In this problem, I want you to extend this analysis to two dimensions. For this, assume that we have a circular membrane patch of finite extent that has a radius . The membrane patch has a uniform distribution of fluorescent molecules across its area. Imagine that a laser instantaneously photobleaches a small circular spot in the center of the membrane patch with radius .

a) Find a relation for the concentration of fluorescent molecules inside the bleached spot as a function of the radius from the center of the membrane patch and time, (,). Hint: assume that the solution is a separable function of radius and time, (,) = ()().

b) Calculate the total number of molecules inside the bleached spot as a function of time, (). This quantity corresponds to the integral of the concentration over the bleached region.