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. ` 65 % `
B. ` 45 % `
C. `90 % `
D. `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 2 sqrt 3 r _ A = a rArr p.f. = (1 xx (4 ) /(3) pi r _ A^ 3 + (4 ) /(3) pi (8r_A^ 3 )) /(8 xx 3 sqrt3 r _ A^ 3 ) = ( 9 xx (4 ) /(3) pi ) /(8 xx 3 sqrt 3 ) = ( pi ) /(2 sqrt 3 ) `
P.F. = ` ( pi ) /(2 sqrt 3 ) xx 100 = 90 % `