?Before doing a calculation, sketch how the overlap between a 1s orbital and a 2p

Chapter 9, Problem P9C.2

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Before doing a calculation, sketch how the overlap between a 1s orbital and a 2p orbital directed towards it can be expected to depend on their separation. The overlap integral between an H1s orbital and an H2p orbital directed towards it on nuclei separated by a distance R is S = (\(R / a_{0}\)){1 + (\(R / a_{0}\))+ \(\left.\frac{1}{3}\left(R / a_{0}\right)^{2}\right\} \mathrm{e}^{-R / a_{0}}\). Plot this function, and find the separation for which the overlap is a maximum.

Text Transcription:

R/a_0

13R/a_0^2e^-R/a_0