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# A metal crystallizes in two cubic phases FCC and BCC with unit length equal to 350 pm and 300 pm. The ratio of densities of FCC and BCC is about?

$\begin{array}{1 1} 1.26 \\ 1.36 \\ 1.46 \\ 1.66 \end{array}$

The density is given by the formula $\large\frac{z\;M}{a^3\;N_A}$
Since $N_A$ and $M$ are the same in both cases, we can write the ratio of densities as follows: $\large\frac{\rho_{FCC}}{\rho_{BCC}}$$= \big (\large\frac{z}{a^3}\big)_{FCC}$$\times \big (\large\frac{a^3}{z}\big)_{BCC}$
$\Rightarrow \large\frac{\rho_{FCC}}{\rho_{BCC}}$$= \large\frac{4}{3.5^3}$$\times \large\frac{3^3}{2}$$= 1.26$
edited Jul 15, 2014