Q74 · CSIR-NET Chemistry, June 2019
Paper: CSIR-NET June 2019 · Subject: Physical Chemistry · Chapter: Solid State Chemistry · Topic: Crystal Systems Lattices · Marks: 2 · Difficulty: Medium
The correct relationship among the following, for a tetragonal $\left(a=b \neq c, \alpha=\beta=\gamma=90^{\circ}\right)$ crystal system, is
(a)$\sin ^{2} \theta=\frac{\lambda^{2}}{4 \mathrm{a}^{2}}\left[\mathrm{c}^{2}\left(\mathrm{h}^{2}+\mathrm{k}^{2}\right)+\mathrm{a}^{2} \mathrm{l}^{2}\right]$
(b)$\sin ^{2} \theta=\frac{\lambda^{2}}{4 \mathrm{a}^{2} \mathrm{c}^{2}}\left[\mathrm{c}^{2}\left(\mathrm{h}^{2}+\mathrm{k}^{2}\right)+\mathrm{a}^{2} \mathrm{l}^{2}\right]$
(c)$\sin ^{2} \theta=\frac{\lambda^{2}}{4 \mathrm{c}^{2}}\left[\mathrm{a}^{2}\left(\mathrm{h}^{2}+\mathrm{k}^{2}\right)+\mathrm{c}^{2} \mathrm{l}^{2}\right]$
(d)$\left.\sin ^{2} \theta=\frac{\lambda^{2}}{4 \mathrm{a}^{2}}\left(\mathrm{h}^{2}+\mathrm{k}^{2}\right)+\mathrm{l}^{2}\right]$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
Tetragonal: 1/d² = (h² + k²)/a² + l²/c². With Bragg's law, sin²θ = (λ²/4a²c²)[c²(h² + k²) + a²l²].
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