Calculate the packing fraction for the Ca unit cell, given that Ca crystallizes in a face-centered cubic unit cell.

Explanation

One-eight of each corner atom and one-half of each face-centered atom are contained within the unit cell of Ca giving
`Z=8xx((1)/(8))+6xx((1)/(2))=4`
Further, atomic radius, `r=(sqrt2a)/(4)`
Volume of 4 atoms `=4xx(4)/(3)pir=4xx(4)/(3)xxpi((sqrt(2)a)/(4))^(3)=(sqrt(2)pia^(3))/(6)`
Packing fraction `=(sqrt(2)pia^(3))/(6)//a^(3)=(sqrt(2)pi)/(6)=0.74`