Using X-ray Diffraction When an x-ray beam is scattered off the planes of a crys

Question

Using X-ray Diffraction 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, 2d cos( heta) = m lambda qquad hbox{for } m=1,2, dots. The path difference 2dcos( heta) can be determined from the diagram (Figure 1) . The second condition is known as the Bragg condition. Part A An x-ray beam with wavelength 0.130nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 67.0^circ. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. d = { m nm} SubmitMy AnswersGive Up Try Again; 4 attempts remaining Part B Find the angle theta_2 at which you will find a second maximum. Express your answer in degrees to three significant figures. theta_2 = ^circ SubmitMy AnswersGive Up Part C This question will be shown after you complete previous question(s).

Explanation / Answer

so 2d sin theta = lambda 2*d*cos(67)=0.13 d=0.1664 nm b) 2*0.1664*cos(x)=2*0.13 x=38.62 degrees

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