Some atomic properties depend on the average value of 1/r rather than the average value of r itself. Evaluate the expectation value of 1/r for (a) a hydrogenic 1s orbital, (b) a hydrogenic 2s orbital, (c) a hydrogenic 2p orbital. (d) Does ⟨1/r⟩ = 1/⟨r⟩?

Chemistry: An Atoms First Approach
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Author:Steven S. Zumdahl, Susan A. Zumdahl
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Chapter2: Atomic Structure And Periodicity
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Problem 66E: Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of...
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Some atomic properties depend on the average value of 1/r rather than the average value of r itself. Evaluate the expectation value of 1/r for (a) a hydrogenic 1s orbital, (b) a hydrogenic 2s orbital, (c) a hydrogenic 2p orbital. (d) Does ⟨1/r⟩ = 1/⟨r⟩?

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