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In a middle of the rotatation-vibration band of emission specturm of HCI molecule, where the "Zeroth" line is forbidden by the selcetion rules, the interval between neighbouring lines is Delta omega= 0.79.10^(13) s^(-1). Calculate the distance between the nuclei of an HCI molecule. |
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Answer» Solution :In the ratation vibration band the MAIN TRANSITION is due to change in vibrational quantum number `v rarr v-1`. Together with this roatational quantum number MAY change. The "Zeroeth line" `0 rarr 0` is forbidden in this case so the neighbouring lines arise due to `1 rarr 0 or 0 rarr 1` in the rotaional quantum number. Now `E=E_(v)+(ħ^(2))/(2I)J(J+1)` Thus `ħ OMEGA=ħ omega_(0)+(ħ^(2))/(2I)(+-2)` Hence `Delta omega =(2ħ)/(I)=(2V)/(MUD^(2))` so `d= sqrt((2ħ)/(muDelta omega))` Substitutiongives `d= 0.128nm`. |
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