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Question

# A metal crystallizes into two cubic phases, face centered cubic (FCC) and body centered cubic (BCC), whose unit cell length are 4.5 ∘A and 3 ∘A, respectively. Calculate the ratio of the densities of the BCC to the FCC lattice.

A
1.69
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B
2.66
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C
2.25
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D
1.25
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Solution

## The correct option is A 1.69We know that, total number of atoms per unit cell of FCC is 4 and total number of atoms per unit cell of BCC is 2 So, density in FCC=n1×atomic weightV1×NA Where, V1=volume of unit cell=a3=(4.5×10−8)3 So, density in BCC=n2×atomic weightV2×NA Where, V2=volume of unit cell=a3=(3×10−8)3 Hence, DBCCDFCC=n1×V2n2×V1=2×(4.5×10−8)34×(3×10−8)3=1.69

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