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

Options

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

Answer

D

Explanation

Co. No. is 12 means it is f.c.c. lattice
Co. No. is 8 means it is b.c.c. lattice
f.c.c.
`rho_(1)=(4xxat.mass)/(N_(a)xxa_(1)^(3))` `" "rho_(2)=(2xxat.mass)/(N_(a)xxa_(2)^(3))`
`(rho_(1))/(rho_(2))=(4)/(2)xx(a_(2)^(3))/(a_(1)^(3))=(2xx((4r)/(sqrt(3)))^(3))/((2sqrt(2)r)^(3))`
`=(2xx4xx4xx4)/(2xx2xx2xx2xxsqrt(2)(3sqrt(3)))`
`=(4sqrt(2))/(3sqrt(3))=(2(sqrt(2))^(3))/((sqrt(3))^(3))`