Question

An element (atomic mass = $100\text{u}$) having $BCC$ structure has an edge length of $400pm$. The density of the element is:

• A. $2.14{\text{g/cm}}^3$
• B. $5.21{\text{g/cm}}^3$
• C. $7.29{\text{g/cm}}^3$
• D. $10.38{\text{g/cm}}^3$

Answer 1

The correct option is B $5.21{\text{g/cm}}^3$

Mass of a unit cell $=\frac{Z\times M}{N_A}$
$Z$ is the effective number of atoms per unit cell which is $2$ for BCC
M is the molar mass of the atom = $100\text{g/mol}$
$N_A$ is avagadro number
Volume of the unit cell $=a^3$
Here, a is the edge length = $400\text{pm}$
Density of a unit cell is given by
$\rho =\frac{Z\times M}{N_A\times a^3}$
i.e $\rho =\frac{2\times 100}{6\times {10}^{23}\times (400\times {10}^{-10}{)}^3}=5.21g/c{m}^3$