Question

A metal crystallises into two cubic phases, face-centred cubic(FCC) and body-centred cubic(BCC), whose unit cell lenghts are $3.5\stackrel{\circ }{\text{A}}\text{and}3.0\stackrel{\circ }{\text{A}}$, respectively. Calculate the ratio of the densities of FCC and BCC.

• A. $1.34$
• B. $2.26$
• C. $1.26$
• D. $2.75$

Answer 1

The correct option is C $1.26$

Given,
Edge length of $FCC=3.5\stackrel{\circ }{\text{A}}$;
Edge length of $BCC=3.0\stackrel{\circ }{\text{A}}$
$\frac{{\text{Density}}_{FCC}}{{\text{Density}}_{BCC}}=\frac{{\left(\frac{Z_{eff}\times M}{N_A\times a^3}\right)}_{FCC}}{{\left(\frac{Z_{eff}\times M}{N_A\times a^3}\right)}_{BCC}}$
$\frac{{\text{Density}}_{FCC}}{{\text{Density}}_{BCC}}={\left(\frac{Z_{eff}}{a^3}\right)}_{FCC}\times {\left(\frac{a^3}{Z_{eff}}\right)}_{BCC}=\frac{4\times (3\stackrel{\circ }{\text{A}}{)}^3}{2\times (3.5\stackrel{\circ }{\text{A}}{)}^3}$
$\frac{{\rho }_{FCC}}{{\rho }_{BCC}}=1.26$
Thus, option (c) is the correct answer.