For example, if α = λ = 1/463000, the equation of rise of activity is given by n/n_{0} = 1 - e^{-2λt}, and, in consequence, the increase of activity to the maximum will be far more rapid than in the case of no escape of emanation.
A very slight escape of emanation will thus produce large alterations both in the final maximum and in the curve of recovery of activity.
A number of experiments have been described by Mme Curie in her Thèse présentée à la Faculté des Sciences de Paris on the effect of solution and of heat in diminishing the activity of radium. The results obtained are in general agreement with the above view, that 75 per cent. of the activity of radium is due to the emanation and the excited activity it produces. If the emanation is wholly or partly removed by solution or heating, the activity of the radium is correspondingly diminished, but the activity of the radium compound is spontaneously recovered owing to the production of fresh emanation. A state of radio-active equilibrium is reached, when the rate of production of fresh emanation balances the rate of change in the emanation stored up in the compound. The differences observed in the rate of recovery of radium under different conditions were probably due to variations in the rate of escape of the emanation.
217. It has been shown in section 152 that the emanation is
produced at the same rate in the solid as in the solution, and all
the results obtained point to the conclusion that the emanation is
produced from radium at a constant rate, which is independent
of physical conditions. Radium, like thorium, shows a non-separable
activity of 25 per cent. of the maximum activity, and
consisting entirely of α rays. The β and γ rays arise only from
the active deposit. The emanation itself (section 156) gives out
only α rays. These results thus admit of the explanation given in
the case of thorium (section 136). The radium atoms break up at
a constant rate with the emission of α particles. The residue of
the radium atom becomes the atom of the emanation. This
in turn is unstable and breaks up with the expulsion of an α
particle. The emanation is half transformed in four days. We
