The metal rhodium (Rh) has an FCC crystal structure. If the angle of diffraction for the (311) set of planes occurs at 36.12° (first-order reflection) when monochromatic x-radiation having a wavelength of 0.0711 nm is used, compute the following:
(a) the interplanar spacing for this set of planes, and (b) the atomic radius for a rhodium atom.

Explanation:

Part (a) the interplanar spacing for this set of planes

Applying Bragg's law

where;

d is the distance between set of planes

λ is the wavelength of  monochromatic x-radiation = 0.0711 nm

n is the reaction order = 1

θ is the diffraction angle = 36.12°

Part (b) the atomic radius for a rhodium atom.

Also, a = 2R√2

R = a/(2√2)

R = 0.19999/(2√2)

R = 0.0707 nm