Energy levels

The atom's energy is lowest (most negative) with the electron in the innermost orbit, n = 1. For n = 2, 3, … the magnitude of E shrinks, so the energy rises in the outer orbits.

The lowest state is the ground state: n = 1, orbit radius a₀, E₁ = −13.6 eV. The least energy that frees the electron from the ground state, 13.6 eV, is the ionisation energy of hydrogen, and Bohr's prediction agrees very well with experiment.

At room temperature most hydrogen atoms are in the ground state. Energy from collisions (for example with electrons) can lift the electron to a higher level: the atom is then in an excited state.

E₂ = −3.40 eV, so excitation to the first excited state needs E₂ − E₁ = 10.2 eV. E₃ = −1.51 eV, so the second excited state (n = 3) needs 12.09 eV.

From an excited state the electron can fall back to a lower level, emitting a photon. The higher the excitation (the larger n), the less energy is needed to free the electron.

Fig. 12.7 stacks the levels as horizontal lines, numbered by n from the bottom up in order of rising energy. The top, n = ∞, has E = 0: the electron removed to infinity and at rest. The levels crowd closer together as n increases.

Above E = 0 the electron is free and can have any energy: a continuum of states.