Question

Assuming that atoms are touching each other, calcualte the packing efficiency in case of a crystal of simple cubic metal.

Answer 1

In a simple cubic unit cell : Supporse the edge length of the unit cell = a
and radius of the sphere = r `" "[ therefore a = 2r]`
No.of spheres per unit cell `= (1)/(8)xx 8 =1`
Volume of the sphere `= (4)/(3)pi r^(3)`
Volume of tne cube `= a^(3) = (2r)^(3) = 8r^(3)`
Fraction occupied, i.e, paking fraction `=(((4)/(3)pir^(3)))/(8pir^(3))= (pi)/(6) = 0.524` of occupied = 52.4%