The A B C of Atoms

constant is equal to ε divided by h and the velocity of light. (We have to divide by the velocity of light, because in this chapter we have been speaking of frequencies, while in Chapter IV we were speaking of wave-numbers.) Now ε is easily calculated since we know the charge on a hydrogen nucleus and on an electron, the mass of an electron, and the radius of the minimum orbit; also h and the velocity of light are known. It is found that the calculated value of Rydberg’s constant, from these data, agrees closely with the observed value; this was, from the first, a powerful argument in favour of Bohr’s theory. For different kinds of light, the frequency υ is different; in the visible parts of the spectrum, it determines the colour, being smallest for red and greatest for violet. By measuring the frequencies of the different lines in the hydrogen spectrum, and multiplying each by h, we find out how much energy the above loses in the different transitions from orbit to orbit that are possible. The terms in the spectrum are proportional to the energies in the different possible orbits, and the frequencies of the lines are proportional to the loss of energy in passing from one orbit to another. We can calculate what the different possible orbits should be from the fact that their energies must differ by an amount υ h, where υ is the frequency of some line in the hydrogen spectrum. We can also calculate the possible orbits from the fact that the mass of the electron multiplied by the circumference of an orbit multiplied by the velocity in that orbit must be an exact multiple of h. These two methods lead to the same result, and thus confirm our theory. There are, however, certain minutiæ of the hydrogen spectrum which cannot be explained by Bohr’s theory in its original form. All these, down to the smallest particular, are explained by the generalized form of the theory which is due in the main to Sommerfeld. We shall explain this generalized theory in the next chapter. The quantity h, Planck’s quantum, has been found to be involved in all the very minute phenomena that can be adequately studied. It is one of the fundamental constants to which science is led: for the present, it represents a limit of explanations, since no one knows why there is such a constant or why it is just the size it is. The limits of our explanations in any given stage of science are, while that stage lasts, brute facts; and so Planck’s quantum, for the present, is a brute fact. It is involved in all very small periodic processes; but why this should be the case we do not know. [3] Expressed in the usual C.G.S. units, h = 6.55 · 10²⁷. Its dimensions are those of action or angular momentum. [4] For the mathematical statement of the principle, see Sommerfeld’s Atomic Structure and Spectral Lines, 3rd ed., translated by Henry L. Brose M. A. (Dutton, New York) Chap. IV. and Appendix 7. [5] See Appendix.