Question

A metal crystallizes into two cubic phases, face-centered cubic and body-centered cubic which have unit cell lengths as $3.5\mathring{A}$ and $3.0\mathring{A}$, respectively. Calculate the ratio of densities of fcc and bcc.

• A. $1.26$
• B. $3.25$
• C. $\sqrt{2}$
• D. None of the above

Answer 1

The correct option is A $1.26$

As we know,
Density $\left(\rho \right)=\frac{Z_{eff}\times Mw}{a^3\times N_A}$

For fcc, $Z_{eff}=4$
${\rho }_{fcc}=\frac{4\times Mw}{(3.5\times {10}^{-8}{)}^3\times N_A}$

For bcc, $Z_{eff}=2$
${\rho }_{fcc}=\frac{2\times Mw}{(3\times {10}^{-8}{)}^3\times N_A}$

$\frac{{\rho }_{fcc}}{{\rho }_{bcc}}=\frac{4\times (3{)}^3}{(3.5{)}^3\times 2}=1.26$