Question

For Bragg’s diffraction by a crystal to occur, then the X-ray of wavelength $\lambda$ and interatomic distance d must be?
A. $\lambda$ is greater than 2d.
B. $\lambda$ equals 2d.
C. $\lambda$ is smaller than or equal to 2d.
D. $\lambda$ is smaller than 2d.

Answer 1

Hint: To answer this question, use the formula for Bragg’s law for diffraction which is given as $n\lambda = 2d \sin {\theta}$. Then, substitute the values for first order diffraction i.e. n=1. $\sin {\theta}$ can take maximum value 1 or less than 1. Substitute this value in the equation for first order diffraction and find the relation between wavelength and interatomic distance for Bragg’s diffraction by a crystal to occur.

Formula used:
$n\lambda = 2d \sin {\theta}$

Complete step by step answer:
Bragg’s law for diffraction by a crystal is given by,
$n\lambda = 2d \sin {\theta}$ …(1)
Where, n is the order of reflection
            $\lambda$ is the wavelength
            d is the interatomic distance
            $\theta$ is the angle between the incident beam and reflecting plane
For first order diffraction, n=1,
$\lambda = 2d \sin {\theta}$ …(2)
$\sin {\theta}$ can take the values less than or equal to 1.
$\sin {\theta} \leq 1$ …(3)
Substituting equation. (3) in equation. (2) we egt,
$\lambda \leq 2d$
Thus, the $\lambda$ must be less than or equal to 2d.
Hence, the correct answer is option C i.e. $\lambda$ is smaller than or equal to 2d.

Note:
Students must keep in mind that Bragg’s law is valid only if angle of incidence and angle of reflection are equal to each other and the path difference (d) is equal to an integer number (n) of wavelengths. It explains the molecular structure and crystals being identified using X-ray diffraction techniques. If these conditions are satisfied then constructive interference will occur.