As a simple example, imagine a gas of monatomic hydrogen atoms, set g 0 = g 1 and let ε ε = 13.6 eV = 158 000 K, the ionization energy of hydrogen from its ground state. Let n = 2.69 × 10 m, which is the Loschmidt constant, or particle density of Earth's atmosphere at standard pressure and temperature. At T = 300 K, the ionization is essentially none: x = 5 × 10 and there would almost certainly be no ionized atoms in the volume of Earth's atmosphere. x increases rapidly with T , reaching 0.35 for T = 20 000 K. There is substantial ionization even though this T is much less than the ionization energy (although this depends somewhat on density). This is a common occurrence. Physically, it stems from the fact that at a given temperature, the particles have a distribution of energies, including some with several times T . These high energy particles are much more effective at ionizing atoms. In Earth's atmosphere, ionization is actually governed not by the Saha equation but by very energetic cosmic rays, largely muons. These particles are not in thermal equilibrium with the atmosphere, so they are not at its temperature and the Saha logic does not apply.