Answer to Question #102249 in Optics for BIVEK

Question

The Bragg reflection angle from the (110) planes in bcc iron is 22° for an x-ray
beam with lemda= 1.54 Å. Calculate the lattice constant for iron (take n = 1).

Answer 1

We know that Bragg's law,

$\lambda=2d\sin\theta$

$\Rightarrow d=\dfrac{1.54\times10^{-10}}{2\sin22^\circ}=\dfrac{1.54\times 10^{-10}}{0.74}=2.08\times10^{-10}m$

$d_{hbl}=\dfrac{d}{\sqrt{d^2+h^2+l^2}}$ in a bcc lattic.

$d_{hbl}=d\sqrt{2}=2.08\times \sqrt{2} A^{o}=2.94A^{o}$