If the recovery curve is produced backwards to meet the vertical axis, it does so at a minimum of 25 per cent., and the above conclusions hold more accurately, if the recovery is assumed to start from this minimum. This is clearly shown by [Fig. 48], where the percentages of activity recovered, reckoned from the 25 per cent. minimum, are plotted as ordinates. In the same figure the decay curve, after the second day, is shown on the same scale. The activity of the Th X decays with the time according to an exponential law, falling to half value in about four days. If I₀ is the initial activity and It is the activity after a time t, then
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
where I₀ is the amount of activity recovered when the state of constant activity is reached, It 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].
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.
A large number of results of a similar character have been obtained from other radio-active products, separated from the radio-elements, but the cases of thorium and uranium will suffice for the present to form a basis for the discussion of the processes that are taking place in radio-active bodies.