= 9.65 x 104 coul/g The charge-to-mass ratio of the electron involves two numbers which are independently regarded as fundamental constants of physics. Yet this ratio itself can be said to be a fundamental constant in its own right because first, its determination actually led to the discovery of the electron by J. J. Thomson in 1897, and second, because any equation of motion which involves electrodynamic forces on the electron brings the charge and mass together as this ratio.
It was known in the nineteenth century that it took a certain quantity of electrical charge to deposit out of solution one gram-atomic weight of any univalent ion, i.e., a mass, in grams, equal to the atomic weight of the element. Faraday had determined this fact, and that particular quantity of charge -- 96,488 coulombs -- is called a faraday. It was also known, from kinetic theory, that the number of atoms, No, which correspond to this amount of charge is in order of magnitude about 1023 , so it seemed that the basic charge on each atom was of the order of 10-8 coulombs.
Regardless of what No might be, however, it followed from Faraday's electrolysis experiments that the charge-to-mass ratio of the hydrogen atom is
= 9.65 x 104 coul/g
since one faraday of charge liberated one gram of hydrogen. The ratio for all other substances was, of course, smaller.
Just before 1900, many workers were doing experiments with electrical discharges in low pressure gases, and in particular, with "cathode rays", strange emanations from discharge cathodes, which could be collimated into thin beams by the use of masks having small 'pinholes" in them. These rays usually caused a blue or green phosphorescent glow wherever they en countered the walls of the glass tube in which they were produced; the ray position, or trajectory, was usually detected in this manner.
Several facts were known:
There was a general suspicion that cathode rays consisted of fast negatively charged particles, but this was not proven before J. J. Thomson performed his classic experiments in 1897. His apparatus is shown schematically in Fig. 1.
Figure 1
The cathode and anode at the left established a discharge in the gray region; cathode rays emerged through the small anode hole, were further collimated by a mask, and proceeded as a thin beam to the end of the tube. They passed, along the way, between a pair of plates of length L and separation d.
Now, when a voltage V was established between the plates, the beam was bent downward as shown, for the bottom plate positive. Thomson now added a magnetic field directed perpendicular to both the rays and the applied electric field, or out from the plane of the paper as we have drawn Fig. 1. He then in creased this field until the spot on the tube end returned to its original undeflected position.
The electric deflection S or the beam position as it emerged from the plates could be determined from the shift of the end spot; this distance, together with the plate geometry, potential V, and magnetic field B necessary for cancellation of the deflection then allowed the calculation of e/m, as follows: (We will do this in mks units.)
The transverse electric field or. the particles is Ex = V/d, and this exerts a force Fx = eV/d. However, the magnetic field results in a transverse force also; it is Fx = evzBy , and has been adjusted to exactly cancel the electric contribution. This gives, then,
,
or,
Without B, however, the transverse E field deflects the particles a distance s in a length L. Now,
S = 
where ax is acceleration and t is time. So,
S = 
and when we insert Eq. 2,
.
Thomson obtained a value for e/m which was more than three orders of magnitude larger than that of hydrogen. This could result from either a large e or a very small m, and he correctly surmised that the latter was true. For a long time these particles were called corpuscles, since the name electron had been given previously to the unit of electrical charge. Gradually, however, the usage changed to what we know today.