Discussion
The first reflection from FCC crystal is observed at Bragg angle θ = 21.5°, the θ corresponding to the second reflection is :
Answer: C
The second reflection is at about 25.0°.
In an FCC lattice reflections appear only when h, k, l are all odd or all even, so the first two are (111) and (200). With \(d = a/\sqrt{h^{2} + k^{2} + l^{2}}\), Bragg's law gives \(\sin\theta \propto \sqrt{h^{2} + k^{2} + l^{2}}\):
\[ \begin{aligned} \sin\theta_{2} &= \sin 21.5^{\circ}\sqrt{\tfrac{4}{3}} \\ &= 0.3665 \times 1.1547 = 0.4232 \\ \theta_{2} &= 25.0^{\circ} \end{aligned} \]
The second reflection must come at a larger angle than the first, which rules out 13.5° and 18.5°. 36.8° would be the angle for (220), which is the third FCC reflection, not the second.
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