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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 R 2 e ( , ) = E rot ( , ) , Upon setting R 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 j,m j ( , ) = Y j,m j ( , ) 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 E state = X j,m j e j,m j X levels level e level = X j =0 (2 j + 1)e j rotational temperature: rot = ~ 2 2 Ik B from E rot = ~ 2 2 I j ( j + 1) rot T j ( j + 1) (i) For temperatures T such that T rot , q rot ( T ) can be written as q rot ( T ) 1 + 3e 2 rot /T + 5e 6 rot /T + (ii) For temperatures T such that T rot , we have q rot ( T ) =...
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This note was uploaded on 04/11/2010 for the course CHEM 1101 taught by Professor Leroy during the Spring '10 term at University of Toronto Toronto.
 Spring '10
 Leroy

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