Page 54 - Materials Science and Engineering An Introduction

26 • Chapter 2 / Atomic Structure and Interatomic Bonding

Figure 2.7 Schematic representation of the
filled and lowest unfilled energy states for a
sodium atom. 3p
3s

Increasing energy 2s 2p

1s

worth noting. First, the smaller the principal quantum number, the lower the energy
level; for example, the energy of a 1s state is less than that of a 2s state, which in turn
is lower than that of the 3s. Second, within each shell, the energy of a subshell level in-
creases with the value of the l quantum number. For example, the energy of a 3d state is
greater than that of a 3p, which is larger than 3s. Finally, there may be overlap in energy
of a state in one shell with states in an adjacent shell, which is especially true of d and f
states; for example, the energy of a 3d state is generally greater than that of a 4s.

Electron Configurations
electron state The preceding discussion has dealt primarily with electron states—values of energy
that are permitted for electrons. To determine the manner in which these states are
Pauli exclusion filled with electrons, we use the Pauli exclusion principle, another quantum-mechanical
principle concept, which stipulates that each electron state can hold no more than two electrons
that must have opposite spins. Thus, s, p, d, and f subshells may each accomodate, re-
spectively, a total of 2, 6, 10, and 14 electrons; the right column of Table 2.1 notes the
maximum number of electrons that may occupy each orbital for the first four shells.
Of course, not all possible states in an atom are filled with electrons. For most
atoms, the electrons fill up the lowest possible energy states in the electron shells and
subshells, two electrons (having opposite spins) per state. The energy structure for a
sodium atom is represented schematically in Figure 2.7. When all the electrons occupy
the lowest possible energies in accord with the foregoing restrictions, an atom is said to
ground state be in its ground state. However, electron transitions to higher energy states are possible,
as discussed in Chapters 18 and 21. The electron configuration or structure of an atom
electron configuration
represents the manner in which these states are occupied. In the conventional notation,
the number of electrons in each subshell is indicated by a superscript after the shell–
subshell designation. For example, the electron configurations for hydrogen, helium,
2
1
6
1
2
2
and sodium are, respectively, 1s , 1s , and 1s 2s 2p 3s . Electron configurations for some
of the more common elements are listed in Table 2.2.
At this point, comments regarding these electron configurations are necessary.
valence electron First, the valence electrons are those that occupy the outermost shell. These electrons
are extremely important; as will be seen, they participate in the bonding between atoms
to form atomic and molecular aggregates. Furthermore, many of the physical and chemi-
cal properties of solids are based on these valence electrons.
In addition, some atoms have what are termed stable electron configurations—
that is, the states within the outermost or valence electron shell are completely filled.
Normally, this corresponds to the occupation of just the s and p states for the outermost
shell by a total of eight electrons, as in neon, argon, and krypton; one exception is he-
lium, which contains only two 1s electrons. These elements (Ne, Ar, Kr, and He) are