Question

The $\text{γ}$ - form of iron has fcc structure (edge length 386 pm) and $\text{β}$ - form has bcc structure (edge length 290 pm). The ratio of density in $\text{γ}$ - form and $\text{β}$ - form is :

• A. 0.848
• B. 1.02
• C. 1.57
• D. 0.6344

Answer 1

Answer: (A)

$\frac{\text{d}_{\gamma }}{\text{d}_{\beta }} = \frac{\text{d}_{\text{fcc}}}{\text{d}_{\text{bcc}}}$
$= \frac{4 \times \frac{\text{A}}{\left(\text{N}\right)_{\text{a}}} \times \frac{1}{\text{a}_{\text{fcc}}^{3}}}{2 \times \frac{\text{A}}{\left(\text{N}\right)_{\text{a}}} \times \frac{1}{\text{a}_{\text{bcc}}^{3}}} = 2 \left(\frac{\left(\text{a}\right)_{\text{bcc}}}{\left(\text{a}\right)_{\text{fcc}}}\right)^{3}$
$= 2 \times \left(\frac{2 9 0}{3 8 6}\right)^{3} = \text{0.848}$