----- = q – (λ + α)n.
dt
The same equation is obtained when no emanation escapes, with the difference that the constant λ + α is replaced by λ. When a steady state is reached, dn/dt is zero, and the maximum value of n is equal to q/(λ + α).
If no escape takes place, the maximum value of n is equal to q/λ. The escape of emanation will thus lower the amount of activity recovered in the proportion λ/(λ + α). If n₀ is the final number of emanation particles stored up in the compound, the integration of the above equation gives
The curve of recovery of activity is thus of the same general form as the curve when no emanation escapes, but the constant λ is replaced by λ + α.
For example, if α = λ = ¹⁄₄₆₃₀₀₀, the equation of rise of activity is given by
and, in consequence, the increase of activity to the maximum will be far more rapid than in the case of no escape of emanation.
A very slight escape of emanation will thus produce large alterations both in the final maximum and in the curve of recovery of activity.