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.

Explanation

`f.c.c.` unit cell length `=3.5`Å
`b.c.c.` unit cell length `=3.0`Å
Density in `f.c.c. (z_(1)xxat.wt.)/(V_(1)xxAv. no .)`
Density in `b.c.c. (z_(2)xxat.wt.)/(V_(2)xxAv. no .)`
`rho_(f.c.c.)/(rho_(b.c.c.))=(z_(1))/(z_(2))xx(V_(2))/(V_(1))`
Now, `z_(1)` for `f.c.c.=4,`
Also, `V_(1)=a^(3)=(3.5xx10^(-8))^(3)`
`z_(2)` for `b.c.c.=2,`
Also, `V_(2)=a^(2)=(3.0xx10^(-8))^(3)`
`(rho_(f.c.c.))/(rho_(b.c.c.))=(4xx(3.0xx10^(-8))^(3))/(2xx(3.5xx10^(-8)))=1.259`