Ionization energy is the minimum energy needed to remove a ground-state electron from an atom and leave a positive ion behind. The ionization energy of hydrogen is 13.60 eV because the ground-state energy is $E_1=-13.60\text{eV}$. FIGURE 41.22 shows the experimentally measured ionization energies of the first 60 elements in the periodic table.

FIGURE 41.22 Ionization energies of the elements up to $Z=60$.

The ionization energy is different for each element, but there’s a clear pattern to the values. Ionization energies are $\approx 5\text{eV}$ for the alkali metals, on the left edge of the periodic table, then increase steadily to $\ge 15\text{eV}$ for the inert gases before plunging back to $\approx 5\text{eV}$. Can the quantum theory of atoms explain this recurring pattern in the ionization energies?

Indeed it can. The inert-gas elements (helium, neon, argon, . . .) in the right column of the periodic table have closed shells. A closed shell is a very stable structure, and that is why these elements are chemically nonreactive (i.e., inert). It takes a large amount of energy to pull an electron out of a stable closed shell; thus the inert gases have the largest ionization energies.

The alkali metals, in the left column of the periodic table, have a single $s$-electron outside a closed shell. This electron is easily disrupted, which is why these elements are highly reactive and have the lowest ionization energies. Between the edges of the periodic table are elements such as beryllium $\left(1s^{2}2s^2\right)$ with a closed $2s$ subshell. You can see in Figure 41.22 that the closed subshell gives beryllium a larger ionization energy than its neighbors lithium $\left(1s^{2}2s\right)$ or boron $\left(1s^{2}2s^{2}2p\right)$. However, a closed subshell is not nearly as tightly bound as a closed shell, so the ionization energy of beryllium is much less than that of helium or neon.

All in all, you can see that the basic idea of shells and subshells, which follows from the Schrödinger-equation energy levels and the Pauli principle, provides a good understanding of the recurring features in the ionization energies.