Q. The cubic unit cell of Al$\ \left( molar\ mass\ 27\ g\ {mol}^{- 1} \right)$has an edge length of 405 pm. Its density is 2.7 g ${cm}^{- 3}.$ The cubic unit cell is
A) Face centred
B) Body centred
C) Primitive
D) Edge centred
Explanation
(a)
Density$\ (\rho) = \frac{Z \times M}{a^{3} \times N_{0}}$
$2.7 = \frac{Z \times 27}{\left( 405 \times 10^{- 10} \right)^{3} \times 6.023 \times 10^{23}}$
$\ \ \ Z = \frac{2.7 \times (405)^{3} \times 10^{- 30} \times 6.023 \times 10^{23}}{27} = 4$
For face centred cubic unit cell, number of atoms are 4.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.