chaptre 10 - Chem140B Physical Chemistry II Lecture...

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Chem140B – Physical Chemistry II Lecture Homework #8 April 7, 2009 due April 14, 2009 Q10.1) Show that the Slater determinant formalism automatically incorporates the Pauli exclusion principle by evaluating the He ground-state wave function of Equation (21.9), giving both electrons the same quantum numbers. () () () () () () () () () () () () () 11 1 11 1 11 1 , 2 1 1 2 2 1 1 2 2 12 2 12 2 22 1, 2 0 ss αα ψ == = It is seen that the wave function is zero if two electrons have the same quantum numbers. Q10.7) Explain why shielding is more effective by electrons in a shell of lower principal quantum number than by electrons having the same principal quantum number. Electrons in a shell of lower principal quantum number have a higher probability of being found between the nucleus and the electrons having the same principal quantum number. Therefore, they are more effective in shielding. Q10.8) Why does the effective nuclear charge ζ for the 1 s orbital increase by 0.99 in going from oxygen to fluorine, but for the 2 p orbital only increases by 0.65? Because the radial probability distribution of the 1 s electrons are quite localized, there are no orbitals localized between the 1 s and the nucleus, and no n=1 electrons are added to the atom in going from oxygen to fluorine, the 1 s electron feels the full increase in the nuclear charge in going from oxygen to fluorine. By contrast, the 2 p electrons are more delocalized. As an additional p electron is added in going from oxygen to fluorine, only a part of the increase in the nuclear charge is negated by shielding due to the additional 2 p electron. Adding an electron in the same shell is not as effective in shielding as adding an electron in an inner shell.
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P10.10) You have commissioned a measurement of the second ionization energy from two independent research teams. You find that they do not agree and decide to plot the data together with known values of the first ionization energy. The results are shown here.
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This note was uploaded on 06/14/2009 for the course CHEM CHEM 2080 taught by Professor Pathivan during the Spring '05 term at Indian Institute of Technology, Chennai.

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chaptre 10 - Chem140B Physical Chemistry II Lecture...

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