?Note: Answers to all odd-numbered Problems, numbered in blue, can

Chapter 2, Problem 95

(choose chapter or problem)

Note: Answers to all odd-numbered Problems, numbered in blue, can be found in Appendix III. Exercises in the Problems by Topic section are paired, with each odd-numbered problem followed by a similar even-numbered problem. Exercises in the Cumulative Problems section are also paired but more loosely. Because of their nature, Challenge Problems and Conceptual Problems are unpaired.

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

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

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

where \(a_{0}\) is a constant \(\left(a_{0}=53 \mathrm{pm}\right)\) 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.

Text Transcription:

1s psi=(1/pi)^{1/2}(1/a_0^{3/2}) exp (-r/a_0)\)

2s psi=(1/32 pi)^{1/2}(1 / a_{0}^{3/2})(2-r/a_0) exp (-r  a_0)\)

a_0

a_0=53pm