Page 51 - Materials Science and Engineering An Introduction

2.3 Electrons in Atoms • 23

0 0 Figure 2.2 (a) The first three electron
energy states for the Bohr hydrogen atom.
3d
–1.5 n = 3 3p (b) Electron energy states for the first three
3s shells of the wave-mechanical hydrogen atom.
(Adapted from W. G. Moffatt, G. W. Pearsall, and J.
2p
–3.4 n = 2 Wulff, The Structure and Properties of Materials, Vol.
2s I, Structure, p. 10. Copyright © 1964 by John Wiley &
Sons, New York.)
–5
Energy (eV) –1 × 10 –18 Energy (J)

–10

–2 × 10 –18
–13.6 n = 1 1s

–15
(a) (b)
wave-mechanical models for the hydrogen atom. Both models are used throughout the
course of this text; the choice depends on which model allows the simplest explanation.

Quantum Numbers
In wave mechanics, every electron in an atom is characterized by four parameters called
quantum number quantum numbers. The size, shape, and spatial orientation of an electron’s probability
density (or orbital) are specified by three of these quantum numbers. Furthermore,
Bohr energy levels separate into electron subshells, and quantum numbers dictate
the number of states within each subshell. Shells are specified by a principal quantum
number n, which may take on integral values beginning with unity; sometimes these
shells are designated by the letters K, L, M, N, O, and so on, which correspond, respec-
tively, to n 1, 2, 3, 4, 5, . . . , as indicated in Table 2.1. Note also that this quantum

Table 2.1 Summary of the Relationships among the Quantum Numbers n, l, m l and Numbers of Orbitals
and Electrons
Value of n Value of l Values of m l Subshell Number of Orbitals Number of Electrons
1 0 0 1s 1 2
0 0 2s 1 2
2
1 1, 0, 1 2p 3 6
0 0 3s 1 2
3 1 1, 0, 1 3p 3 6
2 2, 1, 0, 1, 2 3d 5 10
0 0 4s 1 2
1 1, 0, 1 4p 3 6
4
2 2, 1, 0, 1, 2 4d 5 10
3 3, 2, 1, 0, 1, 2, 3 4f 7 14
Source: From J. E. Brady and F. Senese, Chemistry: Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley &
Sons, Inc.