Page:Radio-activity.djvu/475

 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 N_{A}, N_{B}, N_{C} be the number of atoms of the products A, B, C present per gram in radio-active equilibrium. Let λ_{A}, λ_{B}, λ_{C} be the corresponding constants of change. Then if q is the number of the parent atoms breaking up per second, per gram,

q = λ_{A}N_{A} = λ_{B}N_{B} = λ_{C}N_{C}.

Consider the case of the radium products, where the value of q is 6·2 × 10^{10} (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 × 10^{21} atoms (section 39). The results are shown in the following table:—

+-+-+-+ +-+-+-+-+ +-+-+-+
 * |  Value of    |   Number of atoms,  | Weight of product |
 * Product    |   λ    |   N, present per  | in milligrams per |
 * | (sec)^{-1}   |        gram         |  gram of radium   |
 * Radium emanation | 2·0 × 10^{-6} |   3·2 × 10^{16}    |    8 × 10^{-3}    |
 * [v]       |               |                     |                   |
 * Radium A     | 3·8 × 10^{-3} |    1·7 × 10^{13}    |    4 × 10^{-6}    |
 * [v]       |               |                     |                   |
 * Radium B     | 5·4 × 10^{-4} |    1·3 × 10^{14}    |    3 × 10^{-5}    |
 * [v]       |               |                     |                   |
 * 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 A, B and C are too small to weigh. It may be possible, however, to detect their presence by means of the spectroscope.

In the case of thorium, the weight of the product Th X, which is present in greatest quantity, is far too small to be detected. Since the value of λ for Th X is about the same as for the radium emanation, the maximum weight present per gram is about 4 × 10^{-12} of a gram, remembering that q for radium is about 2 × 10^6 times the value for thorium. Even with a kilogram of