Question

When an x-ray beam is scattered off the planes of a crystal, the scattered beam creates an interference pattern. This phenomenon is called Bragg scattering. For an observer to measure an interference maximum, two conditions have to be satisfied:

1. The angle of incidence has to be equal to the angle of reflection.
2. The difference in the beam's path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength; that is,

2dsin(θ)=mλfor m=1,2,…2dsin⁡(θ)=mλfor m=1,2,….

Part A

An x-ray beam with wavelength 0.130 nmnm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 28.0 ∘∘. What is the spacing ddd between the planes of the crystal?

Express your answer in nanometers to four significant figures.

Part B:

Part B

Find the angle θ2θ2theta_2 at which you will find a second maximum.

Express your answer in degrees to three significant figures.

Answer 1

Part A

2dsin = m

here, m = 1 ( first order)

2 * d * sin 28 = 1 * 0.130e-9

so,

d = 0.1385 nm

__________________

Part B

2dsin = m

this time, m = 2 ( second order)

so,

sin = 2 * 0.130 / 2 * 0.1385

sin = 0.9389

= arcsin ( 0.9389)

= 69.9 degree