BioPHYSICAL chemistry

only a limited number of orbitals, the light is emitted only at a limited

number of frequencies.

For reasons discussed in Chapter 10, this model was qualitatively useful

but could not provide an accurate prediction for complex multi-electron

atoms. However, the Bohr model represented a fundamentally new para-

digm for understanding the atom and provided a compelling reason for

the development of detailed theories of quantum mechanics.

Principles of quantum theory

The inability of classical mechanics to provide explanations for experi-

ments such as the ones described above led to the introduction of several

postulates concerning the behavior of matter. These various postulates were

developed into a coherent theory in the 1920s. There were two parts to

this development. First, a physical picture of the theory was developed by

Louis de Broglie, called the wave–particle duality. Second, classical theory

was modified by Erwin Schrödinger to provide a mathematical formalism

describing the quantum effects leading to the Nobel Prize in Physics in

1933. This new formalism introduced the ideal that objects are not fully
      described according to the classical picture but the wave and particle nature
      of objects must be combined in a new description called the wavefunction.
      These developments had some unexpected predictions whose merits were
      debated for many years, with one example known as Schrödinger’s cat,
      discussed at the end of this chapter.

Wave–particle duality

Classically, particles and waves have distinct parameters:

• Particles: mass m, position r, velocity 9 , charge q


• Waves: wavelength λ, frequency ν, velocity 9 , amplitude A

However, the experiments described above could only be interpreted if

light was assumed to have particle-like properties; that is, if light was com-

posed of discrete objects with quantized energies. This led to the idea

that particles and waves could not be treated as distinct objects.

Experimentally this could be tested directly as it impliesthat

particles would have wave properties. Diffraction was a prop-

erty that had been thought to be unique for waves. In 1925,

Clinton Davisson and Lester Germer tested the possibility of a

wave property for particles using diffraction experiments and

found that electrons would diffract in a grating (Figure 9.5).

Subsequently, it was shown that other types of particle could

also diffract.

182 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY

Electron
beam

Diffracted

electrons

Nickel

crystal

Figure 9.5A beam
of electrons strikes a
nickel crystal and
the outward beam
shows the variation
of intensity
characteristic of a
diffraction pattern.