What was the wavelength of the X-ray radiation in nm ?

Question

For a certain crystal X-ray diffraction showed the distance between the layer of atoms was 230 pm. If the crytal was held at an angle of 20.0o to the beam. What was the wavelength of the X-ray radiation in nm ?

Answer 1

From the theory of diffraction and constructive interference, the difference in path lengths between rays reflected at different angles has to be equal to the wavelength (actually, any whole number of wavelengths, but I assume you want the longest wavelength).

By geometry (there should be a diagram of this in your text), this gives you

wavelength = 2 d sin theta

where in this case d = 230 pm = 0.230 nm, theta = 20.0o

if "held at an angle" means what I think it means.

Actually, the question is inside out. People usually do this experiment to find out the spacing from the wavelength, not the other way round.