Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. the unit cell edge length is `50%` more in soild 2 than in 1 . What is the approximate packing efficiency in solid 2?

Options

A. 0.65
B. 0.45
C. 0.9
D. 0.75

Explanation

P.F. `((z_(eff) xx (4)/(3) pi r_(A)^(3))_(A) + ( z_(eff) xx (4)/(3) pi r_(B)^(3))_(B) )/(a^(3))`
` 2(r_(A) + r_(B)) = sqrt(3) a `
`rArr " " 2(r_(A) + 2r_(A)) = sqrt(3a)`
`rArr " " 2sqrt(3) r_(A) = a `
`rArr " " P.F. = (1 xx (4)/(3) pi r_(A)^(3) + (4)/(3) pi(8 r_(A)^(3)))/(8 xx 3sqrt(3) r_(A)^(3) ) = ( 9 xx (4)/(3) pi )/(8 xx 3 sqrt(3)) = (pi)/(2sqrt(3))`
`P.F. = (pi)/(2sqrt(3)) xx 100 = 90` %