is Planck’s quantum,
multiplied by
is the energy lost by the atom in the transition which gives rise to the line in question. There are three principal lines in X-ray spectra, called, respectively, the K, L, and M lines. For any given atom, the K line has the greatest frequency and the M line the least. The K line represents a transition by an outer electron to the inmost ring, the L line represents a transition to the second ring, and the M line to the third. Each line, closely examined, is found not to be single, but to consist of several neighbouring lines corresponding to different starting-points for the electron, but all having the same end-point. Since we can observe the frequencies of the different lines, we can infer from the X-ray spectra what are the differences between energies of electrons in different rings. Everything confirms the theory of the structure of atoms which was suggested by the hydrogen spectrum and the facts upon which the periodic table is based.
Another very instructive fact which emerges from the study of X-ray spectra concerns the “fine structure,” of which, as we saw in Chapter VII, the explanation is to be sought in the substitution of Einstein’s principles for Newton’s. In the case of hydrogen, the different lines of the five structures are so near together that accurate measurements of their distance apart are very difficult. But the distance between them, as we pass to later elements, ought to increase roughly as the fourth power of the atomic number, so that measurements become much easier for high atomic numbers. On this point, the empirical evidence obtained from X-ray spectra agrees closely with the theory developed by Sommerfeld. This theory depended, it will be remembered, on the fact that, according to the doctrine of relativity, an electron which moves in an eccentric orbit has to go rather more than once round its orbit before getting back to the point at which it is nearest to the nucleus. The X-ray observations establish this theory much more firmly than is possible by the help of optical spectra alone.
It must be understood that, so far as quantum numbers are concerned, the actual orbits of electrons in atoms that have many rings are the same as the possible orbits of the one electron in the hydrogen atom. The partial dimensions are not the same; the radius of the minimum circle, roughly speaking, varies inversely as the atomic number, so that in uranium it might be expected to be about 92 times smaller than in hydrogen. The velocity of the inside electron in its minimum orbit varies roughly as the atomic number, and the number of revolutions per second roughly as the square of the atomic number. But the radius multiplied by the velocity is independent of the atomic number. To a first approximation, the mass of the electron multiplied by its velocity multiplied by the circumference of its orbit (when it moves in a circle) will always be
in the inmost ring,
