hw_4 - static homogeneous electric field of E z = 1,000...

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Physics 780.04 Winter Quarter 2007 Dr. Herbst HOMEWORK ASSIGNMENT # 4 DUE: MONDAY, 12 FEBRUARY 2007 1. Determine the internuclear separation (Angstroms) in the v=0 vibrational state of CO from the frequency of the J = 1-0 transition of 115271.2 MHz. Assume the molecule to be rigid. 2. Bernath, page 202, problem 11a 3. Bernath, page 203, problem 20 (the rotational energies and eigenfunctions for linear molecules are the same as for diatomic molecules, although the rotational constants are more complicated). 4. A rigid diatomic rotor with B = 20 GHz in its J=1 state undergoes an (unallowed) transition between its |M J | = 1 and 0 levels at a frequency of 1 MHz in the presence of a
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Unformatted text preview: static homogeneous electric field of E z = 1,000 volts/cm. What is the permanent dipole moment of the molecule? The so-called Stark Effect constant μE/ h = 0.50348 MHz/Debye(volt/cm) x μ (Debye) x E (volt/cm). 5. Calculate the overall rotational-nuclear spin degeneracies of the lowest five rotational levels of 35 Cl 2 . The ground electronic state of 35 Cl 2 is totally symmetric and the nuclear spin of 35 Cl is 3/2. 6. Develop a formula for the Q-branch lines of a diatomic molecule vibrational-rotational band. 7. Using the relations among D e , ω e , and e x e for the Morse oscillator, find an expression for the number of bound vibrational states in terms of x e ....
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