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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
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))`