Given: $\lambda=1.40 \times 10^{-10} \mathrm{~m}, \mathrm{~m}_{\mathrm{n}}=1.66 \times 10^{-27} \mathrm{~kg}$, $\mathrm{K}=$ Boltzmann constant $=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{kg}$
Now, $\mathrm{E}=\frac{\mathrm{h}^2}{2 \mathrm{~m} \lambda^2}$ (done in Q.14)
$$
\begin{aligned}
&=\frac{\left(6.6 \times 10^{-34}\right)^2}{2 \times 1.66 \times 10^{-27} \times\left(1.4 \times 10^{-10}\right)^2} \\
&=\frac{43.56 \times 10^{-68}}{6.51 \times 10^{-47}}=6.735 \times 10^{-21} \mathrm{~J} .
\end{aligned}
$$
(b) $\begin{aligned} \mathrm{E} &=\frac{3}{2} \mathrm{KT}=\frac{3}{2} \times 1.38 \times 10^{-23} \times 300 \\ &=6.21 \times 10^{-21} \mathrm{~J} \end{aligned}$
$$
\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}
$$
$$
\begin{aligned}
&=\frac{6.6 \times 10^{-34}}{\sqrt{2 \times 1.66 \times 10^{-27} \times 6.21 \times 10^{-21}}} \\
&=\frac{6.6 \times 10^{-34}}{\sqrt{20.617 \times 10^{-48}}}=\frac{6.6 \times 10^{-34}}{4.54 \times 10^{-24}} \\
&=1.46 \times 10^{-10} \mathrm{~m}=1.46 Å .
\end{aligned}
$$