In this problem, you will calculate the probability of finding an electron within a sphe...

In this problem, you will calculate the probability of finding an electron within a sphere of radius r for the H atom in its ground state.

a. Show using integration by parts, , that .

b. Using this result, show that the probability of finding the electron within a sphere of radius r for the hydrogen atom in its ground state is

c. Evaluate this probability for r =.25 a₀, r = 2.25 a₀, and r = 5.5 a₀.