in section 93 that one gram of radium bromide emits about 1·44 × 10^{11} α particles per second. The corresponding number for 1 gram of radium (Ra = 225) is 2·5 × 10^{11}. Now it has been calculated from experimental data in section 94, that the average kinetic energy of the α particles expelled from radium is 5·9 × 10^{-6} ergs. Since all of the α particles are absorbed either in the radium itself or the envelope surrounding it, the total energy of the α particles emitted per second is 1·5 × 10^6 ergs. This corresponds to an emission of energy of about 130 gram calories per hour. Now the observed heating effect of radium is about 100 gram calories per hour. Considering the nature of the calculation, the agreement between the observed and experimental values is as close as would be expected, and directly supports the view that the heat emission of radium is due very largely to the bombardment of the radium and containing vessel by the α particles expelled from its mass.
249. Heating effect of the radium emanation. The
enormous amount of heat liberated in radio-active transformations
which are accompanied by the expulsion of α particles is very well
illustrated by the case of the radium emanation.
The heat emission of the emanation released from 1 gram of radium is 75 gram calories per hour at its maximum value. This heat emission is not due to the emanation alone, but also to its further products which are included with it. Since the rate of heat emission decays exponentially with the time to about half value in four days, the total amount of heat liberated during the life of the emanation from 1 gram of radium is equal to
[integral]_{0}^[infinity] 75e^{-λt}dt = 75/λ = 10,000 gram calories approximately,
since λ = ·0072(hour)^{-1}. Now the volume of the emanation from 1 gram of radium is about 1 cubic millimetre at standard pressure and temperature (section 172). Thus 1 cubic centimetre of the emanation would during its transformation emit 10^7 gram calories. The heat emitted during the combination of 1 c.c. of hydrogen and oxygen to form water is about 2 gram calories. The emanation thus gives out during its changes 5 × 10^6 times as much energy as the combination of an equal volume of hydrogen and oxygen
