In face-centred cubic (FCC) and body centred cubic (BCC), whose unit cell lengths are 3.5 and 3.0 Å respectively, a metal crystallises into two cubic phases. What is the ratio of densities of FCC and BCC?

Options

A. `1. 259`
B. `3. 0`
C. `12.5`
D. `0. 59`

Answer

A

Explanation

`d _( F C C ) = Z _( F C C ) xx (( M )/( N _(A))) xx (1)/( ( a _( F C C ))^(3))`
` d _( B C C) = Z _( B C C ) (( M )/( N _(A))) (1)/( a _(B C C ) ^(3))`
`(d _( F C C ))/( d _( B C C)) = ( Z _( F C C ))/( Z _( B C C )) xx ( a _( B C C )^(2))/( a _(F C C ^(3)))`
`= (4)/(2) xx (( 3. 0 )/( 3. 5)) ^(3)`
`= 2 xx 0 . 6295`
`= 1. 259`