1. Most Probable Radius vs. Average Radius for a 3d orbital.

a. Calculate the average value of r, , for an electron described by the function R₃₂.

b. Calculate the most probable radius (r_mp) and compare it to . Rationalize this result based on the plot of the radial distribution function.

c. Carefully set up the integral that when evaluated will yield the probability of finding a 3d electron of the hydrogen atom between r = 0 and r = r_mp. Evaluate the integral.