Calculate the number of particles in Body Centered Cubic (BCC) lattice.

Explanation

In `/_\ABG`
`b^2=a^2+a^2" ":.b^2=2a^2`
In `/_\AGD`
`C^2=a^2+b^2=a^2+2a^2" ":.C=sqrt(3a)`
Radius of the atom=r
Length of the body diagonal C=4r
`sqrt3a=4r,a=(4r)/(sqrt3)`
Edge length of the cube`=a=(4r)/(sqrt3)`
Volume of the cubic unit cell`=a^3=((4r)/(sqrt3))^3`
Volume of one particle (sphere)`=4/3pir^3`
The number of particles per unit cell of a BCC=2
Total volume occupied by two spheres`=2xx4/3pir^3`
Packing efficiency`=("Total volume occupied by the two spheres")/("Volume of a cubic unit cell")xx100`
`(4/3pir^3xx2)/((4/(sqrt3)r)^3)xx100=(8/3pir^3)/((64)/(3sqrt3)r^3)xx100=68%`