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Question

# A metal crystallises into two cubic phases, face center cubic (fcc) and body centered cubic (bcc), whose unit cell lengths are 3.5˚A and 3.0˚A, respectively. The ratio of densities of (bcc) is:

A
1.259 : 1
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B
1 : 1.259
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C
3 : 2
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D
1.142 : 1
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Solution

## The correct option is A 1.259 : 1Theoretical density of crystal, ρ=nMNoa3 g/cm3 For fcc, n=4; a=3.5×10−8 cm So, ρ1=4×MNo×(3.5)3×(10−8)3 g/cm3.....(i) For bcc, n=2; a=3×10−8 cm So, ρ2=2×MNo×(3)3×(10−8)3 g/cm3.....(ii) So (i)/(ii) ⇒ρ(fcc)ρ(bcc)=4×(3)32×(3.5)3=2×2742.875=1.2591Hence, Option "A" is the correct answer.

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