Using as a variational parameter in the normalized function allows one to vary the size...

Using as a variational parameter in the normalized function allows one to vary the size of the orbital. Show this by calculating the probability of finding the electron inside a sphere of radius a₀ for different values of using the standard integral

a. Obtain an expression for the probability as a function of .

b. Evaluate the probability for = 1.5, 2.5, and 3.5.