Question

Statement: The relation between the d-spacing formula and Bragg's equation for a cubic crystal for first-order reflection is given by the relation:

$\text{sin}\theta =\frac{\lambda }{2a}(h^2+k^2+l^2{)}^{\frac{1}{2}}$

State whether the given statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

We know that for a cubic crystal,

$d=\frac{a}{\sqrt{h^2+k^2+l^2}}$ $....\left(i\right)$, where $a=$ lattice parameter and $h,k,l=$ Miller indices

For first order reflection, $n=1$

Bragg's equation is as follows:

$n\lambda =2d_{\text{hkl sin}}\theta$ $....\left(ii\right)$

From equations $\left(i\right)$ and $\left(ii\right)$, we get

$sin\theta =\frac{\lambda }{2a}(h^2+k^2+l^2{)}^{\frac{1}{2}}$

Hence, the given statement is $\text{true}$