# quantum number of the most intensely populated rotational state as a function of temperature

Using the Boltzmann distribution given below, determine Jmax (quantum number of the most intensely populated rotational state) as a function of temperature. Then find Jmax for CN+ at 298 K and 1100 K.

and CN+ bond length is 0.129 nm

the Boltzman distribution: (Ni/N)= (exp(-ei/KT))/(sigma j exp(-Ej/KT)).

https://brainmass.com/chemistry/general-chemistry/populated-rotational-state-function-temperature-41276

#### Solution Preview

The attachment references a CO2 Laser but the theory and path is shown

you have a bond length to start with so you can use the reduced mass calculation and the bond length to obtain the moment of inertia and B and Jmax as function of temperature.

------------------------------------

The data portion of this shows the developed equations that you require.

Nj/N0 = ...

#### Solution Summary

The solution determines Jmax (quantum number of the most intensely populated rotational state) as a function of temperature based on the given Boltzmann distribution.