Question

The density of chromium metal is $7.2$ g cm${}^{-3}$. If the unit cell is cubic with edge length of $289$ pm, determine the type of unit cell (simple, body centred or face centred).

[Atomic mass of $Cr=52$ amu, $N_A=6.02\times {10}^{23}$ mol${}^{-1}$]

• A. SC
• B. BCC
• C. FCC
• D. HCP

Answer 1

Answer: (B)

BCC

The expression for density is as follows:

Density $=d=\frac{n\times M}{a^3\times N_A}$

GIven: $d=7.2$ g cm${}^{-3}$
$a=289$ pm $=289\times {10}^{-10}$ cm
Molecular weight of Cr $=52$ g mol${}^{-1}$
$n=\frac{d\times a^3\times N_A}{M}=\frac{7.2\times (289\times {10}^{-10}{)}^3\times 6.023\times {10}^{23}}{52}$
$n=\frac{7.2\times 2.41\times {10}^{-23}\times 6.023\times {10}^{23}}{52}$
$n=\frac{7.2\times 2.41\times 6.023}{52}=2$
Since there are $2$ Cr atoms in a unit cell, Cr crystallizes in bcc unit cell.