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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?

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

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Answer: 1.26
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$
answered Jul 15, 2014 by balaji.thirumalai
edited Jul 15, 2014 by balaji.thirumalai

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