The Filled Shell Rules

In our discussion of the periodic table, we saw how trends in the ionization energies of a select group of elements suggested the existence of electron shells. Figure 1 expands the graph of ionization energies presented previously to include 26 of the first 36 elements. The data in the figure are color coded by row in the periodic table. The first row consists of hydrogen and helium. The second row contains lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, and neon.The large decrease in ionization energy that occurs between helium and lithium defines the end of the first row and the beginning of the second. A similar pattern defines the other rows.

Figure 1

Ionization Energies as a Function of Atomic Number

The electrons associated with each element of a row are assigned to electron shells. Each shell is designated by its principal quantum number, n. When n is 1, the shell is designated s. When n equals 2, there are two sub-shells, s and p. When n is 3, there are three sub-shells, s, p, and d. Not surprisingly, when n equals 4, there are four sub-shells; s, p, d, and f. The s, p, d, and f sub-shells can accomodate 2, 6, 10, and 14 electrons, respectively. The electron configuration of an atom specifies the number of electrons in each electron shell or sub-shell. Figure 2 summarizes the information that is required to completely describe the electron configuration of an atom, using boron as an example.

Figure 2

Specifying Electron Configurations

Notice in Figure 1, that for n = 1, 2, 3, and 4, the element with the highest ionization energy has an electron configuration in which the valence shell is filled. The high energy required to remove an electron from those atoms is just one line of evidence suggesting a relationship between electron configuration and stability. Additional evidence comes from a consideration of the second ionization energies, a process represented in general terms by Equation 1.

Figure 3 compares the first and second ionization energies of six elements, using the same color coding as Figure 1. In all cases the second ionization energy is greater than the first. This is because it is more difficult to separate an electron from a positively charged ion than it is from the corresponding neutral atom. The interesting feature of Figure 3 is that the second ionization energies of Be, Mg, and Ca are all much less than the second ionization energies of the elements that precede them, i.e. Li, Na, and K, respectively. Not surprisingly, this result may be rationalized in terms of electron configurations.

Figure 3

Comparison of the 1st and 2nd Ionization Energies of 6 Elements

Figure 4 offers an alternative view of the information presented graphically in Figure 3. Creating a comparable scheme for the other elements in Figure 3 should help you understand how that information led to the idea of filled shells

Figure 4

1st and 2nd Ionization Energies: A Different View

The association between stability and electronic structure is a general phenomenon. It is summarized by the filled shell rule: Atoms are most stable when they have a filled valence shell. The electron shell with a principal quantum number of 1 is filled when it contains 2 electrons. In this case the filled shell rule is sometimes called the duet rule. The only atom we will be concerned with in terms of the duet rule is hydrogen. When the principal quantum number equals 2, the filled valence shell contains eight electrons, and the filled shell rule is referred to as the octet rule. We will use the octet rule as a guideline when we consider valence bond theory. Bonding rules provides a summary of the implications of the filled shell rules on bonding in organic molecules.