IGNOU MPH 16 2026 - The rotational constant for the excited electronic state of a particul

Question

The rotational constant for the excited electronic state of a particular molecule is 20% smaller as compared to the rotational constant of its ground electronic state. Determine the values for the first 15 lines of the R-branch. Discuss the variation of the separation between successive transition lines of this branch.

19 Jan 2026

Answer :

Word Count : 443

For a diatomic molecule, the rotational energy levels in a given electronic-vibrational state are expressed as: [ E_J = B J(J+1) ] where (B) is the rotational constant, and (J = 0, 1, 2, ...) is the rotational quantum number. The rotational constant in the excited electronic state ((B')) is given to be 20% smaller than that in the ground electronic state ((B)), so [ B' = 0.8 B ] For the R-branch transitions ((\Delta J = +1)), the transition wavenumbers (\tilde{\nu}_R(J)) are given by: [ \tilde{\nu}_R(J) = \tilde{\nu}_0 + (B' + B)(J+1) + (B' - B)(J+1)^2 ] Here (\tilde{\nu}_0) is the band origin corresponding to the electronic-vibrational transition, and (J) refers to the rotational quantum number of the lower (ground) state. Substituting (B' = 0.8B): [ \tilde{\nu}_R(J) = \tilde{\nu}_0 + (B +

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