Question: Consider a container of volume Vo with No molecules. Assume that the molecules are independently distributed…..

Instructions

Consider a container of volume Vo with No molecules. Assume that the molecules are independently distributed in the container. 1) when No 1 what is the probability p of finding the molecule in a region of volume V located anywhere in the container? 2) what is the probability P(N,V) of finding N molecules in V and No – N elsewhere? What is the name of this distribution? 3) show that (N-Σ_oNP(N.V) = Nop and 〈N*)-(N)-Nop(1-p) hint: write N2 N(N -1)+N 4) show that if both Nop and No(1 – p) are big numbers, the function P(N,V) has a Gaussian form. Where is the center of the gaussian and what is its width? hint : set x = N-Nop, rewrite logP(N, V) as a function of x and use Stirling’s formula. Assume x <くNop and x << MO (1-p), expand for smallx