Page:Radio-activity.djvu/407

 Curve I (Fig. 89) shows the experimental curve. At the moment of removal of the body from the emanation (disregarding the initial rapid change), the matter must consist of both B and C. Consider the matter which existed in the form C at the moment of removal. It will be transformed according to an exponential law, the activity falling by one-half in 28 minutes. This is shown in curve II. Curve III represents the difference between the ordinates of curves I and II. It will be seen that it is identical in shape with the curve (Fig. 87) showing the variation of the activity for a short exposure, measured by the β rays. It passes through a maximum at the same time (about 36 minutes). The explanation of such a curve is only possible on the assumption that the first change is a rayless one. The ordinates of curve III express the activity added in consequence of the change of the matter B, present after removal, into the matter C. The matter B present gradually changes into C, and this, in its change to D, gives rise to the radiation observed. Since the matter B alone is considered, the variation of activity with time due to its further changes, shown by curve III, should agree with the curve obtained for a short exposure (see Fig. 87), and this, as we have seen, is the case.

The agreement between theory and experiment is shown in the following table. The first column gives the theoretical curve of decay for a long exposure deduced from the equation

I_{t}/I_{0} = (λ_{2}/(λ_{2} - λ_{3}))e^{-λ_{3}t} - (λ_{3}/(λ_{2} -λ_{3}))e^{-λ_{2}t}

taking the value of λ_{2} = 5·38 × 10^{-4} and λ_{3} = 4·13 × 10^{-4}.

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 * Time in | Calculated | Observed |
 * minutes |  values   |  values  |
 * 0   |    100     |  100     |
 * 10   |     96·8   |   97·0   |
 * 20   |     89·4   |   88·5   |
 * 30   |     78·6   |   77·5   |
 * 40   |     69·2   |   67·5   |
 * 50   |     59·9   |   57·0   |
 * 60   |     49·2   |   48·2   |
 * 80   |     34·2   |   33·5   |
 * 100   |     22·7   |   22·5   |
 * 120   |     14·9   |   14·5   |