Question

An X-ray beam with λ = 157 pm incident on the surface of a crystal produced a maximum reflection at an angle of θ = 28.5 ∘. Assuming n=1, calculate the separation between layers of atoms in the crystal.

Answer 1

Answer:

The separation between layers of atoms in the crystal is 164.52 pm.

Explanation:

Formula used

$n \lambda = 2d\sin \theta$ (Bragg's law)

Where :

n = an order of reflection (integer)

$\lambda$ = wavelength of the beam incident X-ray

d = spacing between the layer

θ = incident angle ( angle between ray and scatter plane)

We have :

λ = 157 pm

θ = 28.5°

n = 1

d = ?

$1\times 157 pm= 2d\sin (28.5^o)$ (Bragg's law)

$d=\frac{1\times 157 pm}{2\times \sin (28.5^o)}=164.52 pm$

The separation between layers of atoms in the crystal is 164.52 pm.