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,….

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,….

https://session.masteringphysics.com/problemAsset/1332603/5/1332603.jpg

Part A

An x-ray beam with wavelength 0.150 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 67.0 . What is the spacing dbetween 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.

Express your answer in degrees to three significant figures.

i got 0.185 they said it wrong and i tried 1.84*10^-11 it still wrong.

i need help please .

Explanation / Answer

A)

Use eqn,

2dcos=m

Plug m=1, =67.0 deg, =0.150nm

2*d*cos67=1*0.150*10^-9

d=1.92*10^-10 m = 19.2 nm

B)

Use eqn,

2dcos=m

Plug m=2, =0.150nm , d=19.2nm

2*19.2*10^-9*cos=2*0.150*10^-9

cos=(2*0.150*10^-9)/(2*19.2*10^-9)

cos=0.00125

=cos^-1(0.0078125)

= 89.6deg

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