198. Case 2. A primary source supplies the matter A at a constant rate and the process has continued so long that the amount of the products A, B, C, ... has reached a steady limiting value. The primary source is then suddenly removed. It is required to find the amounts of A, B, C, ... remaining at any subsequent time t.
In this case, the number n₀ of particles of A, deposited per second from the source, is equal to the number of particles of A which change into B per second, and of B into C, and so on. This requires the relation
n₀ = λ1P₀ = λ2Q₀ = λ3R₀ (6),
where P₀, Q₀, R₀ are the maximum numbers of particles of the matter A, B, and C when a steady state is reached.
The values of P, Q, R at any time t after removal of the source are given by equations of the same form as (3) and (5) for a short exposure. Remembering the condition that initially
P = P₀ = n₀/λ1,
Q = Q₀ = n₀/λ2,
R = R₀ = n₀/λ3,
it can readily be shown that
