A radioactive sample is undergoing α decay, At any time t _ 1 , its...

Let initial activity be ${A}_{0}$

$A = {A}_{0}{e}^{- \lambdat} . . . \left(1\right)$

$\dfrac{A}{5} = {A}_{0}{e}^{- \lambda{t}_{2}} . . . \left(2\right)$

\left(1\right) \div \left(2\right)$</p><p>$5 = {e}^{\lambda\left({t}_{2} - {t}_{1}\right)}$</p><p>$\lambda = \dfrac{\ln 5}{{t}_{2} - {t}_{1}} = \dfrac{1}{τ}$</p><p>$τ = \dfrac{{t}_{2} - {t}_{1}}{\ln 5}$