Iron exhibits `bcc` structure at roomj temperature. Above `9000^(@)C`, it transformers to `fcc` structure. The ratio of density of iron at room temperature to that at `900^(@)C` (assuming molar mass and atomic radii of iron remains constant with temperature) is

Options

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

Answer

C

Explanation

`d = (ZM)/(a^(3) N_(A))`
` {:("For bcc",|,"For fcc"),(Z=2,,Z=4),(4r=sqrt(3)a,,4r=sqrt(2)a),(ora=(4r)/(sqrt(3)),,or a=(4r)/(sqrt(2))):}`
`(d_("bcc"))/(d_("fcc")) = ((Z_("bcc")M)/((a_("bcc"))^(3) N_(A)))/((Z_("fcc") M)/((a_("fcc"))^(3) N_(A))) = (Z_("bcc") // (a_("bcc"))^(3))/(Z_("fcc")// (a_("fcc"))^(3))`
`((2)/((4r // sqrt3)^(3)))/((4)/((4r // sqrt3)^(3))) = (2)/(4) ((sqrt3)/(sqrt(2)))^(3) = (3)/(4) sqrt((3)/(2))`