Bragg's Law Example Question

NaCl is often used to test X-ray diffractometers.

The distance between a set of planes in NaCl is 5.64Å.

Using a 16.5keV X-ray source at what diffraction angle ($2\theta$) should peaks be recorded for the first order of diffraction (n = 1) ?

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$E=hc/\lambda$ , therefore $\lambda =hc/E$ . $h=6.626\ast 10^{-34}$ , $c\approx 3\ast 10^8$, $E=16.5\ast 10^4$ $\lambda =0.75\ast 10^{-10}m=0.75\mathring{A}$

Braggs law: $n\lambda =2d\sin (\theta )$

$$\theta ={\sin }^{-1}\left(\frac{1\ast 0.75}{2\ast 5.64}\right)=3.8^o$$

$2\theta =7.6^o$