Question

Which of the following relation is correct for first order Bragg's diffraction?

• A. $\sin \theta=\frac{2 a}{\lambda}\left(h^{2}+k^{2}+l^{2}\right)$
• B. $\sin \theta=\frac{2 a}{\lambda}\left(h^{2}+k^{2}+l^{2}\right)^{1 / 2}$
• C. $\sin \theta=\frac{\lambda}{2 a}\left(h^{2}+k^{2}+l^{2}\right)^{1 / 2}$
• D. $\sin \theta=\frac{\lambda}{2 a}\left(h^{2}+k^{2}+l^{2}\right)^{2}$

Answer 1

Answer: (C)

$n \lambda=2 d \sin \theta$

$d=\frac{\lambda}{2 \sin \theta}$...(i) (for first order diffraction)

$d=\frac{a}{\sqrt{h^{2}+k^{2}+l^{2}}}$...(ii)

Comparing equation (i) and (ii)

$\frac{\lambda}{2 \sin \theta}=\frac{a}{\sqrt{h^{2}+k^{2}+l^{2}}}$

$\sin \theta=\frac{\lambda}{2 a}\left( h ^{2}+ k ^{2}+l^{2}\right)^{1 / 2}$