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Question

An element crystallizes bothe in fcc and bcc lattices. If the density of the element in the two forms is the same, the ratio of unit cell volume of fcc to that of bcc lattice is:

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Solution

We know,
Density,d=z×MV×NA
For fcc, zeff=4
For bcc, zeff=2
dfcc=4×MVfcc×NA (i)
dbcc=2×MVbcc×NA (ii)
On dividing (i) by (ii)
dfccdbcc=4×MVfcc×NA2×MVbcc×NA
1=4×Vbcc2×Vfcc
Vfcc=2×Vbcc
VfccVbcc=2

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