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Show that the frequency intervals between the neighbouring spectral lines of a true ratational spectrim of a diatomic molecules are equal. Find the moment of intertial and the distance between the nuclei of a CH molecule if the intervals between the neighbouring lines of the true rotational spectrum of these molecules are equal to Delta omega= 5.47.10^(12)s^(-1) |
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Answer» SOLUTION :From `E_(J)=( ħ^(2))/(2l)J(J+1)` and the SELECTION rule `DeltaJ=1 or J rarr J-1` for a pure rational specturm we get `omega(J,J-1)=( ħJ)/(I)` Thus transition lines are equispaced in frequency `Delta omega=( ħ)/(I)` In the case of `CH` molecule `I=( ħ)/(Delta omega)= 1.93xx19^(-40)gm cm^(2)` Also `I=(m_(c )m_(H))/(m_(c )+m_(H))d^(2)` so `d= 1.117xx10^(-8)cm= 111.7 p m` |
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