1. Relate wavelength, frequency, and energy of electromagnetic radiation.
2. Use the Balmer-Rydberg equation to calculate the wavelength and energy of a photon absorbed or released when an electron changes orbitals in the hydrogen atom.
3. Use a set of quantum numbers to describe a particular orbital.
4. Sketch and name each of the s, p, and d orbitals.
5. Predict ground-state electron configurations for elements and ions; use orbital-filling diagrams to determine the number of unpaired electrons in these species.
6. Write general valence-shell electron configuration for each group of the periodic table, and identify the blocks in which the elements are located.
7. Given a set of atoms, determine which atom is expected to have the largest radius.

The periodic table is the most important organizing principle in chemistry. If you know the chemical and physical properties of any one element in a group (vertical column) of the periodic table, you can make a good guess at the chemical and physical properties of every other element in the same group and even of the elements in neighboring groups.

To see why it’s called the periodic table, look at the graph of atomic radius versus atomic number in Figure 5.1. The graph shows a clearly periodic, rise-and-fall pattern. Beginning on the left with atomic number 1 (hydrogen), the size of the atoms increases to a maximum at atomic number 3 (lithium), then decreases to a minimum, then increases again to a maximum at atomic number 11 (sodium), then decreases, and so on. It turns out that all the maxima occur for atoms of group 1A elements—Li (atomic number, Z = 3), Na (Z = 11), K (Z = 19), Rb (Z = 37), Cs (Z = 55), and Fr (Z = 87)—and that the minima occur for atoms of the group 7A elements.

FIGURE 5.1  A graph of atomic radius in picometers (pm) versus atomic number shows a clear rise-and-fall pattern of periodicity. The maxima occur for atoms of group 1A elements (Li, Na, K, Rb, Cs, Fr); the minima occur for atoms of the group 7A elements. (Accurate data are not available for the group 8A elements.)

There’s nothing unique about the periodicity of atomic radii shown in Figure 5.1. Any of several dozen other physical or chemical properties can be plotted in a similar way with similar results. We’ll look at several examples of such periodicity in this chapter and the next.

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