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:
The angle of incidence has to be equal to the angle of reflection.

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(?)=m?for m=1,2,….

Part A

An x-ray beam with wavelength 0.240 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 22.5 ?. What is the spacing d between the planes of the crystal?

Express your answer in nanometers to four significant figures.

Part B

Find the angle ?subcript2at which you will find a second maximum.

Express your answer in degrees to three significant figures.