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,

2dcos()=mfor m=1,2,….

The path difference 2dcos() can be determined from the diagram (Figure 1) . The second condition is known as the Bragg condition.

A. An x-ray beam with wavelength 0.270 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 68.5 . What is the spacing d between the planes of the crystal?

Express your answer in nanometers to three significant figures.

Part B

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

Explanation / Answer

a)

Just use the formula given in the intro:

2dsin() = m

2d * sin(68.5) = 1 * 0.270 nm
d = 0.145 nm

b)

Just use the same formula, only change m to “2 and use the value of d that you found in Part A:

2 * 0.145 nm * sin() = 2 * 0.270 nm
sin() = 1.86

but here i think your given angle should be less.

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