Physics - Modern Physics Question with Solution | TestHub

We have, ${\mathrm{N}}_{\mathrm{t}}={\mathrm{N}}_0{\left(\frac{1}{2}\right)}^{\frac{\mathrm{t}}{{\mathrm{T}}_{1/2}}}$, When $\begin{array}{l}{\mathrm{N}}_{\mathrm{t}}=\text{ number of atoms present after time t }\\ {\mathrm{N}}_0^{\mathrm{t}}=\text{ initial number of atoms }\\ {\mathrm{T}}_{1/2}=\text{ half life of the nuclide }\\ \therefore \frac{{\mathrm{N}}_{\mathrm{t}}}{{\mathrm{N}}_0}={\left(\frac{1}{2}\right)}^{\frac{\mathrm{t}}{{\mathrm{T}}_{1/2}}}\text{ or }\frac{1}{16}={\left(\frac{1}{2}\right)}^{\frac{2}{{\mathrm{T}}_{1/2}}}\\ \text{ or }{\left(\frac{1}{2}\right)}^4={\left(\frac{1}{2}\right)}^{\frac{2}{{\mathrm{T}}_{1/2}}}\Rightarrow 4=\frac{2}{{\mathrm{T}}_{1/2}}\\ \Rightarrow {\mathrm{T}}_{1/2}=\frac{2}{4}\mathrm{Hr}=\frac{1}{2}\mathrm{Hr}\therefore {\mathrm{T}}_{1/2}=30\min \end{array}$