Physics - Modern Physics Question with Solution | TestHub

$\mathrm{N}\mathrm{ }=\mathrm{ }{\mathrm{N}}_0(1-\mathrm{ }{\mathrm{e}}^{-\mathrm{\lambda t}})$, N - The amount of substance decayed.

$\Rightarrow \frac{{\mathrm{N}}_0-\mathrm{N}}{{\mathrm{N}}_0}={\mathrm{e}}^{-\mathrm{\lambda t}}$

$\therefore \mathrm{ }\frac{1}{8}={\mathrm{e}}^{-\mathrm{\lambda t}}$

$\Rightarrow \mathrm{ }8={\mathrm{e}}^{\mathrm{\lambda t}}$

$\Rightarrow$ $3\ln 2\mathrm{ }=\mathrm{\lambda t}$

$\Rightarrow \mathrm{\lambda }=\frac{3\mathrm{ }\times \mathrm{ }0.693}{15}$

Half-life period

$\mathrm{\lambda } = 5 \min$