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)

$\frac{{\text{d}}_{\gamma }}{{\text{d}}_{\beta }}=\frac{{\text{d}}_{\text{fcc}}}{{\text{d}}_{\text{bcc}}}$
$=\frac{4\times \frac{\text{A}}{{\left(\text{N}\right)}_{\text{a}}}\times \frac{1}{{\text{a}}_{\text{fcc}}^3}}{2\times \frac{\text{A}}{{\left(\text{N}\right)}_{\text{a}}}\times \frac{1}{{\text{a}}_{\text{bcc}}^3}}=2{\left(\frac{{\left(\text{a}\right)}_{\text{bcc}}}{{\left(\text{a}\right)}_{\text{fcc}}}\right)}^3$
$=2\times {\left(\frac{290}{386}\right)}^3=\text{0.848}$