Q. The longest wavelength that can be analysed by a sodium chloride crystal of spacing $d = 2.82\ A{^\circ}$ in the second order is
A) $2.82\ A{^\circ}$
B) $5.64\ A{^\circ}$
C) $8.46\ A{^\circ}$
D) $11.28\ A{^\circ}$
Explanation
(a) Use Bragg’s $X$-ray diffraction Law
$n\lambda = 2d\sin\theta$
$\therefore\lambda = \frac{2d\sin\theta}{n}$
For longest wavelength take sin $\theta = 1$
$\therefore\lambda = \frac{2 \times 2.82\lbrack\mathring{\mathrm{A}}\rbrack}{2}\lbrack\because n = 2\ $for second order]
$= 2.82\ \mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.