OTHER SPECTRA The Series Constant.—The mathematical difficulties of a complete solution of the motion of electrons in atoms with more than one electron have proved insuperable, but a physical idea of the process of radiation by such atoms can be formed. It is supposed, as a first approximation, that passages from orbit to orbit are performed mainly by a single electron, the others mean while revolving unchanged in their normal orbits. In such a case, if the dimensions of the orbits of the roving electron are large compared with the dimensions of the rest of the atom (the core, as it is called), the latter may be regarded as a single positive charge, E (equal and opposite to the charge, e, of an electron), round which the roving electron moves. The calculation made for hydrogen is then approximately applicable, and gives a formula in which the Rydberg constant, R, recurs. The deviation from exactitude results in the change of m (the denominator in the expression for the hydrogen terms) from an integer to a mixed number. Its new value—(m+ i.) in the Rydberg formula—is known as the effective quantum number.
Ionised Atoms.—The universal occurrence of the constant R is thus explained, and a natural extension of the theory provides a simple explanation of the fact that for the successive spectra of each element, it must be multiplied by etc. For, consider an atom subjected to a gradually increasing stimulus. Its trav elling electron will be able to move out to more and more distant orbits until a point is reached when it absorbs enough energy to leave the atom altogether. The atom is then said to be ionised. The remainder of the atom, being still subjected to the exciting stimulus, will be able to absorb energy only by the removal of a second electron to outer orbits, and the new transitions of this electron will generate a spectrum different from that given by the unionised atom. For in this case the positive charge, E, of the core is 2e—i.e., twice the charge of an electron—and the 2 mM expression for R becomes 4 • ch3 • in+ m —approximately four times the value of R for hydrogen. In a similar way, a still greater stimulus will remove a second electron from the atom, which is then said to be doubly ionised, and the spectrum gen erated by the movements of a third electron will give a spectrum involving a constant approximately 9R, and so on.
It should be observed that the values of the constant for the corresponding spectra of different elements are not exactly the same because of the factor Mm/(M-}-m). Here M is the mass of the core, which is practically equal to the atomic weight of the element, and it is easily seen that the variation of M brings about a slight, but only a slight, variation of Mm/(M-I-m). The effect of this variation, however, is of some importance in the case of atomic systems containing only one electron. Thus, the line of the Balmer series, of hydrogen, for example, would clearly be identical in position with the line of Hell if R were exactly equal to R'. Actually, however, the lines are separated by about 21A. It was on account of this and similar separations, predicted by the Bohr theory, that it was first realized that the lines of Hell were not due to hydrogen.