Substituting this value of Q in (2), it can readily be shown that
where
Fig. 72.
The variation of the values of P, Q, R with the time t, after removal of the source, is shown graphically in [Fig. 72], curves A, B, and C respectively. In order to draw the curves for the practical case which will be considered later corresponding to the first three changes in radium A, the values of λ1, λ2, λ3 were taken as 3·85 × 10-3, 5·38 × 10-4, 4·13 × 10-4 respectively, i.e., the times required for each successive type of matter to be half transformed are about 3, 21, and 28 minutes respectively.
The ordinates of the curves represent the relative number of atoms of the matter A, B, and C existing at any time, and the value of n, the original number of atoms of the matter A deposited, is taken as 100. The amount of matter B is initially zero, and in this particular case, passes through a maximum about 10 minutes later, and then diminishes with the time. In a similar way, the amount of C passes through a maximum about 37 minutes after removal. After an interval of several hours the amount of both B and C diminishes very approximately according to an exponential law with the time, falling to half value after intervals of 21 and 28 minutes respectively.