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: 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, An x-ray beam with wavelength 0.290 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 64.5 degree. What is the spacing d between the planes of the crystal? Express your answer in nanometers to three significant figures. d = .161 nm Find the angle theta_2 at which you will find a second maximum. Express your answer in degrees to three significant figures. Theta_2 = ____

Explanation / Answer

Part A:

2dsin() = m

2d * sin(64.5) = 1 * 0.290
d = 0.1606 nm

Part B:

2d * sin(64.5) = 1 * 0.290
2 * sin(64.5) * sin() = 2 * 0.290
sin() = 0.3213
= 18.74°

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