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

Let .a. be the edge length of unit cell
.r. be the radius of each particle
From `hat(EFD):b^(2)=a^(2)+a^(2)=2a^(2)`
From `hat(AFD),c^(2)=b^(2)+a^(2)`
`=2a^(2)+a^(2)rArr 3a^(2)`
`c=4r`
`4r=sqrt3a`
`a=(4r)/(sqrt3)`
`"Volume of cubic unit cell "=a^(3)=((4r)/(sqrt3))^(3)`
`"Number of particles per BCC unit cell"=2`
`"Packing efficiency"=("Volume occupied by 2 particles "xx100)/("Volume of unit cell")=(2xx4pir^(3))/(3xx((4r)/(sqrt3))^(3))xx100=68%`
b. Given :
a = 408.6 pm
`d=?`
`M=108gmol^(-1)z=4`
`N_(A)=6.022xx10^(23)`
`d=(zm)/(a^(3).NA)=(4xx108)/((408.6)^(3)xx6.022xx10^(23)xx10^(-30))`
`d=10.5gcm^(-1)`