Since the activity of the emanation falls to half value in 1 minute
λ = ¹⁄₈₇,
and N₀ = 87q₀, or the number of emanation particles present when a steady state is reached is 87 times the number produced per second.
Radium Emanation.
144. Discovery of the emanation. Shortly after the discovery of the thorium emanation, Dorn[[236]] repeated the results, and, in addition, showed that radium compounds also gave off radio-active emanations, and that the amount given off was much increased by heating the compound. The radium emanation differs from the thorium emanation in the rate at which it loses its activity. It decays far more slowly, but in other respects the emanations of thorium and radium have much the same properties. Both emanations ionize the gas with which they are mixed, and affect a photographic plate. Both diffuse readily through porous substances but are unable to pass through a thin plate of mica; both behave like a temporarily radio-active gas, mixed in minute quantity with the air or other gas in which they are conveyed.
145. Decay of activity of the emanation. Very little emanation escapes from radium chloride in the solid state, but the amount is largely increased by heating, or by dissolving the compound in water. By bubbling air through a radium chloride solution, or passing air over a heated radium compound, a large amount of emanation may be obtained which can be collected, mixed with air, in a suitable vessel.
Experiments to determine accurately the rate of decay of activity of the emanation have been made by P. Curie[[237]], and Rutherford and Soddy[[238]]. In the experiments of the latter, the emanation mixed with air was stored over mercury in an ordinary gas-holder. From time to time, equal quantities of air mixed with the emanation were measured off by a gas pipette and delivered into a testing vessel. The latter consisted of an air-tight brass cylinder carrying a central insulated electrode. A saturation voltage was applied to the cylinder, and the inner electrode was connected to the electrometer with a suitable capacity in parallel. The saturation current was observed immediately after the introduction of the active gas into the testing vessel, and was taken as a measure of the activity of the emanation present. The current increased rapidly with the time owing to the production of excited activity on the walls of the containing vessel. This effect is described in detail in [chapter VIII].
The measurements were made at suitable intervals over a period of 33 days. The following table expresses the results, the initial activity being taken as 100.
| Time in hours | Relative Activity |
|---|---|
| 0 | 100 |
| 20·8 | 85·7 |
| 187·6 | 24·0 |
| 354·9 | 6·9 |
| 521·9 | 1·5 |
| 786·9 | 0·19 |
The activity falls off according to an exponential law with the time, and decays to half value in 3·71 days. With the usual notation