Percentage of free space in cubic close packed struchure and in body centred structure are respectively.

Options

A. 48% and 26%
B. 30% and 26%
C. 26% and 32%
D. 32% and 48%

Answer

C

Explanation

For FCC or CCP
`4r=sqrt(2)a`
`P . F =(nxx(4)/(3)pir^(3))/(a^(3))`
`n=4,a=2sqrt(2r)`
P.F. = 74%
Free space = 100 - 74 = 26%
For BCC
`4r=sqrt(3)a`
P.E. `=(2xx(4)/(3)pir^(3))/((4)/(sqrt(3))r)^(3)`
P.F. = 68%
Free space = 32%