A Metal crystallises into two cubic faces namely face centered (fcc) and body centered (bcc). Whose unit cell edge length are `3.5 Å` respectively .Fi

Correct Answer - Ratio of densities `.(d_(fc c))/(d_(bc c)) =1.26`
Edge length of unit cell of fcc metal `=3.5 Å = 3.5 Å = 3.5 xx 10^(-8)` cm
Edge length of unit cell of the bcc metal `=3 Å = 3 xx 10^(-8) cm`
Density `d= (z xx M)/(a^(3) xx N_(A))`
Where z= Number of the Fe atoms in the unit cell
M= atomic mass of metal
a= Edge length of unit cell
`N_(A) =` Avogadro number
`:.` For fcc unit cell = z =4
For bcc unit cell = z= 2
`:. ("Density of fcc unit cell ")/("Density of bcc unit cell") = (d_("fcc"))/(d_("bcc"))`
`(z_("fcc")xx M)/(a_("fcc")^(3)) xx (N_(A))/(z_("bcc")xxM)(a_("bcc")^(3))xx N_(A)`
`=(z_("fcc"))/(z_("bcc")).(a_("bcc"))/(a_("fcc")^(3))`
`=(4)/(2) (3xx10^(-8))/(3.5xx 10^(-8))`
`= 1.26`