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General Chemistry Principles, Patterns, and Applications, 2011

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completely populated), so they do not make a net contribution to bonding in the solid. The energy<br />

difference between the highest level of one b<strong>and</strong> <strong>and</strong> the lowest level of the next is the b<strong>and</strong> gap. It<br />

represents a set of forbidden energies that do not correspond to any allowed combinations of atomic<br />

orbitals.<br />

Figure 12.22 The B<strong>and</strong> Structures of the Period 3 Metals Na, Mg, <strong>and</strong> Al<br />

The 3s <strong>and</strong> 3p valence b<strong>and</strong>s overlap in energy to form a continuous set of energy<br />

levels that can hold a maximum of eight electrons per atom.<br />

Because they extend farther from the nucleus, the valence orbitals of adjacent atoms (3s <strong>and</strong> 3p in )<br />

interact much more strongly with one another than do the filled core levels; as a result, the valence b<strong>and</strong>s<br />

have a larger b<strong>and</strong>width. In fact, the b<strong>and</strong>s derived from the 3s <strong>and</strong> 3patomic orbitals are wider than the<br />

energy gap between them, so the result is overlapping b<strong>and</strong>s. These have molecular orbitals derived from<br />

two or more valence orbitals with similar energies. As the valence b<strong>and</strong> is filled with one, two, or three<br />

electrons per atom for Na, Mg, <strong>and</strong> Al, respectively, the combined b<strong>and</strong> that arises from the overlap of the<br />

3s <strong>and</strong> 3p b<strong>and</strong>s is also filling up; it has a total capacity of eight electrons per atom (two electrons for each<br />

3s orbital <strong>and</strong> six electrons for each set of 3p orbitals). With Na, therefore, which has one valence electron,<br />

the combined valence b<strong>and</strong> is one-eighth filled; with Mg (two valence electrons), it is one-fourth filled;<br />

<strong>and</strong> with Al, it is three-eighths filled, as indicated in . The partially filled valence b<strong>and</strong> is absolutely crucial<br />

for explaining metallic behavior because it guarantees that there are unoccupied energy levels at an<br />

infinitesimally small energy above the highest occupied level.<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

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