The Foundations of Chemistry

Solution

(a) m9.11 10
^28 g9.11 10
^31 kg

Substituting into the de Broglie equation,



m

h

v

5.87 10 
^11 m

Though this seems like a very short wavelength, it is similar to the spacing between atoms in
many crystals. A stream of such electrons hitting a crystal gives measurable diffraction patterns.

(b) m5.25 oz0.149 kg

v41.3

Now, we substitute into the de Broglie equation.



m

h

v

1.08^10 
^34 m

This wavelength is far too short to give any measurable effects. Recall that atomic diameters
are in the order of 10
^10 m, which is 24 powers of 10 greater than the baseball “wavelength.”

You should now work Exercise 64.

As you can see from the results of Example 5-7, the particles of the subatomic world
behave very differently from the macroscopic objects with which we are familiar. To talk
about the behavior of atoms and their particles, we must give up many of our long-held
views about the behavior of matter. We must be willing to visualize a world of new and
unfamiliar properties, such as the ability to act in some ways like a particle and in other
ways like a wave.
The wave behavior of electrons is exploited in the electron microscope. This instru-
ment allows magnification of objects far too small to be seen with an ordinary light
microscope.

THE QUANTUM MECHANICAL PICTURE OF THE ATOM

Through the work of de Broglie, Davisson and Germer, and others, we now know that
electrons in atoms can be treated as waves more effectively than as small compact parti-
cles traveling in circular or elliptical orbits. Large objects such as golf balls and moving
automobiles obey the laws of classical mechanics (Isaac Newton’s laws), but very small

5-14

6.626 10
^34 

kg

s

m^2





(0.149 kg)41.3 

m

s



m



s

1000 m



1 km

1.609 km



1 mile

1 h



3600 s

92.5 miles



h

1 kg



2.205 lb

1 lb



16 oz

6.626 10
^34 

kg

s

m^2





(9.11 10 
^31 kg)1.24 107 

m

s



1 kg



1000 g

A color-enhanced scanning electron

micrograph of human red blood

cells, magnified 1200.

5-14 The Quantum Mechanical Picture of the Atom 205

A modern electron microscope.