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

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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)).

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

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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.

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The data portion of this shows the developed equations that you require.
Nj/N­­0­­ = ...

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