133. Rate of decay of activity. It has been shown that the activity of Ur X and Th X decays according to an exponential law with the time. This, we shall see later, is the general law of decay of activity in any type of active matter, obtained by itself, and freed from any secondary active products which it may, itself, produce. In any case, when this law is not fulfilled, it can be shown that the activity is due to the superposition of two or more effects, each of which decays in an exponential law with the time. The physical interpretation of this law still remains to be discussed.
It has been shown that in uranium and thorium compounds there is a continuous production of active matter which keeps the compound in radio-active equilibrium. The changes by which the active matter is produced must be chemical in nature, since the products of the action are different in chemical properties from the matter in which the changes take place. The activity of the products has afforded the means of following the changes occurring in them. It now remains to consider the connection between the activity at any time, and the amount of chemical change taking place at that time.
In the first place, it is found experimentally that the saturation ionization current it, after the active product has been allowed to decay for a time t, is given by
where i₀ is the initial saturation current and λ the constant of decay.
Now the saturation current is a measure of the total number of ions produced per second in the testing vessel. It has already been shown that the α rays, which produce the greater proportion of ionization in the gas, consist of positively charged particles projected with great velocity. Suppose for simplicity that each atom of active matter, in the course of its change, gives rise to one projected α particle. Each α particle will produce a certain average number of ions in its path before it strikes the boundaries or is absorbed in the gas. Since the number of projected particles per second is equal to the number of atoms changing per second, the number of atoms nt which change per second at the time t is given by
where n₀ is the initial number which change per second. On this view, then, the law of decay expresses the result that the number of atoms changing in unit time, diminishes according to an exponential law with the time. The number of atoms Nt which remain unchanged after an interval t is given by