The thorium-nitrate which had been freed from Th X was allowed to stand for one month, and then it was again subjected to the same process. The activity of the Th X was found to be the same as that obtained from an equal amount of the original thorium-nitrate. In one month, therefore, the Th X had been regenerated, and had reached a maximum value. By leaving the thorium time to recover fully its activity, this process can be repeated indefinitely, and equal amounts of Th X are obtained at each precipitation. Ordinary commercial thorium-nitrate and the purest nitrate obtainable showed exactly the same action, and equal amounts of Th X could be obtained from equal weights. These processes thus appear to be independent of the chemical purity of the substance[[229]].
The process of the production of Th X is continuous, and no alteration has been observed in the amount produced in the given time after repeated separations. After 23 precipitations extending over 9 days, the amount produced in a given interval was about the same as at the beginning of the process.
These results are all in agreement with the view that the Th X is being continuously produced from the thorium compound at a constant rate. The amount of active matter produced from 1 gram of thorium is probably extremely minute, but the electrical effects due to its activity are so large that the process of production can be followed after extremely short intervals. With a sensitive electrometer the amount of Th X produced per minute in 10 grams of thorium-nitrate gives a rapid movement to the electrometer needle. For larger intervals it is necessary to add additional capacity to the system to bring the effects within range of the instrument.
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
