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 [Pg 105] 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 [Pg 106] 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, in the second, in the third, and so on. The important thing to know about an orbit is what are its quantum numbers, i.e. what multiples of are involved. This is just as true in regard to X-ray spectra as in regard to optical spectra.