Solution to 2008 Problem 52

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.

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