physical properties. Such a connection is of interest as indicating a possible origin of the recurrence of properties in the atoms of the elements, as exemplified by the periodic law. The connection between thorium and actinium is especially close both as regards the number and nature of the products. The period of transformation of the successive products, though differing in magnitude, rises and falls in a very analogous manner. This indicates that the atoms of these two elements are very similarly constituted.
258. Amount of the products. By application of the theory of successive changes, the probable amount of each of the products present in radium and the other radio-elements can readily be estimated.
Since each radio-atom expels one α particle of atomic weight about that of hydrogen or helium, the atoms of the intermediate products will not differ much in weight from the parent atom.
The approximate weight of each product present in a gram of radium can be readily deduced. Let NA, NB, NC be the number of atoms of the products A, B, C present per gram in radio-active equilibrium. Let λA, λB, λC be the corresponding constants of change. Then if q is the number of the parent atoms breaking up per second, per gram,
Consider the case of the radium products, where the value of q is 6·2 × 1010 (section 93). Knowing the value of λ and q, the value of N can at once be calculated. The corresponding weight can be deduced, since in one gram of matter of atomic weight about 200, there are about 4 × 1021 atoms (section 39). The results are shown in the following table:—
| Product | Value of λ (sec) -1 | Number of atoms, N , present per gram | Weight of product gram of radium |
|---|---|---|---|
| Radium emanation | 2·0 × 10 -6 | 3·2 × 10 16 | 8 × 10 -3 |
| Radium A | 3·8 × 10 -3 | 1·7 × 10 13 | 4 × 10 -6 |
| Radium B | 5·4 × 10 -4 | 1·3 × 10 14 | 3 × 10 -5 |
| Radium C | 4·1 × 10 -4 | 1·6 × 10 14 | 4 × 10 -5 |
With the small quantities of radium available, the amounts of the products radium