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For an HF molecule find the number of rotational levels located between the zeroth and first excited vibrational levels assuming rotational states to be independent of vibrational ones. The natural vibration frequency of this molecule is equal to 7.79.1014 rad/s, and the distance between the nuclei is 91.7 pm.

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If the vibrational frequency is ω0 the excitation energy of the first vibrational level will be hωo. Thus if there are J rotational levels contained in the band between the ground state and the first vibrational excitation, then

where as stated in the problem we have ignored any coupling between the two. For HF molecule

For J = 14 , J (J + 1 ) = 210 . For J - 13, J (J + 1) = 182. Thus there lie 13 levels between the ground state and the first vibrational excitation.

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