## Electron Shells and the Periodic Table

### Periodicity of the Elements

You’re probably already familiar with the periodic table, which organizes the elements according to their chemical properties. Each column lists elements with similar properties. For example, all of the elements in the first column (with the exception of hydrogen) are soft, silvery metals that are highly reactive; the last column lists gases that are colorless, odorless, and chemically inert. What you may not know is that much of the periodic table had already been arranged and organized years before the modern theory of atomic structure was developed. The periodicity of the elements—that is, the fact that chemical properties are repeated periodically when the elements are listed in order by weight—was recognized as early as the 1860s by John Newlands and Dmitri Mendeleev. The reason for this pattern, however, was not understood until the middle of the twentieth century, when the theory of quantum mechanics was developed. One of the most remarkable achievements of quantum mechanics is its explanation why the periodic table works. As we’ll see in a moment, the periodic table mirrors the arrangement of electron orbitals in an atom.

As discussed earlier in this chapter, Rutherford discovered that the nucleus of an atom contains one or more protons, and the number of protons determines the type of atom. Hydrogen atoms have one proton, helium atoms have two, lithium atoms have three, and so on. The number of protons is called the atomic number. The periodic table lists the elements in order of their atomic numbers, arranged from left to right and top to bottom (the same way we read paragraphs of English writing).

Since protons have positive charge, each element has a unique amount of positive charge in its nucleus. Because positive and negative charges attract, electrons are pulled toward the nucleus with a force that varies depending on the atomic number: the more protons in the nucleus, the stronger the pull. For this reason, elements with higher atomic numbers also hold more electrons. A complete atom has as many electrons as protons, and therefore has neutral charge. However, when chemical bonds form between atoms, electrons are exchanged or shared in a way that gives each atom a net positive or negative charge, causing the atoms to stick together. We’ll return to this point shortly.

The amount of charge in the nucleus also determines the energies of the atom’s orbitals. (This is because the strength of the electromagnetic force determines how fast an electron has to move in order to maintain a stable “orbit,” as explained in the discussion of Bohr’s model earlier in this chapter.) Nevertheless, there are repeating patterns in the arrangement of orbitals, and these patterns hold for all atoms. The orbitals are arranged in groups of similar energies, called electron shells, and all atoms have a similar set of shells. The arrangement of elements in the periodic table mirrors the arrangement of orbitals in electron shells, as I will explain presently.

A law of quantum mechanics (namely, the Pauli exclusion principle, which will be introduced in the next chapter) forbids more than two electrons from occupying the same orbital simultaneously.The Pauli exclusion principle says that identical fermions cannot occupy the same quantum state at the same time. We’ll learn what fermions are in chapter 5, and what a “quantum state” is in chapter 7. When two electrons occupy the same orbital, they must have opposite “spin,” so that they are in different quantum states. Spin is a quantum mechanical property that is essentially equivalent to angular momentum, except that it has discrete (non-continuous) values. The first shell of an atom consists of just one orbital, so the Pauli exclusion principle implies that it can hold no more than 2 electrons at a time. This corresponds to the first row of the periodic table, which has 2 elements: hydrogen and helium. An atom’s second shell consists of four orbitals and therefore can hold up to 8 electrons. This corresponds to the second row of the periodic table, which has 8 elements, and so on for the remaining rows of the periodic table. Each row of the table corresponds to another electron shell, and the number of elements in that row is the same as the number of electrons that shell can hold.

I’ve oversimplified the above explanation a bit. Some of rows of the periodic table correspond to subshells rather than whole shells, but the distinction between shells and subshells need not concern us.
An atom will remain in its ground state unless something disturbs it—a wave of light, for instance, or a collision with another atom. If bumped into an excited state, an atom quickly returns to its ground state by emitting energy in the form of light, as discussed earlier in this chapter.

Let me clarify this point in terms that will be useful later. The periodic table corresponds to the way electrons arrange themselves when atoms have the least possible energy. When an atom’s electrons have their lowest possible energies, the atom is said to be in the ground state. (Otherwise, it is in an excited state.) Hydrogen and helium atoms are in the ground state, for instance, when their electrons occupy the lowest-energy shell. Lithium, on the other hand, has three electrons; and there is no room for a third electron in the lowest-energy shell. So when a lithium atom is in the ground state, one of its electrons occupies the second shell. In fact, all of the elements in that second row of the periodic table have a full first shell and a non-empty second shell when they are in the ground state. Similarly for the third row. While in the ground state, all of the elements in the third row have at least some electrons in their third shells; their first and second shells are full. And so on. Each new row of the periodic table represents a new shell for electrons in the ground state. (In an excited state, of course, an atom may have electrons in any of its shells.)

Columns of the periodic table also corresponds to the arrangement of electrons in the ground state. Elements in the rightmost column (noble gases) have no partly-filled shells in the ground state: all of the occupied shells are full. Elements in the second-from-right column (halogens) have room for exactly 1 more electron in their highest non-empty shell. Elements in the third-from-right column (chalcogens) have room for 2 more electrons in that shell. Elements in the fourth-from-right column have room for 3 more, and so on. This pattern holds for all columns except the first two. Elements in the first column (hydrogen and the alkali metals) have exactly 1 electron in their highest non-empty shell. Elements in the second column (alkaline earth metals) have exactly 2 electrons in their highest non-empty shell. This pattern also continues through the 16th column of the fully expanded periodic table, but not for the remaining columns. In other words, the pattern stops at the column beginning with the element scandium, which is actually the 17th column but is usually depicted as the 3rd column because columns 3-16 are placed in a footnote.

Elements in each column usually have similar chemical properties, for reasons that will be explained on the next page.