When an x-ray beam is scattered off the planes of a crystal, the scattered beam creates an interference pattern. This ph

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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:
2dsin(θ)=mλfor m=1,2,…2dsin⁡(θ)=mλfor m=1,2,….
The path difference 2dsin(θ)2dsin⁡(θ) can be
determined from the diagram (Figure 1). The second condition
is known as the Bragg condition.
Part A
An x-ray beam with wavelength 0.280 nmnm is directed
at a crystal. As the angle of incidence increases, you observe the
first strong interference maximum at an angle 22.0 ∘∘. What is
the spacing ddd between the planes of the crystal?
Express your answer in nanometers to four significant
figures.
Part B
Find the angle θ2θ2theta_2 at which you will find a
second maximum.
Express your answer in degrees to three significant figures.