quiz10soln - where ν is in the units of sec-1 2.1 Solution...

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1 Problem 1 The rotational constant, B e , for IBr determined from microwave spectroscopy is 0.2241619 cm - 1 . Approximate the bond length of this molecule. 1.1 Solution From the Handbook: B e = h 8 π 2 μ R 2 e Rearranging gives the required form for solving for the equilibrium bond length of the molecule: R e = s h 8 π 2 μ B e 2 Problem 2 How would you compute the energy change associated with a rotation- vibration transition of a diatomic molecule from n=0 to n=1, and J=1 to J=2, using as many corrections to the rotational and vibrational energetics of the molecule. Provide the solution in terms of wavenumbers. Recall that ω e = 2 π ν
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Unformatted text preview: , where ν is in the units of sec-1 . 2.1 Solution The energy for a given vibrational state, n , and rotational state, J , is given by (considering the higher corrections for anharmonicity, centrifugal distor-tion, and vibration-rotation coupling: E =-D e + ± n + 1 2 ² ¯ h ω e-± n + 1 2 ² ¯ h x e ω e + h B n J ( J + 1)-h D c J 2 ( J + 1) 2 Compute the above expression for the two states given. This gives the energy in convenional units. To convert to wavenumbers, we divide by h c , where c is the speed of light. 1...
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