a. Calculate the packing efficiency in a Body Centered Cubic (BCC) lattice.
b. Silver forms a ccp lattice. The edge length of its unit cell is 408.6 pm. Calculate the density of silver. `(N_(A)=6.022xx10^(23)," Atomic mass of Ag "=108 g mol^(-1))`

Explanation

bcc diagram.
Edge length `=a=(4r)/(sqrt(3))`
Packing efficiency`=("Volume of sphere" xx 2xx100)/("Volume of unit cell")`
`=((4)/(3)pi r^(3)xx2xx100)/((4)/(sqrt(3)J))=68%`
Detailed Answer:
Packing efficiency in body centred cubic (bcc) lattice.
The number of atoms per unit cell in bcc is two.
So, the volume of two atoms (two spheres) `=2xx(4)/(3)pi r^(3)`
Let the edge length a. be the radius of the sphere.
The body diagonal `" "AF=y`
and face diagonal `" " FD=b`,
Then `" "AF=y=4r`
In `DeltaEFD`

`FD^(2)=EF^(2)+ED^(2)`
`b^(2)=a^(2)+a^(2)=2a^(2)`
`b=sqrt(2)a`
Now in `DeltaAFD`
`AF^(2)=AD^(2)+FD^(2)`
`y^(2)=a^(2)+b^(2)`
`=a^(2)+2a^(2)=3a^(2)`
`y=sqrt(3)a`
But `y = 4r`
`:.sqrt(3)a=4r`
`a=(4r)/(sqrt(3))`
Volume of unit cell `=a^(3)+((4r)/(sqrt(3)))^(3)`
`:.`Paking efficiency `=("volume of two atoms in unit cell")/("volume of unit cell")xx100`
`=(2xx(4)/(3)pir^(3))/(((4r)/(sqrt(3)))^(3))xx100%=((8)/(3)pi r^(3))/((64pi r^(3))/(3sqrt(3)))xx 100%`
`=68%`