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

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18 • Chapter 2 / Atomic Structure and Interatomic Bonding

Orbital electron

Nucleus

Figure 2.1 Schematic representation of the Bohr

atom.

This Bohr model was eventually found to have some significant limitations be-

cause of its inability to explain several phenomena involving electrons. A resolution

wave-mechanical was reached with awave-mechanical model,in which the electron is considered to

model exhibit both wave-like and particle-like characteristics. With this model, an electron

is no longer treated as a particle moving in a discrete orbital; rather, position is con-

sidered to be the probability of an electron’s being at various locations around the

nucleus. In other words, position is described by a probability distribution or elec-

tron cloud. Figure 2.3 compares Bohr and wave-mechanical models for the hydrogen

atom. Both these models are used throughout the course of this book; the choice

depends on which model allows the more simple explanation.

Quantum Numbers

Using wave mechanics, every electron in an atom is characterized by four parameters

quantum number calledquantum numbers.The size, shape, and spatial orientation of an electron’s

00

–1 × 10 –18

–2 × 10 –18

(a) (b)

–5

–10

–15

n = 1 1 s

Energy (eV) Energy (J)

n = 2

n = 3

2 s

3 s

2 p

3 p

3 d

–1.5

–3.4

–13.6

Figure 2.2 (a)The

first three electron

energy states for the

Bohr hydrogen atom.

(b) Electron energy

states for the first

three shells of the

wave-mechanical

hydrogen atom.

(Adapted from W. G.

Moffatt, G. W.

Pearsall, and J. Wulff,

The Structure and

Properties of

Materials,Vol. I,

Structure,p. 10.

Copyright©c1964 by

John Wiley & Sons,

New York. Reprinted

by permission of John

Wiley & Sons, Inc.)