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    • https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Stellar_Atmospheres_(Tatum)/08%3A_Boltzmann's_and_Saha's_Equations/8.04%3A_Boltzmann's_Equation
      A dynamic equilibrium between collisional excitations and radiative de-excitations leads to a certain distribution of the atoms among their various energy levels. Most of the atoms will be in low-lyin...A dynamic equilibrium between collisional excitations and radiative de-excitations leads to a certain distribution of the atoms among their various energy levels. Most of the atoms will be in low-lying levels; the number of atoms in higher levels will decrease exponentially with energy level. The lower the temperature, the faster will be the population drop at the higher levels. Only at very high temperatures will high-lying energy levels be occupied by an appreciable number of atoms.
    • https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Essential_Graduate_Physics_-_Statistical_Mechanics_(Likharev)/02%3A_Principles_of_Physical_Statistics/2.08%3A_Systems_of_independent_particles
      However, it is convenient to keep, for the time being, the discrete-state language, with the understanding that the average number Nk of particles in each of these states, usually...However, it is convenient to keep, for the time being, the discrete-state language, with the understanding that the average number Nk of particles in each of these states, usually called the state occupancy, is very small.

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