begin mathsize 36px style x equals e to the power of negative fraction numerator B. h. c. J left parenthesis J plus 1 right parenthesis over denominator K subscript B T end fraction end exponent space semicolon space space bevelled N subscript j over N subscript 0 equals x space end style

 NJ = Number of molecule in J state ; N0 = Number of molecule in the ground state ( J= 0 ) ; K=Bolzmann Constant ; T = Temperature ; B = Rotational Constant; h = Plank Constant ; x=Relative Population; c = Velocity of light ; J = Rotational Quantum Number 





By Boltzmann distribution formula one can calculate the relative population in different rotational energy states to the ground state. The relative population is governed by the energy difference from the ground state and the temperature of the system. A higher magnitude of the energy difference leads to lower population in the higher energy state. However, higher temperature leads to higher population in the higher energy state. 

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