Question

In a radioactive sample the number of active nuclei remains 6.25% of its initial value in 6 hr . find the half life of radioactive sample.

Answer 1

$N=N_0{e}^{-\lambda t}$
$\log \frac{N}{N_o}=\lambda t$
$log\frac{N_o}{N}=\lambda t$
$\frac{1}{t}log\frac{N_o}{N}=\lambda$
$\frac{1}{t}log\frac{100}{6.25}=\lambda$
$T_{1/2}=\frac{log2}{\lambda }$
$T_{1/2}=\frac{log2}{\frac{1}{6}log{2}^4}=\frac{log2}{\frac{4}{6}log2}$
$T_{1/2}=\frac{6}{4}=\frac{3}{2}=1.5$