When an x-ray beam is scattered off the planes of a crystal, the scattered beam

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:

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()=mfor m=1,2,….

The path difference 2dsin() 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 0.300 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 20.5 . What is the spacing d between the planes of the crystal?

d= ? nm

Part B

Find the angle 2 at which you will find a second maximum.

Express your answer in degrees to three significant figures.

Explanation / Answer

2dsin()=m

Where m= order of maximum,

a)

m=1, = 0.3 nm, = 20.5°

Therfore,

d=m/(2*sin())

d= 1*0.3*10-9/(2*sin(20.5)

d= 0.428* 10-9 m

b)

Here second maximum is m=2 with the same d,,

2= sin-1(m/2d)

= 44.5°

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