47rMC The quantum theory was first applied to the phenomenon by Debye and by Sommerfeld in 1916. Their methods were equi valent to fixing the stationary states in the way already described (equations [41] ) ; using the extended integrals, and then apply ing Bohr's postulate. This leads, with the help of the corres pondence principle, to the result given by the classical theory and only succeeds in explaining what is known as the normal Zeeman effect. In fact the last term in equation (46) becomes and the correspondence principle indicates, just as in the Stark effect, that must be +1, --I, or o. The anomalous phenom enon (observed when the magnetic field is not too intense) may be concisely described in the following way : the "magnetic" term in (46) has to be put in the form As a matter of fact the newer developments of the quantum theory (see "Wave Mechanics" below), as well as the actual facts of band spectra, show that in some cases the energy of rotation is given by A similiar remark applies to the energy of a simple harmonic vibration which is expressed by (n-I-1)hp instead of it liv.
The energy of gas molecules is very largely kinetic energy of rotation, and therefore equation (47b) has played an important part in the theory of the specific heats of gases and their depend ence on the temperature.
An electron orbit, constituting, as it does, an electric current, possesses a magnetic moment, and the existence of stationary states involves the consequence that the magnetic moment of an electron orbit must be an integral multiple of a certain smallest value or unit. It is easy to establish that this unit of mag Elementary considerations show that the mutual energy of a magnet and an external field is equal to M,H, apart from a constant which we may take to be zero, where 31, means the component of the magnetic moment of the magnet in the direc tion of the field and H is the intensity of the field. If now we
turn to equation (46) and remember that where is an integer, we see that the mutual energy of an electron orbit and a magnetic field is Only such transitions are permitted for which +I, o, or — I, and the same rules determine the polarization as in the case of the normal effect.
Miscellaneous.—The principles of the quantum theory have been applied with great success to the study of X-ray emission and absorption spectra and the disentangling of the very com plicated features of band spectra (see BAND SPECTRUM) has been greatly facilitated by, and indeed would hardly have been possi ble without, the indications which the theory has provided. The main features of these spectra can be ascribed to changes in the rotational and vibrational energy of molecules. The kinetic energy of a rotating body is expressed by (47) where p is its angular momentum, and K the corresponding moment of inertia, and since p is restricted to the values n where n is an integer, we must have an integral multiple of a Bohr magneton. We must infer from this that the angle between the axis of the electron orbit and the applied field cannot vary continuously, but is restricted to certain quite definite values. If, for example, the total magnetic moment of the orbit were one Bohr magneton, then its axis must be directed along the external field, or along the opposite direction, or at right angles to the field according to the simple theory we have given. This kind of restriction is sometimes called spatial quantization and has received remarkable con firmation in the experiments of Gerlach and Stern. (See MAGNE TISM.) More direct confirmation of the hypothesis of stationary states is furnished by the extensive investigations of critical potentials of gases and vapours.