases. It has been shown that fine particles of matter, such as gamboge suspended in water, obey the same laws that have been applied successfully to molecules. Some of this work has provided experimental foundation for the theory that the average energy of motion of the particles or molecules of a mass of matter depends only upon the temperature of the matter and not upon the mass of the particles. It was also shown that these particles, although very much larger than molecules, had an average energy of rotation equal to their average energy of translation. This also added support to the prevalent theory.

It is seen that the study of Brownian movements contributed much toward the establishment of the kinetic theory of matter.

The atomistic principle rendered a very great service in the development of a picture of gases which could account for such properties as pressure. Newton’s mechanics, which contributed so much toward our knowledge of the stellar universe, finds a beautiful application to the molecules of a gas. Although the conception of the idea of the kinetic theory of gases can be traced further back, Clausius ( 1857) really founded it after Joule (185 I) had attempted to calculate the velocity of a hydrogen molecule. The calculations were inexact, but they mark the beginning of an actual atomic view of matter as distinguished from the mere symbolic view of the chemist up to that time.

The molecules of a solid are considered to be bound to certain positions which result in equilibrium, but this is not the case in gases. The molecules of a gas are continually in motion, excepting at absolute zero, about 491 degrees Fahrenheit below the melting-point of ice. At first they were likened to elastic spheres shooting in all directions and colliding with each other. At ordinary temperatures and pressures a gas-molecule will suffer several billion collisions each second. Although the modern ideas of the atom are not fully developed in relation to the kinetic theory of gases, it is likely that the molecules do not actually collide in the ordinary sense. The modern conception is that atoms are tiny planetary systems of electrons revolving around a positive nucleus. Doubtless they are surrounded by electric forces so that instead of a collision we have a repulsion of the electric forces. At any rate the true picture is of little consequence here because it will not alter the actual facts.

The pressure on the sides of a vessel containing a gas is due to the billions of collisions of the molecules with the sides. The force of an impact is determined by the mass and the velocity. The pressure is the result of the number of impacts per second. If the density of the gas is doubled there will be twice as many impacts in a second on a given area of the vessel and, therefore, the pressure will be doubled. This relation of density and number of molecules was suggested by Boyle (1627-1691) which gave rise to Boyle’s law. This law states that, for a given temperature, the product of the pressure and the volume is constant.

The temperature of a gas is determined by the mean energy of motion of a molecule. Here again Newton’s mechanics enter, for the energy of motion of a molecule is proportional to its mass and to the square of its velocity. As the temperature decreases, the energy of motion (kinetic energy) of a molecule decreases until at absolute zero there is no motion. Hence, at absolute zero the pressure of any gas is zero. It may be of interest to know that absolute zero has not quite been reached in the laboratory, but it has been approached to within less than a degree Centigrade.

The atomistic idea has not been limited to the structure of matter by any means. It is associated with several properties or characteristics of matter such as heat, gas-pressure, and light or radiant energy. The early idea of heat was that it was a fluid. Count Rumford (1753-1814) a little more than a century ago was one of the first to relegate this idea to the discard by experiments which suggested that heat was a mode of molecular motion. It is true that Roger Bacon (12141294) suggested heat was a matter of agitated particles such as molecules, but as in other phases of science, experimental data were lacking. Mayer and Joule (1842) discovered that mechanical work was converted into heat and that the amount of heat was always exactly proportional to the amount of work and vice versa.

It had long been recognized as a direct consequence of Newton’s laws of motion, that energy could not be destroyed. This is the well established law of conservation of energy. For example, if a moving body collided with another body, the resultant mechanical energy remained equal to the total before the collision. The total mechanical energy required to produce a certain amount of heat (agitation of the molecules of the body in which the heat was generated) would remain unaltered. The molecules of the body now possessed so much more mechanical energy; in other words, they were sufficiently more agitated so that their excess mechanical energy was just equal to the mechanical energy required to produce the amount of heat that the body received.

Thus we see not only the atomistic idea of matter used to account for a change in temperature (due to the production of a certain quantity of heat), but also Newton’s laws of motion applied to the molecules of the body. It is a beautiful picture of unification. For example, suppose a large iron ball is dropped from a height and it strikes a thick iron plate of great mass. The mechanical energy of the falling ball at the moment before striking the plate is proportional to its mass and the square of its velocity. Actually the ball will bounce a few times, but let us assume it always hits in the same place and comes to rest there. The energy of the ball is now distributed among myriads of molecules of iron both in the plate and in the ball. Owing to the minuteness of the agitated molecules we cannot see their increased movements, but we can feel the result of the increase. The two bodies are of a higher temperature at first only near the points of contact, but the heating effect rapidly spreads and equalizes. This is what we term conduction of heat and is really a communication of the increased agitation to other molecules. It should be noted that the molecules of a body are always in a state of agitation (excepting at absolute zero), the degree of agitation being indicated by the temperature.

Perhaps to a primitive mind the earth consists of stones, grains of sand, dust particles, drops of water, and similar things. In other words, it is made up of parts. One cannot contemplate Nature for long without noting that disintegration and transformation are continually going on. Ice melts to water; the water vaporizes; the vapor condenses again to water; it freezes to ice. Clouds dissipate themselves in rain or snow. Rock disintegrates into sand; the sand into dust; the dust is carried away by wind and water. Thus, visible things become invisible and the invisible may become visible.

It is not surprising that Anaxagoras (500-428 B.C.) propounded the principle that the material of Nature was compounded of and could be resolved into elementary seeds of matter. This idea found advocates throughout the ages, although it was little more than a speculation in early centuries. Leucippus believed that the universe consisted of limitless empty space and of matter, the latter consisting of numberless, indivisible atoms. He also thought that atoms were always in motion. As usual, there were many fantastic ideas interwoven in these speculations.

Democritus (460-370 BC), a pupil of Leucippus, developed the theories of his teacher to such an extent that generally his name is the only one associated with these early speculations of empty space and atoms as elements of the cosmos. He also developed the idea that all the material of the universe was produced by the motions of these atoms. He was an extreme sceptic as indicated by the remark attributed to him, “We know nothing; not even if there is anything to know.”

Although many of his speculations can be very easily modified to fit the facts of the physical world as we know it today, he contributed little of real note to science excepting an example of the value of a critical attitude. Nevertheless, the idea of atomism had to have a beginning and it matters not if it began in metaphysics and alchemy. It has eventually arrived a definite reality. It aided in the development of chemistry which in turn developed atomism. Spectroscopy did much to place the atomic theory of matter on a firm foundation. Finally radio-activity, that marvelous exhibition of the birth of one element from another, has made us even better acquainted with the atom.

In the development of the atomic theory of matter, the foundational laws of the great stellar world were applied to the tiny worlds far beyond the revealing power of the microscope. The great laws which were developed to explain the motions of the Moon, planets, and other celestial bodies and were so clarified by Newton, soon began to serve to explain the structure and properties of matter and eventually of atoms themselves. Motions and masses were attributed to minute molecules, atoms, and electrons with the result that the energy of motion of these small particles became a very important factor in explaining various physical phenomena. Hence, the introduction of the term, kinetic energy. As will be shown later, modern developments impose limitations upon the applications of Newtonian mechanics, but for the present we need not consider them in detail.

If we contemplate for a few moments the portion of the physical world before us we conclude that it is made up of matter and space. As the moments pass by, one event following another leads us to the conception of another factor time. It is obvious that motion involves space and time; that is, the displacement from one portion in space to another requires a certain amount of time and the whole process is termed motion. For a period in scientific development it was thought that all physical phenomena might be explained eventually in terms of matter, space and time. That is, there was hope for a single law which would explain all the physical things, events, and relationships in terms of movements of matter. But as scientific data accumulated, such a simplification became hopeless. In other words, a purely materialistic view could not account for the force of gravitation, for example.

Let us give some consideration to the apparently uninteresting fundamental which we term matter. At least it is important and is certainly the very foundation of the universe. Without it we would have only space and time which are not material. In fact, we would not have them for we would not exist. The physical universe as we know it would reduce to nothingness.

All matter has weight, that is, a certain degree of heaviness.

In our infancy we become familiar with weight so that by the time we reach an age of reason we accept this as a fundamental of all things. Owing to the commonplaceness of the phenomenon of weight, only an unsually observing and thoughtful person would even suspect that there might be a reason for it. Certainly in the centuries when there were relatively few accurate and correlated data of the physical world, we could not expect mankind to see much in common among a number of phenomena such as the weight of the body, the tides, a swinging pendulum, running water, the falling of an apple, the rotundity of the earth, the motion of the moon, the movements of planets and comets. But all these and many more movements of matter are bound together by law and a common property.

The Earth’s Attraction

As we see a “strong man” lifting a heavy weight we do not visualize a pulling contest between him and the Earth. Nevertheless, that is just what takes place. As we climb a mountain we are in a competition with the Earth. Our muscles ache under the strain of overcoming the Earth’s pull upon us. We dislodge rocks and they go rolling downward. We see nothing remarkable in that because they always roll downward. We would be surprised, indeed, it would be marvelous, if they rolled upward. But, after all, it is just as wonderful that they roll downward as upward. The difference is that in the one case it is natural; in the other it is unnatural. This exemplifies the confidence we have in the orderliness of Nature. In fact, the very basis of scientific inquiry and argument is the assumption that there is a reason for any given event of the physical world and that it is always the same for the same fundamental event. In other words, the assumption is that Nature is orderly and is always so; that is, that there are no exceptions, no miracles. We cannot prove that yonder object is heavy until we lift it. We cannot prove that the Sun will rise tomorrow, but we are confident enough for all practical purposes because of our faith in the orderliness of Nature.

Perhaps the foregoing has served the purpose of emphasizing how we take for granted what in our experience has always been. Are most persons today any less indifferent toward what is natural or commonplace than those of any earlier time even in the primitive eras of little knowledge of the physical world? Of course, many persons now have had the advantage of some study of physics at least. But if we will visualize earlier centuries when science had not progressed far or even with much certainty, we can, perhaps, appreciate more fully the men who first began to inquire why things sought a lower level.