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# A sample of crystalline solid scatters a beam of X-rays of wavelength 70.93pm at an angle $2\theta$ of $14.66^{\large\circ}$.If this is a second order reflection (n=2),calculate the distance between the parallel planes of atoms from which the scattered beam appears to have been reflected.

$\begin{array}{1 1}555.94pm\\455.94pm\\255.94pm\\155.94pm\end{array}$

We know that $n\lambda=2d\sin \theta$
$2\theta=14.66^{\large\circ}$
$\theta=7.33^{\large\circ}$
$\lambda =70.93pm=70.93\times 10^{-12}m$
$d=\large\frac{n\lambda}{2\sin \theta}$
$\;\;\;=\large\frac{2\times 70.93\times 10^{-12}}{2\sin 7.33}$m
$\;\;\;=555.94$pm