For a hydrogen atom in a state with and , we have to find the probability of finding the electron somewhere within the smaller of the two maxima of its radial probability density function.

Solution:             Click For PDF Version

The wave function for the state and is

.

The radial probability density is given by

For finding out the maxima of , we calculate

.

We find

It can be shown that is a minimum and the maxima of are the roots of the equation

The smaller of the maxima of the radial probability function is

.

The probability of finding the electron somewhere within the smaller of the two maxima of its radial probability density function will therefore be

The probability is 2%.