Since the nature of the universe depends on the size of Planck's constant, we are all dependent on the size of the piece of action it represents. Planck, in other words, had sought and found the piece of the action. (I understand that others have been searching for a piece of the action ever since, but where's the point since Planck has found it?)
And what is the exact size of h? Planck found it had to be very small indeed. The best value, currently ac cepted, is: 0.0000000000000000000000000066256 erg seconds,or 6.6256 x 10-2" erg-seconds.
Now let's see if I can find a way of expressing just how small this is. The human body, on an average day, con sumes and expends about 2500 kilocalories in maintaining itself and performing its tasks. One kilocalorie is equal to 1000 calories, so the daily supply is 2,500,000 calories.
One calorie, then, is a small quantity of energy from the human standpoint. It is 1/2,500,000 of your daily store. It is the amount of energy contained in 1/113,000 of an ounce of sugar, and so on.
Now imagine you are faced with a book weighing one pound and wish to lift it from the floor to the top of a bookcase three feet from the ground. The energy expended in lifting one pound through a distance of three feet against gravity is just about 1 calorie,.
Suppose that Planck's constant were of the order of a calorie-second in size. The universe would be a very strange place indeed. If you tried to lift the book, you would have to wait until enough energy had been accumu lated to make up the tremendously sized quanta made necessary by so large a piece of action. Then, once it was accumulated, the book would suddenly be three feet in the air.
But a calorie-second is equal to 41,850,000 erg-seconds, and since Planck's constant is 'Such a minute fraction of one erg-secoiid, a single calorie-second equals 6,385,400, 000,000,000,000,000,000,000,000,000 Planck's constants, or 6.3854 x 10:1@' Planck's constants, or about six and a third decillion Planck's constants. However you slice it, a calorie-second is equal to a tremendous number of Planck's constants.
Consequently, in any action such as the lifting of a one pound book, matters are carried through in so many tril lions of trillions of steps, each one so tiny, that motion seems a continuous glide.
When Planck first introduced his "quantum theory 91 in 1900, it caused remarkably little stir, for the quanta seemed to be pulled out of midair. Even Planck himself was dubious-not over his equation describing the dis tribution of black-body radiation, to be sure, for that worked well; but about the quanta he had introduced to explain the equation.
Then came 1905, and in that year a 26-year-old theo retical physicist, Albert Einstein, published fivo separate scientific papers on three subjects, any one of which would have been enough to establish him as a first-magnitude star in the scientific heavens.
In two, he worked out the theoretical basis for "Brown ian motion" and, incidentally, produced the machinery by which the actual size of atoms could be established for the first time. It was one of these papers that earned him his Ph.D.
In the third paper, he dealt with the "photoelectric effect" and showed that although Classical Physics could not explain it, Planck's quantum theory could.
This really startled physicists. Planck had invented quanta merely to account for black-body radiation, and here it turned out to explain the photoelectric effect, too, something entirely different. For quanta to strike in two different places like this, it seemed suddenly very reason able to suppose that they (or something very like them) actually existed.
(Einstein's fourth and fifth papers set up a new view of the universe which we call "The Special Theory of Rela tivity." It is in these papers that he introduced his famous equation e = MC2; see Chapter 13.
These papers on relativity, expanded into a "General Theory" in 1915, are the achievements for which Einstein is known to people outside the world of physics. Just the same, in 1921, when he was awarded the Nobel Prize for Physics, it was for his work on the photoelectric effect and not for his theory of relativity.)
The value of h is so incredibly small that in the ordinary world we can ignore it. The ordinary gross events of everyday life can be considered as though energy were a continuum. This is a good "first approximation."
However, as we deal with smaller and smaller energy changes, the quantum steps by which those changes'must take place become larger and larger in comparison. Thus, a flight of stairs consisting of treads 1 millimeter high and 3 millimeters deep would seem merely a slightly roughened ramp to a six-foot man. To a man the size of an ant, how ever, the steps would seem respectable individual obstacles to be clambered over with difficulty. And to a man the size of a bacterium, they would be mountainous precipices lin the same way, by the time we descend into the world within the atom the quantum step has become a gigantic thing. Atomic physics cannot, therefore, be described in Classical terms, not even as an approximation.
The first to realize this clearly was the Danish physicist Niels Bohr. In 1913 Bohr pointed out that if an electron absorbed energy, it had to absorb it a whole quantum at a time and that to an electron a quantum was a large piece of en 'ergy that forced it to change its relationship to the rest of the atom drastically and all at once.
Bohr pictured the electron as circling the atomic nucleus in a fixed orbit. When it absorbed a quantum of energy, it suddenly found itself in an orbit farther from the nucleus - there was no in-between, it was a one-step proposition.
Since only certain orbits were possible, according to Bohr's treatment of the subject, only quanta of certain size could be absorbed by the atom-only quanta large enoug to raise an electron from one permissible orbit to another.
When the electrons dropped back down the line of per missible orbits, they emitted radiations in quanta. They emitted just those frequencies which went along with the size of quanta they could emit in going from one orbit to another.
In this way, the science of spectroscopy was rational ized. Men understood a little more deeply why each ele ment (consisting of one type of atom with one type of energy relationships among the electrons making up that type of atom) should radiate certain frequencies, and cer tain frequencies only, when incandescent. They also under stood why a substance that could,absorb certain frequen cies should also emit those same frequencies under other circumstances.
In other words, Yirchhoff had started the whole problem and now it had come around fuil-circle to place his em pirical discoveries on a rational basis.
Bohr's initial picture was oversimple; but he and other men gradually made it more complicated, and capable of explaining finer and finer points of observation. Finally, in 1926, the Austrian physicist Erwin Schri3dinger worked out a mathematical treatment that was adequate to an alyze the workings of the particles making up the interior of the atom according to the principles of the quantum theory. This was called "quantum mechanics," as opposed to the "classical mechanics" based on Newton's three laws of motion and it is quantum mechanics that is the founda- tion of Modern Physics.
15. Welcome, Stranger!
There are fashions in science as in everything else. Con duct an experiment that brings about an unusual success and before you can say, "There are a dozen imitations!" there are a dozen imitations!
Consider the element xenon (pronounced zee'non), dis covered in 1898 by William Ramsay and Morris William Travers. Like other elements of the same type it was iso lated from liquid air. The existence of these elements in air had remained unsuspected through over a century of ardent chemical analysis of the air, so when they finally dawned upon the chemical consciousness they were greeted as strange and unexpected newcomers. Indeed, the name, xenon, is the neutral form of the Greek word for "strange," so that xenon is "the strange one" in all literalness.