A metal, under different sets of conditions, can crystallise in a face-centred cubic (fcc) structure with a unit cell edge length of 3.5Å and in a body-centered cubic (bcc) structure with a unit cell edge length of `3.0Å`. Find the ratio of the densities of fcc and bcc structures.

Explanation

We know, `rho=(ZxxM)/(Nxxa^(3))`
Suppose, the densities of fcc and bcc crystals are `rho_(1)andrho_(2)` respectively.
For an fcc crystal: `rho_(1)=(Mxx4)/(Nxx(3.5xx10^(-8))^(3))g*cm^(-3)`
For a bcc crystal: `rho_(2)=(Mxx2)/(Nxx(3xx10^(-8))^(3))g*cm^(-3)`
`therefore" "rho_(1)/rho_(2)=4/2xx((3xx10^(-8))^(3))/((3.5xx10^(-8))^(3))=1.26`