For a decay chain stable product with decay constants (parent) and (daughter)

PHYSICS · Subjective · A Level · Physics · Nuclear physics · Nuclear physics

Problem

For a decay chain

X \to Y \to

stable product with decay constants

\lambda_1

(parent) and

\lambda_2

(daughter), prove that the time

t_{\!\max}

at which the activity of

Y

is maximum is given by

t_{\!\max}=\frac{1}{\lambda_2-\lambda_1}\,\ln\left(\frac{\lambda_2}{\lambda_1}\right), \quad (\lambda_2>\lambda_1).