a
For inelastic collision \(\mathrm{v}^{\prime}=\frac{\mathrm{m}_{1}}{\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right)} \mathrm{v}\)

\(=\frac{1}{(1+1)} v=\frac{v}{2}\)

\(\mathrm{n} \rightarrow \mathrm{v}(\mathrm{H}) \quad\)            Before

\((n)(H) \rightarrow \frac{v}{2} \quad\)         After Loss in \(K.E.\)

\(=\frac{1}{2} m v^{2}-\frac{1}{2}(2 m)\left(\frac{v}{2}\right)^{2}=\frac{1}{4} m v^{2}\)

\(K.E.\) lost is used to jump from \(1\,st\) orbit to \(2\,nd\) orbit \(\Delta \mathrm{K} . \mathrm{E}=10.2 \mathrm{eV}\)

\(\Rightarrow \frac{1}{4} m v^{2}=10.2\)

Minimum \(K.E.\) of neutron for inelastic collision

\(\frac{1}{2} m v^{2}=2 \times 10.2=20.4 \mathrm{eV}\)