text: The probability of a transition taking place is the most important factor influencing the intensity of an observed rotational line. This probability is proportional to the population of the initial state involved in the transition. The population of a rotational state depends on two factors. The number of molecules in an excited state with quantum number J, relative to the number of molecules in the ground state, N/N is given by the Boltzmann distribution as
  where k is the Boltzmann constant and T the absolute temperature. This factor decreases as J increases. The second factor is the degeneracy of the rotational state, which is equal to . This factor increases as J increases. Combining the two factors
  The maximum relative intensity occurs at
  The diagram at the right shows an intensity pattern roughly corresponding to the spectrum above it.