Ans : (d)
Interatomic spacing depends upon the path difference. Interatomic spacing is
$d =\large\frac{n\lambda}{2}$ and de- Broglie wave is formed between interatomic spacing.
$d_1 = \large\frac{n \lambda}{2} \: and\: d_2 = \large\frac{(n+1) \lambda}{2}$
So,$ \large\frac{ \lambda}{2} = d_2 – d_1$
$ \Rightarrow \lambda = 2(d_2 – d_1) = 2(2.5 – 2) = 1\: A^{\circ}$
$ \lambda=\large\frac{h}{p} \: \: or \: \: p = \large\frac{h}{ \lambda}$
$E = \large\frac{1}{2} mv^2$
$= \large\frac{1}{2m} (m^2v^2 ) = \large\frac{p^2}{2m}$
$ \Rightarrow E = \large\frac{h^2}{2m \lambda^2}$
$ \Rightarrow E = \large\frac{(6.6 \times 10^{-34})^2}{ [ 2 \times 9.1 \times 10^{-31} \times (10^{-10} )^2 ]} = 150.95 \: eV$