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,
.

The path difference can be determined from the diagram . The second condition is known as the Bragg condition

An x-ray beam with wavelength 0.280 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 27.5 degrees. What is the spacing d between the planes of the crystal in nm?

B) Find the angle Theta2 at which you will find a second maximum.

Explanation / Answer

d=(lamda/2sin(theta))

=0.280/(2*Sin27.5)=0.28/2*0.462=0.303nm

theta 2 = [ sin^-1(2sin(theta))]

=sin^-1(2*0.462)

=67.51 degrees

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