Question

When heated above ${916}^{\circ }C$, iron changes its BCC crystalline form to FCC without the change in the radius of atom. The ratio of density of the crystal before heating and after heating is (Given : $\sqrt{3}=1.73and\sqrt{2}=1.41$):

• A. $1.069$
• B. $0.917$
• C. $0.725$
• D. $1.231$

Answer 1

The correct option is B $0.917$

$\text{Density}=\frac{z\times M}{a^3\times N_A}$
where
$z=\text{number of atoms in the unit cell}M=\text{molecular mass}a=\text{edge length of the unit cell}{N}_A=\text{Avogardo's number}$
In BCC,
$a=\frac{4r}{\sqrt{3}}$
In FCC,
$a=\frac{4r}{\sqrt{2}}$
$\therefore \frac{d_{BCC}}{d_{FCC}}=\frac{(2M\times 3\sqrt{3}/(N_A\times 64r^3\left)\right)}{(4M\times 2\sqrt{2}/(N_A\times 64r^3\left)\right)}=0.917$