The Foundations of Chemistry

particles such as electrons, atoms, and molecules do not. A different kind of mechanics,

called quantum mechanics,which is based on the waveproperties of matter, describes

the behavior of very small particles much better. Quantization of energy is a consequence

of these properties.

One of the underlying principles of quantum mechanics is that we cannot determine

precisely the paths that electrons follow as they move about atomic nuclei. The Heisen-

berg Uncertainty Principle,stated in 1927 by Werner Heisenberg (1901–1976), is a

theoretical assertion that is consistent with all experimental observations.

It is impossible to determine accurately both the momentum and the position of an

electron (or any other very small particle) simultaneously.

Momentum is mass times velocity, mv. Because electrons are so small and move so rapidly,

their motion is usually detected by electromagnetic radiation. Photons that interact with

electrons have about the same energies as the electrons. Consequently, the interaction of

a photon with an electron severely disturbs the motion of the electron. It is not possible

to determine simultaneously both the position and the velocity of an electron, so we resort

to a statistical approach and speak of the probability of finding an electron within speci-

fied regions in space.

With these ideas in mind, we list some basic ideas of quantum mechanics.

1.Atoms and molecules can exist only in certain energy states. In each energy state,

the atom or molecule has a definite energy. When an atom or molecule changes its

energy state, it must emit or absorb just enough energy to bring it to the new energy

state (the quantum condition).

Atoms and molecules possess various forms of energy. Let us focus our attention on

their electronic energies.

2.When atoms or molecules emit or absorb radiation (light), they change their ener-

gies. The energy change in the atom or molecule is related to the frequency or

wavelength of the light emitted or absorbed by the equations:

Eh or Ehc/

This gives a relationship between the energy change, E, and the wavelength, , of

the radiation emitted or absorbed. The energy lost (or gained) by an atom as it goes from higher

to lower (or lower to higher) energy states is equal to the energy of the photon emitted (or absorbed)

during the transition.

3.The allowed energy states of atoms and molecules can be described by sets of

numbers called quantum numbers.

The mathematical approach of quantum mechanics involves treating the electron in an

atom as a standing wave.A standing wave is a wave that does not travel and therefore has

at least one point at which it has zero amplitude, called a node. As an example, consider

the various ways that a guitar string can vibrate when it is plucked (Figure 5-18). Because

both ends are fixed (nodes), the string can vibrate only in ways in which there is a whole

number of half-wavelengthsin the length of the string (Figure 5-18a). Any possible motion

of the string can be described as some combination of these allowed vibrations. In a similar

way, we can imagine that the electron in the hydrogen atom behaves as a wave (recall the

de Broglie relationship in the last section). The electron can be described by the same

This is like trying to locate the
position of a moving automobile by
driving another automobile into it.

206 CHAPTER 5: The Structure of Atoms

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 7.9, Heisenberg’s Uncertainty
Principle.

Recall that  c, so c/.