Question

An x-ray beam of wavelength 1.4×10−10m makes an angle of 20° with a set of planes in a crystal(the Bragg angle)causing first order constructive interference.10)(5pts) At what Bragg angle will the second order line appear?

Answer 1

Answer:

Second order line appears at 43.33° Bragg angle.

Explanation:

When there is a scattering of x- rays from the crystal lattice and interference occurs, this is known as Bragg's law.

The Bragg's diffraction equation is :

$n\lambda=2d\sin\theta$      .....(1)

Here n is order of constructive interference, λ is wavelength of x-ray beam, d is the inter spacing distance of lattice and θ is the Bragg's angle or scattering angle.

Given :

Wavelength, λ = 1.4 x 10⁻¹⁰ m

Bragg's angle, θ = 20°

Order of constructive interference, n =1

Substitute these value in equation (1).

$1\times1.4\times10^{-10} =2d\sin20$

d = 2.04 x 10⁻¹⁰ m

For second order constructive interference, let the Bragg's angle be θ₁.

Substitute 2 for n, 2.04 x 10⁻¹⁰ m for d and 1.4 x 10⁻¹⁰ m for λ in equation (1).

$2\times1.4\times10^{-10} =2\times2.04\times10^{-10} \sin\theta_{1}$

$\sin\theta_{1} =0.68$

θ₁ = 43.33°