where
Fig. 73.
The relative numbers of atoms of P, Q, R existing at any time are shown graphically in [Fig. 73], curves A, B, C respectively. The number of atoms R₀ is taken as 100 for comparison, and the values of λ1, λ2, λ3 are taken corresponding to the 3, 21, and 28-minute changes in the active deposit of radium. A comparison with [Fig. 72] for a short exposure brings out very clearly the variation in the relative amounts of P, Q, R in the two cases. Initially the amount of R decreases very slowly. This is a result of the fact that the supply of C due to the breaking up of B at first, nearly compensates for the breaking up of C. The values of Q and R after several hours decrease exponentially, falling to half value in 28 minutes.
199. Case 3. Suppose that a primary source has supplied the matter A at a constant rate for any time T and is then suddenly removed. Required the amounts of A, B, C at any subsequent time.
Suppose that n₀ particles of the matter A are deposited each second. After a time of exposure T, the number of particles PT of the matter A present is given by
