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A metal crystallizes into two cubic phas...

A metal crystallizes into two cubic phases, face-centred cubic and body-centred cubic, which have unit cell lengths `3.5` and `3.0 A`, respectively. Calculate the ration of densities of fcc and bcc.

Text Solution

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Density `(rho)=(ZxxM)/(a^3xxN_0)`
For fcc, Z=4,a=3.5 Å =`3.5xx10^(-8)` cm
`therefore rho_"fcc"=(4xxM)/((3.5xx10^(-8))xxN_0)`
For bcc, Z=2, a=3.0 Å =`3.0xx10^(-8)`cm
`therefore rho_"bcc"=(2xxM)/((3.0xx10^(-8))^3xxN_0) therefore rho_"fcc"/rho_"bcc"=(4xx(3.0xx10^(-8))^3)/(2xx(3.5xx10^(-8))^3)=1.259`
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