Iron exhibits bcc structure at room temperatutre .Above `900^(@)C` .it transitions to fcc structure .The ratio of density of ions at room temperature to that at `900^(@)C`(assuming molar mass and atomic , radii of ion remain s constant with temperature ) is

Options

A. `sqrt(3)/sqrt(2)`
B. `(4sqrt(3))/(3sqrt(2))`
C. `(3sqrt(3))/(4sqrt(2))`
D. `1/2`

Answer

C

Explanation

`d_(b)/d_(f) = ((2M)/(a_(b)^(3)N_(A)))/((4M)/(a_(f)N_(A))) = 2/a_(b)^(3) xx a_(f)^(3)/4, b rArr bc c, f rArr fc c`
`=1/2[a_(f)/a_(b)]^(3) =1/2 [((4r)/sqrt(2))^(3)/((4r)/sqrt(3))^(3)]`
`=1/2 (sqrt(3)/sqrt(2))^(3) = 1/2 (3sqrt(3))/(2sqrt(2)) =(3sqrt(3))/(4sqrt(2))`