where I₀ is the initial intensity and It the intensity after any time t; λ1 = ¹⁄₂₄₂₀, λ2 = ¹⁄₁₈₆₀. The numerical constant a = 4·20. After an interval of 2·5 hours, the logarithmic decay curve is nearly a straight line, that is, the activity falls off according to an exponential law with the time, decreasing to half value in about 28 minutes.
The full explanation of this equation, and of the peculiarities of the various decay curves of the excited activity of radium, will be discussed in detail in chapter XI.
As in the case of the excited activity from thorium, the rate of decay of the excited activity from radium is for the most part independent of the nature of the body made active. Curie and Danne (loc. cit.) observed that the active bodies gave off an emanation itself capable of exciting activity in neighbouring bodies. This property rapidly disappeared, and was inappreciable 2 hours after removal. In certain substances like celluloid and caoutchouc, the decay of activity is very much slower than for the metals. This effect becomes more marked with increase of time of exposure to the emanation. A similar effect is exhibited by lead, but to a less marked degree. During the time the activity lasts, these substances continue to give off an emanation.
It is probable that these divergencies from the general law are not due to an actual change in the rate of decay of the true excited activity but to an occlusion of the emanation by these substances during the interval of exposure. After exposure the emanation gradually diffuses out, and thus the activity due to this occluded emanation and the excited activity produced by it decays very slowly with the time.
183. Active deposit of very slow decay. M. and Mme Curie9 have observed that bodies which have been exposed for a long interval in the presence of the radium emanation do not lose all their activity. The excited activity at first decays rapidly at the normal rate, falling to half value in about 28 minutes, but a residual activity, which they state is of the order of ½0,000 of the initial activity, always remains. A similar effect was observed by Giesel. The writer has examined the variation of this residual activity, and has found that it increases for several years. The results are discussed in detail in chapter XI. It will there be shown that this active deposit of slow transformation contains the radio-active constituents present in polonium, radio-tellurium and radio-lead.