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 `3.0Å` . Respectively . Calculate the ratio of densities of fcc and bcc.

Answer 1

Correct Answer - 1.259 or 1.259:1
Unit cell length of fcc =3.5 `overset(@)A`
unit cell length of bcc `=3.0 overset(@)A`
`therefore` Density in fcc `=(n_(1)xxat. Wt.)/(V_(1)xxN_(0))`
Density in bcc `=(n_(2)xxat.wt.)/(V_(1)xxN_(0))`
Or `("Density(fcc"))/("Density(bcc"))=(n_(1))/(n_(2))xx(V_(2))/(V_(1))=(4)/(2)xx(V_(2))/(V_(!))[For fcc, `n_(1)=4` for bcc, `n_(2)=2`]
Volume for fcc `=V_(1)=a^(3)=(3.5xx10^(-8))^(3)cm^(3)`
`therefore `("Density(fcc"))/("Density(bcc"))=(4)/(2)xx((3.0xx10^(-8))^(3))/((3.5xx10^(-8))^(3))=1.259`
or `1.259:1`