We use the Bragg diffraction formula
$\begin{align*}2 d \sin \theta = n \lambda\end{align*}$
which describes the condition for constructive interference of scattered x rays. We are told that the smallest angle for which, constructive interference occurs is $\theta = 14.5^{\circ}$ , so $n = 1$ when $\theta = 14.5^{\circ}$ , and the Bragg diffraction formula becomes
$\begin{align*}2 d \sin 14.5^{\circ} = \lambda\end{align*}$
Plugging in $\lambda = 0.250 \mbox{ nm}$ and $\sin 14.5^{\circ} \approx 1/4$ gives
$\begin{align*}d \approx \boxed{0.500 \mbox{ nm}}\end{align*}$
Therefore, answer (C) is correct.

Solution to 2008 Problem 52