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Q.

A metal crystallizes in 2 cubic phases face – centred cubic (FCC) and body – centred cubic (BCC) whose unit cell lengths are 3.5 A⁰ and 3.0 A⁰ respectively. The ratio of the densities of FCC and BCC is:

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a

0.72

b

2.04

c

1.26

d

3.12

answer is C.

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Detailed Solution

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$density of fcc = \frac{Z_{1} \times At . mass}{Av . no . \times V_{1}} density in bcc = \frac{Z_{2} \times At . mass}{Av . no . \times V_{2}} \frac{d_{fcc}}{d_{bcc}} = \frac{Z_{1}}{Z_{2}} \times \frac{V_{2}}{V_{1}} For fcc, Z_{1} = 4; V_{1} = a^{3} = {(3.5 \times 10^{- 8})}^{3} For bcc, Z_{2} = 2; V_{2} = a^{3} = {(3.0 \times 10^{- 8})}^{3} \frac{d_{fcc}}{d_{bcc}} = \frac{4 \times {(3.0 \times 10^{- 8})}^{3}}{2 \times {(3.5 \times 10^{- 8})}^{3}} = 1.259$

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