Physics

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).

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