Question

The $\gamma$-form of iron has fcc structure (edge length $=386$ pm) and $\beta$-form has bcc structure (edge length $=290$ pm). The ratio of density in $\gamma$-form to that in $\beta$-form is :

• A. $0.85$
• B. $1.02$
• C. $1.57$
• D. $0.6344$

Answer 1

Answer: (A)

$0.85$

$\begin{array}{c}{Z}_{eff}\text{for}fcc=4\text{and forbcc}=2/\text{unit cell}\\ \frac{{\rho }_{\lambda }}{{\rho }_{\beta }}=\frac{{\rho }_{fcc}}{{\rho }_{fcc}}=\left(\frac{Z_{eff\left(fcc\right)}}{Z_{eff\left(bcc\right)}}\right)\times {\left(\frac{a_{bcc}}{a_{fcc}}\right)}^3\\ =\frac{4}{2}\times {\left(\frac{290}{386}\right)}^3=0.848\end{array}$