Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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2nd Revise Page

20 • Chapter 2 / Atomic Structure and Interatomic Bonding

Table 2.1 The Number of Available Electron States in Some of the Electron

Shells and Subshells

Principal Number of Electrons

Quantum Shell Number of

Number n Designation Subshells States Per Subshell Per Shell

1 Ks12 2

2 L s^128

p 36

s 12

3 Mp 3618

d 510

s 12

4 Np36 3 2

d 510

f 714

Thus, the Bohr model was further refined by wave mechanics, in which the intro-

duction of three new quantum numbers gives rise to electron subshells within each

shell. A comparison of these two models on this basis is illustrated, for the hydrogen

atom, in Figures 2.2aand 2.2b.

A complete energy level diagram for the various shells and subshells using the

wave-mechanical model is shown in Figure 2.4. Several features of the diagram are

worth noting. First, the smaller the principal quantum number, the lower the energy

level; for example, the energy of a 1sstate is less than that of a 2sstate, which in

turn is lower than the 3s. Second, within each shell, the energy of a subshell level

increases with the value of thelquantum number. For example, the energy of a 3d

state is greater than a 3p, which is larger than 3s. Finally, there may be overlap in

Principal quantum number, n

Energy

1

s

s

p

s

p

s

p

s

p

df sp

s

p

df

d

d

d

f

234567

Figure 2.4 Schematic

representation of the relative

energies of the electrons for the

various shells and subshells. (From

K. M. Ralls, T. H. Courtney, and J.

Wulff,Introduction to Materials

Science and Engineering,p. 22.

Copyright©c1976 by John Wiley &

Sons, New York. Reprinted by

permission of John Wiley & Sons,

Inc.)