Question

Powder diffraction experiments on samples of lead with X-rays of wavelength 1.44 $\text{\AA}$ produce (220) reflection at an angle of $32^\circ$. The lattice parameter of Lead is:

• A. 1.44 $\text{\AA}$
• B. 2.88 $\text{\AA}$
• C. 3.94 $\text{\AA}$
• D. 4.02 $\text{\AA}$

Answer 1

The Correct Option is C

Bragg's law is:
\[ n\lambda = 2d \sin \theta \]
For the (220) reflection, the interplanar spacing $d$ is determined using $d = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$, where $h=k=2$, $l=0$, and $a$ is the lattice parameter:
\[ d = \frac{1.44}{2 \sin(32^\circ)} \approx 3.94 \ \text{\AA} \]