Chapter 8.5, Problem 21E

(a)

To determine

To verify: That the function $p\left(r\right)$ is a probability density function.

(b)

To determine

To find: The value of ${\lim }_{r\to \infty }p\left(r\right)$ the value of r which provides the maximum $p\left(r\right)$ value

(c)

To determine

To Draw: The graph for density function.

(d)

To determine

To calculate: The probability that the electron will be within the sphere of radius $4a_0$ centered at the nucleus.

(e)

To determine

To calculate: The mean distance of the electron from the nucleus in the ground state of the hydrogen atom.