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For an HCI molecule find the rotational quantum numbers of two neighbouring levels whose energies differ by 7.86 meV. Thenuclei of the molecule are separated by distacne of 127.5p m. |
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Answer» SOLUTION :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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