Question

A metal crystallizes into two cubic phases , face-centred cubic (fcc) and body -centred cubic (bcc) whose unit cell lengths are 3.5 and 3.0 Å respectively. Calculate the ratio of the densities of fcc and bcc.

Answer 1

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`