Question

An element having atomic mass $52$ amu occurs in body-centered cubic (bcc) structure with a unit cell edge of $288$ pm. The density of the element is $7.2$ g cm${}^{-3}$. Evaluate Avogadro's number $\left(N_o\right)$.

• A. $2.05\times {10}^{24}$
• B. $3\times {10}^{21}$
• C. $6.02\times {10}^{23}$
• D. $6.04\times {10}^{23}$

Answer 1

The correct option is D $6.04\times {10}^{23}$

Edge length $\left(a\right)$ of unit cell $=288$ pm $=288\times {10}^{-10}$ cm

Volume $\left(V\right)$ of the unit cell $a^3=(288\times {10}^{-10}{)}^3$ $=23.9\times {10}^{-24}$ cm${}^3$
$\text{Density of the unit cell}=\frac{\text{Mass of the unit cell}}{\text{Volume of the unit cell}}$ $=\frac{z\times \text{Atomic mass}}{N_o\times V}$
For bcc structure, z= 2

$7.2=\frac{2\times 52}{N_0\times 23.9\times {10}^{-24}}$ g cm${}^{-3}$
(The density of the unit cell is the same as the density of the element.)
$N_o=\frac{2\times 52}{23.9\times {10}^{-24}\times 7.2}=6.04\times {10}^{23}$

Hence, the correct option is $\text{D}$