Chapter 15 (II)

Chapter 15 (II) - 15.3 Rotational modes of diatomic...

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Unformatted text preview: 15.3 Rotational modes of diatomic molecules ,... 2 , 1 , , ) 1 ( 2 2 = + = l l l L h The rotation is modeled as the motion of a quantum mechanical rigid rotator. The moment of inertia of the molecule rotating around the axis: I=m r r 2 , where m r =m 1 m 2 /(m 1 +m 2 ) is the reduced mass, r is the equilibrium distance between the nuclei. Quantum mechanics states that the allowed values of the angular momentum L meet The rotation energy is given by = ()I 2 . is the angular velocity. Since L=I , =L 2 /2I. So that the quantized energy levels are: r . 2 / ) 1 ( 2 I l l r l h + = (15.13) We introduce a characteristic temperature for rotation: rot 2 /2Ik, So that For a given , the angular momentum projected on a certain axis is L Z =m , the total number of allowed L Z is 2 +1. The motion states of the rotator is determined by and m, while l r is only dependent of . Thus, each energy level has (2 +1) quantum states: . ) 1 ( rot r l k l l + = (15.14) (15.15) l ; ,... 2 , 1 , ,... 1 , l l l m + = l l l l . 1 2 + = l g r l (15.16) .....
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This note was uploaded on 02/28/2011 for the course PHYS 359 taught by Professor Dr.asdas during the Winter '10 term at Waterloo.

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Chapter 15 (II) - 15.3 Rotational modes of diatomic...

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