The inertia of electrons in metals

1—According to the accepted theory of metals, the crystalline field produces a displacement of the energy levels of the moving electrons in a manner which may be regarded as an increase of their apparent mass. Now there exist direct experiments on the masses of electrons in certain metals, and the present work was undertaken to see whether the results of these experiments would support the modern theory. It will be shown that the mass as measured in these experiments is the ordinary mass of the free electron, and is unaffected by the disturbance of the energy levels. The experiments in question are those of Tolman, working with others some 15 years ago. At that time the gyromagnetic anomaly was not understood, and the aim of their work was to find whether it might not be the solid state rather than the magnetism which was responsible for halving the value ofm /e . It is perhaps because this anomaly was so completely cleared up not long afterwards, that these brilliant experiments never seem to have attracted the attention they most certainly deserved. Working with copper, aluminium, and silver, Tolman showed thatm /e for the electrons appeared to be rather larger than the normal value, and certainly not half of it in the way that was needed to explain the gyromagnetic anomaly. Values ofm /e between 10 and 20% too large were obtained, but there were indications of systematic error which suggested that the normal might well be correct. In similar work Barnett confirmed Tolman’s results with copper and got values even nearer to the normal. At the time of all this work there was, of course, no knowledge of the new theory of metals, so that the results seemed entirely natural. With the new theory it becomes worth while to examine whether these increased values might not be genuine, for, if so, much valuable information about the lattice of metals might be derived from experiments on electron inertia. However, we shall see that such experiments will be expected always to yield the normal value ofm /e .