where a0 is a constant (a0 = 53 pm) and r is the distance

Chapter 7, Problem 95E

(choose chapter or problem)

The wave functions for the 1s and 2s orbitals are as follows:

\(1 s \quad \psi=(1 / \pi)^{1 / 2}\left(1 / a_{0}^{3 / 2}\right) \exp \left(-r / a_{0}\right)\)

\(2 s \quad \psi=(1 / 32 \pi)^{1 / 2}\left(1 / a_{0}^{3 / 2}\right)\left(2-r / a_{0}\right) \exp \left(-r / a_{0}\right)\)

where \(a_{0}\) is a constant (\(a_{0}=53 \ \mathrm{pm}\)) and r is the distance from the nucleus. Use a spreadsheet to make a plot of each of these wave functions for values of r ranging from 0 pm to 200 pm. Describe the differences in the plots and identify the node in the 2s wave function.