Question

The density of chromium metal is $7.2{\text{g cm}}^{-3}$. If the unit cell is cubic with an edge length of 289 pm, determine the type of unit cell (simple, body centred or face centred). [Atomic mass of $Cr=52\text{amu},N_A=6.02\times {10}^{23}{\text{mol}}^{-1}]$

• A. SC
• B. BCC
• C. FCC
• D. HCP

Answer 1

The correct option is B BCC

The expression for density is as follows:
Density =d=$\frac{n\times MM}{a^3\times NA}$
Given: d =7.2 $gc{m}^{-3}$
a = 289 pm =$289\times {10}^{-10}cm$
Molecular weight of Cr = 52 $gmo{l}^{-1}$
$n=\frac{d\times a^3\times N_A}{MM}$
$n=\frac{7.2\times (289\times {10}^{-10}{)}^3\times 6.02\times {10}^{23}}{52}$
n = 2
​
Since there are 2 $Cr$ atoms in a unit cell, $Cr$ crystallizes in a bcc unit cell.