Calculate the efficiency of packing in case of a metal of body centered cubic crystal .

Explanation

Packing efficiency in case of a metal of body centred cubic crystal :
in B.C.C. Crystal
`sqrt3 a = 4 r `
`a = (4r)/(sqrt3)`
In this structure total no. of atoms is 2 and their volume = `2 xx ((4)/(3)) pi r^(3)`
Volume of the cube = `a^(3) = ((4)/(sqrt3) ""r)^(3)`
Packing efficiency = `("Volume occupied by two spheres in unit cell")/("Volume of unit cell") xx 100`
`= (2 ((4)/(3)) pi r^(3) xx 100)/([((4)/(sqrt3))r]) = (((8)/(3))pi r^(3) xx 100)/(64 // (3sqrt3) r^(3)) = 68 %`