Page:Radio-activity.djvu/244

 explained in detail in section 208, it will be seen that, after the first two days, the time taken for the thorium to recover half its lost activity is about equal to the time taken by the Th X to lose half its activity. This time in each case is about four days. The percentage proportion of the activity regained by the thorium, over any given interval, is approximately equal to the percentage proportion of the activity lost by the Th X during the same interval.

Fig. 48.

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 I_{0} is the initial activity and I_{t} is the activity after a time t, then

I_{0}/I_{t} = e^{-λt},