The intensity of the radiation I after any time t is given by
where λ is the radio-active constant.
The rate of decay of excited activity, like that of the activity of other radio-active products, is not appreciably affected by change of conditions. The rate of decay is independent of the concentration of the excited activity, and of the material of the body on which it is produced. It is independent also of the nature and pressure of the gas in which it decays. The rate of decay is unchanged whether the excited activity is produced on the body with or without an electric field.
The amount of excited activity produced on a body increases at first with the time, but reaches a maximum after an exposure of several days. An example of the results is given in the following table. In this experiment a rod was made the cathode in a closed vessel containing thoria. It was removed at intervals for the short time necessary to test its activity and then replaced.
| Time in hours | Current |
|---|---|
| 1·58 | 6·3 |
| 3·25 | 10·5 |
| 5·83 | 29 |
| 9·83 | 40 |
| 14·00 | 59 |
| 23·41 | 77 |
| 29·83 | 83 |
| 47·00 | 90 |
| 72·50 | 95 |
| 96·00 | 100 |
These results are shown graphically in Curve B, Fig. 64. It is seen that the decay and recovery curves may be represented approximately by the following equations.
For the decay curve A,
For the recovery curve B,