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Unformatted text preview: CHEM 350 Lecture 19, February 22 2010 • Rotations . First let us review briefly the quantum mechanical description of simple rotational motion for a rigid rotor: ~ 2 c J 2 2 μR 2 e ψ ( θ,φ ) = E rot ψ ( θ,φ ) , Upon setting μR 2 e = I (the moment of inertia of the rotor), we obtain E rot = ~ 2 2 I j ( j + 1) = j , j = 0 , 1 , 2 , ··· The ψ j,m j ( θ,φ ) = Y j,m j ( θ,φ ) are the spherical harmonics: for each value of j , there will be 2 j + 1 values of m j and, as the energy depends only upon j , each level will be (2 j + 1)–fold degenerate! q rot ( T ) ≡ X states e- βE state = X j,m j e- β j,m j ≡ X levels Ω level e- β level = ∞ X j =0 (2 j + 1)e- β j rotational temperature: Θ rot = ~ 2 2 Ik B from βE rot = β ~ 2 2 I j ( j + 1) ≡ Θ rot T j ( j + 1) (i) For temperatures T such that T Θ rot , q rot ( T ) can be written as q rot ( T ) ’ 1 + 3e- 2Θ rot /T + 5e- 6Θ rot /T + ··· (ii) For temperatures T such that T Θ rot , we have q rot ( T ) = ∞...
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- Spring '10
- Atom, Diatomic molecule, homonuclear diatomic molecules, heteronuclear diatomic molecules, homonuclear diatomic molecule, Θrot Qrot