Question

A)

An x-ray beam with wavelength 0.120 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 d between the planes of the crystal?

B)

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

Answer 1

A.)

Since in interference position of maxima is given by Bragg's law,

2*d*sin(theta) = n*lamda

here, d = spacing between planes = ??

theta = position = 67 deg

n = number of maxima = 1

lamda = wavelength = 0.120 nm = 1.2*10^-10 m

So,

d = 1*(1.2*10^-10)/(2*sin(67 deg))

d = 6.5*10^-11 m

d = 0.065 nm

B.)

now for second maxima,

n = 2

then, sin(theta) = (n*lamda)/(2*d)

sin(theta) = (2*1.2*10^-10)/(2*6.5*10^-11)

sin(theta) = 1.85

Since value of sin (theta) can not be greater than 1, So there will be no 2nd maximum.

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