How many ion channels on average must there be in one µm2 of neuronal membranes?
I expect your homework was already due, so...

You're supposed to remember what a membrane time constant is. I'll quote from page 12 of my (by now quite old) copy of "Ion channels of excitable membranes", by Hille:


  For biological membranes the product, RmCm, of membrane resistance and capacitance is often called the membrane time constant, taum.


Since you know tau and C, your goal is then to determine the membrane resistance. You also need to convert the capacitance to square microns (1e-14F per square micron). In this case: 1ms/1e-14F = 1e11Ohms, or 1e-11S, or 10pS. So on average there are 10 channels per square micron, assuming I didn't make any silly mistakes.