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

Explanation

C = 4r
From `Delta^("le")EFD`
`" "FD^(2)=ED^(2)+EF^(2)`
`" "b^(2)=a^(2)+a^(2)=2a^(2)`
From `Delta^("le")AFD`,
`" "AF^(2)=FD^(2)+AD^(2)`
`" "C^(2)=b^(2)+a^(2)`
`" "C^(2)=2a^(2)+a^(2)=3a^(2)`
`" "a=c/sqrt(3)" "therefore a=(4r)/sqrt(3)`
Number of particles per unit cell in BCC = 2
`therefore` Volume occupied by the particles `=2 times 4/3 pir^(3)`
Volume of the unit cell `=a^(3)=((4r)/sqrt(3))^(3)`
`therefore` Packing efficiency `="Volume occupied by 2 particle"/"Volume of unit cell" times 100`
`" "=(2 times 4/3pir^(3))/((64r^(3))/(3sqrt(3)))=68%`