Question

An element crystallizes in BCC unit cell having molecular mass $50g/mol$ . Calculate the density of unit cell, if its edge length is $300pm$.
Take
$N_A=6\times {10}^{23}$

• A. $1.71gc{m}^{-3}$
• B. $3.42gc{m}^{-3}$
• C. $12.34gc{m}^{-3}$
• D. $6.17gc{m}^{-3}$

Answer 1

The correct option is D $6.17gc{m}^{-3}$

Density of the unit cell,
$\rho =\frac{Z\times M}{N_A(a^3\times {10}^{-30})}gc{m}^{-3}$
where,
$Z=\text{No. of atoms in a unit cell}M=\text{Molar mass}{N}_A=\text{Avagadro number}a\text{is edge length in pm}$
For BCC:
$Z=2$
$\rho =\frac{2\times 50}{6\times {10}^{23}\times (3^3\times {10}^{-24})}$
$\rho =6.17gc{m}^{-3}$