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:

2dcos(theta)=m*(wavelength) j for m=1,2.........

Part A:

An x-ray beam with wavelength 0.250nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 66.0 degrees. What is the spacing d between the planes of the crystal (4 sig figs)?

Find the angle theta at which you will find a second maximum (3 sig figs)?

Explanation / Answer

A) 2d cos theta = m*wavelength

here, m=1,

2d*cos 66 = 0.25*10^-9

then d = 3.07*10^-10 m = 0.307 nm.

B)for , second maxima,

2d*cos theta = m*wavelength

here, m=2

2* 3.07*10^-10*cos theta = 2*0.25*10^-9

then theta = 35.4786 degrees.

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