Question

An x-ray beam with wavelength 0.300 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 24.5 degree. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. d = _____nm Find angle theta_2 at which you will find a second maximum. Express your answer in degrees to four significant figures. theta_2 = _____

Answer 1

Given

Wavelength is Lambda = 0.300 nm

angle for the first maximum is theta = 24.5 degrees

spacing between the planes of the crystal is d =?

Part A

From Bragg's law 2d sin theta = n *lambda

d = n*lambda/(2* sin theta)

for n =1

d = (1*0.3*10^-9)/(2*sin24.5) m

d = 3.617131522*10^-10 m

d = 0.3617131522 nm

Part B

for second maximum

d = n*lambda/(2* sin theta)

for n =2

d = (2*0.3*10^-9)/(2*sin24.5) m

d = 7.2342630*10^-10 m

d = 0.72342630 nm