The quantun theory of light
Thus, the absorption and emission spectra of atoms are discontinuous, or line, spectra. This must mean that the energies between electronic levels in atoms must be fixed at certain values, or quantized. The German physicist Max Planck showed that electromagnetic radiation could only be emitted or absorbed by matter is discrete packets of energy called quanta (singular: quantum). He was able to show that the energy of a quantum is directly proportional to the frequency of the radiation:
E = hn
where h is the proportionality constant is known as Planck's constant and has the value 6.626 x 10-34 J-sec.
In 1905, Albert Einstein, then an unknown clerk in the Swiss Patent Office2, published a remarkable paper in which he showed that the light can be regarded as a collection of individual particles. Each particle of light, which we now know as a photon, has associated with it a distinct energy that is proportional to the frequency of the light, and which corresponds to Planck’s energy quanta. The mass of a photon moving at the speed of light is given by the expression
Since h and c are constants, we see that the mass of a photon is inversely proportional to the wavelength. This equation illustrates something very important:
light has both particle (hence we can talk about a photon's mass) and wave (hence we can discuss the wavelength) properties.
This is known as the wave-particle duality of light. In 1923 the young French physicist Louis de Broglie used this idea to calculate the wavelength of a particle by the expression:
where m is the mass of the particle and v is its velocity. Since h is so small, the wavelengths of macroscopically sized particles are so small that they can't be measured. For particles with a very small mass, however, the wavelength can easily be measured. Even individual atoms are sufficiently massive that their wave character is not observable in most kinds of experiments.
Electrons, however, are another matter; the electron was in fact the first particle whose wavelike character was seen experimentally. Electron diffraction has become an important tool for investigating the structures of molecules and of solid surfaces. When an electron microscope is used to achieve very high magnifications, the electrons are exhibiting wave properties in much the same fashion as the light in an ordinary light microscope.
The inability to predict the exact location of subatomic particles was rationalised by the German physicist Werner Heisenberg. In 1927 he summarised these ideas in his famous uncertainty principle:
It is impossible to determine simultaneously the exact position and momentum (p = mv) of a single atomic particle
One interesting consequence of this principle is that even at a temperature of absolute zero, the molecules in a crystal must still possess a small amount of zero point vibrational motion, sufficient to limit the precision to which we can measure their locations in the crystal lattice.
Thus, wave-particle duality is a property of electrons as well as of photons. The particle properties of an electron are expressed in its ability to act only as a single whole. The wave properties of an electron manifest themselves in the features of its motion, and in the diffraction and interference of electrons.