Question

Bragg’s law is given by the equation:
A. $n\lambda = 2\theta \sin \theta $
B. $n\lambda = 2d\sin \theta $
C. $2n\lambda = d\sin \theta $
D. $n\dfrac{\theta }{2} = \dfrac{d}{2}\sin \theta $

Answer 1

Hint: To answer this question, you must recall the Bragg’s law of diffraction. Bragg studied the pattern of X- ray diffraction for various solids. He concluded his study with Bragg's equation which is used to determine the interatomic distance of a crystal using X- rays.

Complete step by step solution:
According to Bragg's Law, Bragg's equation explains the reason behind the reflection of X- ray beams at particular angles by the faces of the crystals. It also gives the distance between two atomic layers using the wavelength of the X- ray beam incident on the crystal surface.
The equation for Bragg's law is given as, $n\lambda = 2d\sin \theta $.
Where, $n$ is the order of reflection
$\lambda $ is the wavelength of the X- ray beam
$d$ is the interatomic distance
And, $\theta $ is the angle of incidence of the beam

Thus, the correct answer is B.

Note: Bragg’s law determines the angles of coherent and incoherent scattering caused by a crystal lattice. When X-rays are incident on an atom, they create an electronic cloud movement just like that made by an electromagnetic wave. These charges move and this causes them to radiate waves again with similar frequency, and this phenomenon is known as the Rayleigh scattering.
The same process takes place on the scattering of neutron waves via nuclei. These wave fields that are re-emitted may interfere with each other either destructively or constructively, and create a diffraction pattern on a detector. The resulting wave interference is the basis of diffraction analysis, and this analysis is called Bragg diffraction.