Answer to Question #84464 in Molecular Physics | Thermodynamics for Ra

Question

Calculate the first order x-ray diffraction angle from the (113) set of planes in fcc platinum which has a lattice parameter of 0.39 nm, given that the wavelength of the x-rays is 0.154 nm

Answer 1

Let’s determine the interplanar spacing for the (113) set of planes:

d_123=a/√(h^2+k^2+l^2 )=0.39/√((1)^2+(1)^2+(3)^2 )=0.12 (nm)

According to the Bragg’s Law,

nλ=2dsinθ

In our case n=1, d=d_123.

Thus:

sinθ=nλ/(2d_123 )=(1∙0.154)/(2∙0.12)=0.6417

The diffraction angle:

θ=40°

Finally,

2θ=80°