The electric deviation of the rays from radium C has not yet been accurately measured, but an approximate determination of e/m for the α particles can be obtained by assuming that the heating effect of radium C is a measure of the kinetic energy of the α particles expelled from it. We have seen in section 246 that the heating effect of the radium C present in one gram of radium in radio-active equilibrium is 31 gram calories per hour, which corresponds to an emission of energy of 3·6 × 105 ergs per second. Now when radio-active equilibrium is reached, the number of α particles expelled from radium C per second is equal to the number of α particles expelled per second from radium at its minimum activity. This number, n, is 6·2 × 1010 (section 93).
Then ½ mnv2 = 3·6 × 105,
or (m/e)v2 = 1·03 × 1016,
substituting the value of n, and the value of the ionic charge e. The value of e in this case has not been assumed, since n = i/e, where i was the measured current due to the charge carried by the α rays.
From the magnetic deflection, it is known that
(m/e)v = 3·98 × 105.
From these two equations we obtain
v = 2·6 × 109 cms. per second.
e/m = 6·5 × 103 electromagnetic units.
These values are in surprisingly good agreement with the previous values of the writer and Des Coudres ([section 91]). On account of the uncertainty attaching to the value of n, not much weight can be attached to the determination by this method of the constants of the α particles.