The Foundations of Chemistry

described by quantum numbers that can have only certain allowed values, and that the

quantum numbers indicate something about where and how stable the electrons are in

these energy levels. The ideas of modern atomic theory have replaced Bohr’s original

theory. But his achievement in showing a link between electronic arrangements and Balmer

and Rydberg’s empirical description of light absorption, and in establishing the quantiza-

tion of electronic energy, was a very important step toward an understanding of atomic

structure.

Two big questions remained about electrons in atoms: (1) How are electrons arranged

in atoms? (2) How do these electrons behave? We now have the background to consider

how modern atomic theory answers these questions.

THE WAVE NATURE OF THE ELECTRON

Einstein’s idea that light can exhibit both wave properties and particle properties suggested

to Louis de Broglie (1892–1987) that very small particles, such as electrons, might also

display wave properties under the proper circumstances. In his doctoral thesis in 1925, de

Broglie predicted that a particle with a mass mand velocity vshould have the wavelength

associated with it. The numerical value of this de Broglie wavelength is given by

h/mv (where hPlanck’s constant)

Two years after de Broglie’s prediction, C. Davisson (1882–1958) and L. H. Germer

(1896–1971) at the Bell Telephone Laboratories demonstrated diffraction of electrons by

a crystal of nickel. This behavior is an important characteristic of waves. It shows conclu-

sively that electrons do have wave properties. Davisson and Germer found that the

wavelength associated with electrons of known energy is exactly that predicted by de

Broglie. Similar diffraction experiments have been successfully performed with other parti-

cles, such as neutrons.

EXAMPLE 5-7 de Broglie Equation

(a) Calculate the wavelength in meters of an electron traveling at 1.24 107 m/s. The mass of

an electron is 9.11 10 
^28 g. (b) Calculate the wavelength of a baseball of mass 5.25 oz trav-

eling at 92.5 mph. Recall that 1 J1 kg m^2 /s^2.

Plan

For each calculation, we use the de Broglie equation



m

h

v



where

h(Planck’s constant)6.626 10 
^34 J s

6.626 10
^34 

kg

s

m^2



For consistency of units, mass must be expressed in kilograms. In part (b), we must also convert

the speed to meters per second.

1 

kg

s

2

m^2





1 J

5-13

Materials scientists study electron
diffraction patterns to learn about
the surfaces of solids.

204 CHAPTER 5: The Structure of Atoms

Be careful to distinguish between the
letter v, which represents velocity, and
the Greek letter nu, , which
represents frequency. (See Section
5-10.)

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 7.8, Wave Properties of the
Electron.