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A metal crystallizes into two cubic phases, face centred cubic (FCC) and body-centred cubic (BCC) whose unit cell lengths are 3.5 and 3.0 A⁰respectively. The ratio of the densities of FCC and BCC is ___

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detailed solution

1.26

Given, Metal Crystallizes
We need to find the ratio of the densities of FCC and BCC is, from the given option.

$Density (ρ) = \frac{Z_{eff} \times Mw}{a^{3} \times N_{A}} fcc, Z_{eff} = 4 ρ_{fcc} = \frac{4 \times Mw}{{(3.5 \times 10^{- 8})}^{3} \times N_{A}} For bcc, Z_{eff} = 2 \begin{array}{l} ρ_{fcc} = \frac{2 \times Mw}{{(3 \times 10^{- 8})}^{3} \times N_{A}} \\ \frac{ρ_{fcc}}{ρ_{bcc}} = \frac{4 \times (3)^{3}}{(3.5)^{3} \times 2} = 1.26 \end{array}$

Therefore, the correct answer is 1.26

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