a) Calculate the packing efficiency of particles in a body centred cube. 

Explanation

In `DeltaEFD, b^(2)=a^(2)+a^(2)=2a^(2)`
`b=sqrt2.a`
`therefore DeltaAFDc^(2)=a^(2)+b^(2)=a^(2)+2a^(2)=3a^(2)`
The length of body diagonal c = 4r
`therefore 3a=4r`
`a=(4r)/(sqrt3)" "r=(sqrt3)/(4)a`
in bcc, total number of atoms in 2,
Their volume is `2xx((4)/(3))pir^(3)`
Volume of the cube `=a^(3)=((4r)/(sqrt3))^(3)`
`"Packing efficiency "=("Volume occupied by two spheres")/("Volume of unit cell")xx100=(2xx((4)/(3))pir^(3))/(((4)/(3)r)^(3))xx100=68%`