When an x-ray beam is scattered off the planes of a crystal, the scattered beam
ID: 1263701 • Letter: W
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,
2dcos(?)=m?for m=1,2,
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, 2dcos(?)=m?for m=1,2,?. The path difference 2dcos(?) 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 0.220nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 62.5 degrees. 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 ?2 at which you will find a second maximum. Express your answer in degrees to three significant figures.Explanation / Answer
2dcos(A) = m(wavelength)
As A = 62.5 degrees, m = 1, solving dor d,
d = 0.2382 nm [ANSWER, PART A]
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Using this d, at m = 2,
A2 = Arccos [m * wavelength / [2d] ]
= 22.6 degrees [ANSWER]
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