D4.3 Periodic Variation in Ionization Energies

In addition to atomic radius, several other properties vary depending on position in the periodic table. Like atomic radius, these properties depend on effective nuclear charge and size of atomic shell.

The quantum mechanics model for the hydrogen atom discussed ionization of the hydrogen atom: excitation of the electron from the n = 1 level to the limit of n → ∞:

 \Delta E\;=\;E_{n \rightarrow \infty}\;-\;E_1\;=\;0\;-\;\dfrac{-k}{1^2}\;=\;k\;=\;2.179\;\times\;10^{-18}\;\text{J}

Ionization energy (IE), the minimum energy required to remove an electron from the atomic orbital it occupies (exciting it to n = ∞), also applies to multi-electron atoms. As shown in this table of ionization energies, there are successive ionization energies, one for each electron.

The first ionization energy (IE1) is the minimum energy required to remove the least tightly bound electron, i.e. the electron in the highest energy orbital. It corresponds to the process:

X(g) → X+(g) + e          ΔE = IE1

The second ionization energy (IE2) is the minimum energy required for removing an electron from the 1+ cation, corresponding to:

X+(g) → X2+(g) + e          ΔE = IE2

And so forth.

Electrons in atoms have lower potential energy than when they are separated from the atom, so energy is always required to remove an electron from atoms or ions. Ionization is an endothermic process and IE values are always positive.

Ionization energies can be determined experimentally from atomic spectra or by shining light on a gas-phase sample and successively increasing the photon energy until ejection of an electron is observed. Such experiments also give us direct information about the atomic orbital the electron was occupying.

Activity: Periodic Variation of First Ionization Energy

Exercise: Periodic Variation of Ionization Energy

In the preceding activity, you developed a general rule that across a period, IE1 increases with increasing atomic number, Z; down a group, IE1 decreases with increasing Z. Look at the Figure: Ionization Energies below and make certain you see how the data in the figure support both trends. There are a few systematic deviations from these trends, which also can be seen in the Figure.

Activity: Deviations from IE Trends

Examine data presented in the figure. Identify all deviations from the trend that ionization energy increases across a period and decreases down a group. Click on each deviation involving an element in Period 1, Period 2, or Period 3.

Figure: Ionization Energies. The first ionization energies of elements in the first five periods are plotted against atomic numbers.
Activity: Explaining Deviations from IE Trends

Another deviation occurs when a subshell becomes more than half filled. For example, oxygen’s IE1 is slightly lower than that for nitrogen. The orbital diagram of oxygen shows that the last electron added (red) is forced to pair with another electron, because the 2p subshell is more than half full.

This figure includes the element symbol O followed by the electron configuration 1 s superscript 2 2 s superscript 2 2 p superscript 4. An orbital diagram follows, which consists of a vertical arrow labeled "Relative Energy" followed by a series of horizontal lines arranged vertically. The lowest line is labeled as, “1 s,” the next lowest is labeled as, “2 s, and is quite a bit higher than "1 s". A little above "2 s" is a grouping of three lines at the same height that are labeled, “2 p.” The lowest, "1 s," and next-lowest, "2 s," lines contain a pair of arrows. One arrow in each pair points up, and one points down. The three "2 p" lines, all at the same height, each have one black arrow pointing upward. The first of the three "2 p" lines also has a red arrow pointing downward.

Loss of the electron (colored red in the orbital diagram) yields a greater reduction of electron–electron repulsion because there are no longer two electrons in the same orbital. This makes it easier to lose one electron from O and the ionization energy is smaller than expected. The same explanation applies to the dip for sulfur after phosphorus in Figure: Ionization Energies.

Looking at the successive IEs in the appendix, we see that for any element, IE1 < IE2 < IE3, and so forth, and this is due to the greater Zeff in successively more positive ions. However, sometimes the increase in successive IE is larger than expected. For example, consider the data in Table 1:

Element IE1 IE2 IE3 IE4 IE5 IE6 IE7
K 419 3069 4438 5876 7975 9620 11385
Ca 590 1145 4941 6465 8142 10496 12350
Sc 633 1244 2388 7130 8877 10720 13314
Ga 579 1982 2962 6194 8299 10874 13585
Ge 760 1537 3301 4409 9012 11183 13981
As 947 1949 2731 4834 6040 12302 14183
Table. Successive Ionization Energies (IEs) for Some Period-4 Elements (kJ/mol)
Activity: Successive Ionization Energies

These observed ionization energies are consistent with the idea of valence electrons—electrons in outer shell(s) that are less bound and more energetically accessible, allowing them to participate in chemical transformations.


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Chemistry 109 Fall 2021 by John Moore, Jia Zhou, and Etienne Garand is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.