3502_15_octo14_LG.1

3502_15_octo14_LG.1 - Chem 3502/5502 Physical Chemistry II(Quantum Mechanics Fall Semester 2009 Laura Gagliardi Lecture 15 3 Credits Solved

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Chem 3502/5502 Physical Chemistry II (Quantum Mechanics) 3 Credits Fall Semester 2009 Laura Gagliardi Lecture 15, October 14, 2009 Solved Homework We are asked to give the minimum energy required for the ionization reaction Be 3+ Be 4+ + e Since Be is atomic number Z = 4, this corresponds to ionization of the electron from a one-electron atom. One-electron atoms are the systems that we know how to deal with exactly based on our work of last lecture. Note that the reason the poorly worded problem presumably says the “minimum energy” is that it has in mind the energy required to just separate the electron from the nucleus and leave both particles at rest (this defines the system’s zero of energy). You could, however, provide more energy, so that not only would the particles be infinitely separated, but they’d have some kinetic energy too, instead of being at rest. However, the problem is poorly worded because the correct answer is that the minimum energy is ε , where ε is a positive number arbitrarily close to zero. How can this be? Well, what if the electronic wave function corresponds to principle quantum number n = 10 9 ? The binding
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This note was uploaded on 12/14/2010 for the course CHEM 3502 taught by Professor Staff during the Spring '08 term at Minnesota.

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3502_15_octo14_LG.1 - Chem 3502/5502 Physical Chemistry II(Quantum Mechanics Fall Semester 2009 Laura Gagliardi Lecture 15 3 Credits Solved

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