Question

Determine the expected diffraction angle for the first-order reflection from the (310) set of planes for bcc chromium when monochromatic radiation of wavelength 0.0735 nm is used. the atomic radius for cr is 0.1249 nm.

Answer 1

Answer : $\theta=42.84\ ^0$

Explanation :

It is given that,

Wavelength, $\lambda=0.0735\ nm=0.0735\times 10^{-9}\ m$

According to bragg's law:

$2d\ sin\theta=n\lambda$

d is inter planer spacing for (310) planes such that :

$d=\dfrac{a}{\sqrt{(3)^2+(1)^2+(0)^2} }$

$d=\dfrac{a}{\sqrt{10} }$

a is lattice parameter, $a=\dfrac{4R}{\sqrt{3}}=0.2884\ nm$

R is atomic radius and for BCC $R=0.1249\ nm$

So, $d_{310}=0.0912\ nm$

$sin\theta=\dfrac{1\times 0.1249\ nm}{2\times 0.0912\ nm}$

$sin\theta=\dfrac{0.1249}{0.1824}$

$sin\theta=0.68$

$\theta=42.84\ ^0$

Hence, this is the required solution.