A metal crystallizes with cubic close-packed structure. The $\sin ^{2} \theta$ values of Bragg reflections of Miller Planes (200) and (111) are 0.18 and 0.14 , respectively. The unit cell length is
(a)$\lambda / 2$
(b)$\lambda / 0.3$
(c)$\lambda / 0.4$
(d)$0.4 \lambda$
Answer
Answer: C ✓ checked by 4AB · confidence high
The source book printed A; on checking, C is correct — see the explanation.
Printed A; λ/2 would need sin²θ(200) = 1.
Explanation
a = λ√(h²+k²+l²)/(2 sin θ); for (200): a = 2λ/(2√0.18) = λ/0.424 ≈ λ/0.4 (consistent with (111): λ√3/(2√0.14) = λ/0.432).