Question

An element (atomic mass = $100g/mole$) having $BCC$ structure has an edge length of $400pm$. The density of the element is (no. of atoms in $BC{C}_Z=2$).

• A. $2.144g/c{m}^3$
• B. $5.2g/c{m}^3$
• C. $7.289g/c{m}^3$
• D. $10.376g/c{m}^3$

Answer 1

The correct option is B $5.2g/c{m}^3$

Mass of a unit cell $=\frac{Z\times M}{N_A}$
Z is the number of atoms per unit cell which is 2 for BCC
M is the molar mass of the atom = 100 g/mol
$N_A$ is avagadro number
Volume of the unit cell $=a^3$
Here, a is the edge length = 400 pm
Density of a unit cell is given by
$\rho =\frac{Z\times M}{N_A\times a^3}$
i.e $\rho =\frac{2\times 100}{6\times {10}^{23}\times (400\times {10}^{-10}{)}^3}$ = $5.2g/c{m}^3$