Q. A metal has bcc structure and the edge length of its unit cell is $3.04\ \mathring{\mathrm{A}}.$ The volume of the unit cell in $cm^{3}$ will be
A) $1.6 \times 10^{- 21}\ cm^{3}$
B) $2.81 \times 10^{- 23}\ cm^{3}$
C) $6.02{\times 10}^{- 23}\ cm^{3}$
D) $6.6 \times 10^{- 24}\ cm^{3}$
Explanation
(b)
Edge length $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \alpha = 3.04\ \mathring{\mathrm{A}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 3.04 \times 10^{- 8}\ cm$
Volume of bcc (cubic) cell $\ = a^{3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left( 3.04 \times 10^{- 8} \right)^{3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2.81 \times 10^{- 23}\ cm^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.