Question

A metal (atomic mass $=50g$) has a body-centered cubic crystal structure. The density of metal is $5.96$ g cm${}^{-3}$. Find the volume (in cm${}^3$) of the unit cell.

• A. $13.9\times {10}^{-24}$
• B. $27.8\times {10}^{-24}$
• C. $6.95\times {10}^{-24}$
• D. $55.6\times {10}^{-24}$

Answer 1

Answer: (B)

Correct option: (B)

Analyzing the given data:

Number of atoms in BCC structure $=2$

Mass of metal $=50gmo{l}^{-1}$

Density of crystal $=5.96gc{m}^{-3}$

Avogadro number $=6.022\times {10}^{23}atoms/mol$

$\text{Density}=\frac{Z\times M}{N_A\times a^3}$

$5.96gc{m}^{-3}=\frac{2\times 50g/mol}{6.022\times {10}^{23}atoms/mol\times a^3}$
$a^3=\frac{100}{6.022\times {10}^{23}\times 5.96}$

$a^3=2.78\times {10}^{-23}=27.8\times {10}^{-24}c{m}^3$
Hence, the volume of the unit cell is $27.8\times {10}^{-24}$ cm${}^3$.