For an `HCI` molecule find the rotational quantum numbers of two neighbouring levels whose energies differ by `7.86 meV`. The nuclei of the molecule are separated by distacne of `127.5p m`.

For an `HCI` molecule find the rotational quantum numbers of two neigh

1.	For an `HCI` molecule find the rotational quantum numbers of two neighbouring levels whose energies differ by `7.86 meV`. The nuclei of the molecule are separated by distacne of `127.5p m`.
Answer» The axis of rotation passes through the centre of mass of the `HCl` molecule.The distance of the two atoms from the centre of mass are `d_(H)=(m_(cl))/(M_(Hcl))d, =(m_(H))/(m_(Hcl))d` Thus `I=` moment of interita about the axis `(4)/(2) m_(H)d_(H)^(2)+m_(cl)d_(cl)^(2)=(m_(H)M_(cl))/(m_(H)+m_(cl))d^(2)` The energy difference between two neighbouring levels whose quantum numbers are `J&J-1` is `( ħ^(2))/(2I).2J=( Jħ^(2))/(I)= 7.86 meV` Hence `J=3` and the levels have quantum numbers `2 & 3`.

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For an `HCI` molecule find the rotational quantum numbers of two neighbouring levels whose energies differ by `7.86 meV`. The nuclei of the molecule are separated by distacne of `127.5p m`.

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