where λ is a constant and e the natural base of logarithms. The experimental curve of the rise of activity from a minimum to a maximum value is therefore expressed by the equation
I_{t}/I_{0} = 1 - e^{-λt},
where I_{0} is the amount of activity recovered when the state of constant activity is reached, I_{t} the activity recovered after a time t, and λ is the same constant as before.
129. Uranium X. Similar results were obtained when
uranium was examined. The Ur X was separated by Becquerel's
method of successive precipitations with barium. The decay of
the separated activity and the recovery of the lost activity are
shown graphically in Fig. 49. A more detailed discussion of this
experiment is given in section 205.
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Fig. 49.
The curves of decay and recovery exhibit the same peculiarities and can be expressed by the same equations as in the case of thorium. The time-rate of decay and recovery is, however, much slower than for thorium, the activity of the Ur X falling to half its value in about 22 days.
