The packing efficiency of the two dimensional square unit cell shown is :

Options

A. `39.27 %`
B. `68.02%`
C. `74.05 %`
D. `78.54 %`

Answer

D

Explanation

Packing efficiency = `("Area covered by particles")/("Total area")`
If a is the length of unit cell
Face diagonal , `AC = sqrt(2)a`
But `AC = 4r`
`sqrt(2)a = 4r`
`a = (4r)/(sqrt(2)) = 2sqrt(2)r`
No. of particles = `4 xx 1/4 + 1 = 2`
Area occupied by particles = `2 xx pi r_^2`
`:.` Packing efficiency = `(2 xx pi r^2)/((2sqrt(2)r)^(2)) = pi/4`
`= 0.7857 " or " 78.57 %`.