Example 4.9: Probability of sedimentation of atoms N atoms of the same kind in exhaust fumes of some industrial complex are blown by wind into the air and deposit on elements of area a of a larger surrounding region of area A. On the average ˙N = dN/dt atoms are deposited per minute on an element

a. Show that the probability 4.6 Problems without Worked Solutions 55 of sedimentation of n atoms on an element of area a in a time interval t is given by the Poisson distribution W(n) =

λn n!

e−λ, (4.65)

where λ = Np, and p is the probability a/A.