all of one kind, which changes into B (thorium B), find the activity of A and B together at any subsequent time. This corresponds to Case I. (section 197). The amount Q of B at any time T* is given by
and the activity I at any time of the two together is proportional to λ1P + Kλ2Q, where K is the ratio of the ionization of B compared with that of A.
Then
where I₀ is the initial activity due to n₀ particles of Th X.
By comparison of this equation with the curve of variation of the activity of Th X with time, shown in Fig. 47, it is found that K is almost ·44. It must be remembered that the activity of the emanation and Th X are included together, so that the activity of thorium B is about half of the activity of the two preceding products.
The calculated values of It/I₀ for different values of t are shown in the second column of the following table, and the observed values in the third column.
| Time | Theoretical value | Observed value |
|---|---|---|
| 0 | 1·00 | 1·00 |
| ·25 days | 1·09 | — |
| ·5 „ | 1·16 | — |
| 1 „ | 1·15 | 1·17 |
| 1·5 „ | 1·11 | — |
| 2 „ | 1·04 | — |
| 3 „ | ·875 | ·88 |
| 4 „ | ·75 | ·72 |
| 6 „ | ·53 | ·53 |
| 9 „ | ·315 | ·295 |
| 13 „ | ·157 | ·152 |