population of energy states
/ pop-yoo-LAY-shun /
Walk into a stadium on a cold evening and the cheap lower seats fill up first, while the high, exposed rows stay nearly empty. The population of energy states is the same idea for molecules: out of a whole crowd of them, what fraction sits in each available energy level. Low levels are packed; high levels are thinly occupied.
More precisely, the population of a state is the number, or fraction, of molecules occupying that state when the system is at thermal equilibrium. The Boltzmann distribution sets those fractions: a state's population is its degeneracy times its Boltzmann factor, divided by the partition function. Raising the temperature lets molecules spread into higher levels; lowering it crowds them back down toward the ground state.
Why it matters: populations are what experiments actually measure. The brightness of a spectral line, the speed of a reaction, the magnetism of a sample — all trace back to how many molecules sit where. The honest caveat is that this neat picture assumes equilibrium; a laser, for instance, works precisely by forcing an 'inverted' population that the Boltzmann rule forbids.
In a hydrogen atom at room temperature, essentially every atom sits in the ground state; the first excited level lies about 10 electron-volts up, hundreds of kT away, so its population is unimaginably small. Heat the gas to thousands of kelvin and only then do excited states begin to glow.
A large energy gap keeps excited states almost unpopulated until the gas is very hot.
A population ratio between two levels depends only on their energy gap and the temperature, through the Boltzmann factor — a fact spectroscopists exploit to read a sample's temperature straight from the relative brightness of its lines.