BioPHYSICAL chemistry

In classical physics, in addition to particles there are
also objects called waves, which are physical objects
extended throughout space. Because waves are not con-
fined at a specific location they cannot be described by
the same parameters as used for particles. Waves can be
described by the parameters wavelength, λ, frequency,
ν, and amplitude, A(Figure 9.1).
These parameters describe stationary waves that do
not change with time, but waves can also travel with
a velocity 9. In this case, the wavelength is related to
the frequency and speed according to:

λν= 9 (9.6)

For the specific case of light, the velocity in a vacuum
is denoted by the constant cand the equation becomes:

λν=c (9.7)

The energy of a wave is given by its intensity, which is proportional to the
square of the amplitude, and is independent of the frequency or wavelength:

E∝A^2 (9.8)

According to classical theory, once all of these parameters are known for
a particle or wave, the theory should be able to predict all properties of
the object. Classical theory was indeed very successful in such predictions;
however, there were some dramatic failures. We will present some of
the failures and discuss how these lead to the development of quantum
mechanics.

Experimental failures of classical physics

Blackbody radiation

When objects get hot they emit radiation. The type of radiation emitted
depends upon the temperature. For example, when you heat something the
color can be a red or blue or even white. In most cases, the color emitted
at different parts of the object will vary due to differences in the temper-
ature. For an ideal emitter called a blackbody, the emitted radiation is in
thermal equilibrium with the object, resulting in a uniform emission of
radiation. A blackbody can be modeled as a sphere in which the light
emitted by the interior walls is trapped – that is, absorbed and re-emitted

• except for a small portion that can escape through a pinhole (Figure 9.2).

CHAPTER 9 QUANTUM THEORY 177

Amplitude, A

Velocity  v

Wavelength, λ

Frequency ν  (^) λv
Figure 9.1
A classical wave
with the wavelength,
λ, and amplitude,
A, marked.
The frequency,
ν, is inversely
proportional to λ.