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hw-molecules - 2 ions when H 2 is ionized by a fast charged...

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Exercises: 1. (a) Find the equilibrium distances of H2 and H2+, the first three vibrational energies of the J=0 states. (b) Find the lowest potential curves of H2 and H2+, respectively, and plot them on the same graph. (c) If the lowest potential curve of H2 and H2+ are approximated by the Morse potential function, find the parameters D e and α [Eq. 13]. Give D e in eV and α in atomic units. (d) Calculate the “classical” vibrational period of H2+ and D2+, expressed your answers in femtoseconds. 2. (a) What is the so-called Franck-Condon principle? (b) The minimum positions of the lowest potential curves for H 2 and H 2 + occur at 0.74 o A and 1.06 o A, respectively. According to the Franck-Condon principle, what is the likely distribution of the vibrational states of H
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Unformatted text preview: 2 + ions when H 2 is ionized by a fast charged particle? Just sketch your answer and give your reasoning. (c ) If the target is a D 2 molecule instead, does the answer to the question in part (b) change? Give your reasoning. 3. The oxygen atom has eight electrons. What is the ground state configuration (L and S) of the oxygen atom? What are the configurations of the first two excited states of the oxygen atom and what are their radiative decay modes? 4. For the O 2 molecules, identify the molecular orbitals occupied by the electrons. It turns out that O 2 has total spin equals to one. Explain why this has to do with the fact that the water molecule has a bond angle (H-O-H angle) of about 105 degrees....
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