FIGURE 38.21 is an energy-level diagram for the hydrogen atom. As we noted earlier, the energies are like the rungs of a ladder. The lowest rung is the ground state, with $E_1=-13.60\text{eV}$. The top rung, with $E=0\text{eV,}$ corresponds to a hydrogen ion in the limit $n\to \infty$. This top rung is called the ionization limit. In principle there are an infinite number of rungs, but only the lowest few are shown. The higher values of $n$ are all crowded together just below the ionization limit at $n=\infty$.

FIGURE 38.21 The energy-level diagram of the hydrogen atom.

The figure shows a $1\to 4$ transition in which a photon is absorbed and a $4\to 2$ transition in which a photon is emitted. For two quantum states $m$ and $n$, where $n>m$ and $E_n$ is the higher energy state, an atom can emit a photon in an $n\to m$ transition or absorb a photon in an $m\to n$ transition.