Q. The largest distance between the interatomic places of a crystal is $10^{7}cm.$ The upper limit for the wavelength of $X$-rays which can be usefully studied with this crystal is
A) $1\ \mathring{\mathrm{A}}$
B) $2\ \mathring{\mathrm{A}}$
C) $10\ \mathring{\mathrm{A}}$
D) $20\ \mathring{\mathrm{A}}$
Explanation
(d) Bragg’s law, $2d\sin\theta = n\lambda\ $or$\ \lambda = \frac{2d\sin\theta}{n}$
For maximum wavelength, $n_{\min} = 1,\ \left( \sin\theta \right)_{\max} = 1$
$\therefore\lambda_{\max} = 2d\ $or$\ \lambda_{\max} = 2 \times 10^{- 7}cm = 20\ \mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.