Problem S5.2. Consider the chemical reaction

where molecule A is a catalyst whose concentration is maintained constant. Assume that the total number of molecules X and Y is constant and equal to N. k(k2) is the probability per unit time that molecule X (Y) interacts with a molecule A to produce a molecule Y (X).

(a) Find the equation of motion for the probability P(n, t) to find n X molecules in the system at time t, and find the generating function, F(2, 1) = "P (n,t).

(b) Find the average number of X molecules in the system at time t, and find the variance in the distribution of X molecules. In the limit, No. how does the variance for the particle distribution compare with that of a Gaussian distribution?

Transcribed Image Text:

ki A+ X=A+Y, k2