Find one wavelength of X-rays, if the lattice constant for copper is 3.615$A^0$ . -

Mumbai university > FE > SEM 1 > Applied Physics 1

Marks: 7M

Year: May 2015

Bragg’s law-

Bragg emphasized on parallel planes & the set of planes are considered as Bragg’s planes. When X-rays are allowed to be incident on this planes, diffraction takes place & diffracted pattern gives information about the structure.

Let us consider parallel planes-

Let AB be my incident ray, which gets reflected along BC, another parallel beam gets incident along E, gets reflected along EF. Drop perpendicular from B such that it meets DE & EF along P & Q.

Now,

∆ = PE + EQ

∴ ∆ = BE.sin θ + BE.sin θ

∴ ∆ = 2 BE.sin θ

∴ ∆ = 2d.sin θ

But, ∆ = nλ ………here we consider constructive interference

∴ nλ = 2d.sinθ

This, is the required expression for Bragg's Law

Given:

n=1

θ=20

Miller indices is (2 1 2)

a = 3.615A or $3.615×10^{-10}$

To find: λ=?

Solution:

$d =\frac{a}{\sqrt{2^2 + 1^2 + 2^2}}$

$= \frac{3.615 × 10^{-10}}{\sqrt{9}}$

$= \frac{3.615 × 10^{-10}}{3}$

d= 1.205×10-10 m

By Bragg’s law-

$$n λ = 2d.sinθ$$

$ λ = 2 × 1.205 × 10^{-10}sin20/1$

$ λ = 8.243 × 10^{-11}m$

$ λ = 0.824A$