Verify the statement that p dir 2 = 2 /6 = a 2 /N n , in which the distance a is the

Verify the statement that p_dirλ² = ℓ²/6 = a²/N_n, in which the distance a is the unit-cell edge, ℓ the actual jump length, λ its projection onto the unit cell edge direction, and N_n is the number of nearest neighbors of the vacancy, for 

(a) Primitive cubic, 

(b) bcc,

(c) fcc packing of spheres.