Element X crystallizes in a 12 co-ordination fcc lattice. On applying high temperature it changes to 8 coordination bcc lattice. Find the ratio of the density of the crystal lattice before and after applying high temperature?

Options

A. `1:1`
B. `3:2`
C. `sqrt2:sqrt3`
D. `2(sqrt2)^(3):(sqrt3)^(3)`

Answer

D

Explanation

12 coordination (fcc): 8 coordination (bcc)
`(4xxM_(x))/(N_(A)xxa^(3)):(2xxM_(x))/(N_(A)xxa^(3))` (Ratio of density)
For fcc, lattice, `a=(4r)/(sqrt(2)),` For bcc lattice, `4r=sqrt(3)aimplies a=(4r)/(sqrt(3))`
Ratio of density`=(4//N_(a)xxM_(x))/(((4r)/(sqrt2))^(3)):(2//N_(a)xxM_(x))/(((4r)/(sqrt3))^(3))=2xx(sqrt2)^(3):(sqrt3)^(3)`