(a) Calculate the average orbital radius of a 3d electron in the hydrogen atom. Compare with the Bohr radius for a n = 3 electron. (b) What is the probability of a 3d electron in the hydrogen atom being at a greater radius than the n = 3 Bohr electron?
Strategy We used a similar strategy in Example 7.12 to find the expectation (or average) value of r. We determine the probability of a 3d electron being in a certain radial position (greater than r_{3}=n^{2} a_{0}=3^{2} a_{0}=9 a_{0}) by integrating over the probability density from 9 a_{0} \text { to } \infty.