The photoelectric effect and the Compton effect again point to the duality of the nature of electromagnetic radiation. The models of light as a wave and also as a particle complement each other. When the photons of electromagnetic radiation are of relatively high energy, the wavelengths are short. Then the photon acts more like a particle than a wave. For example, the Compton photons were high‐energy x‐rays. When the photons of electromagnetic radiation have relatively low energy, the wavelengths are long. Radio waves are an example of less energetic photons that act more like waves than particles.
De Broglie waves
Louis de Broglie (1892–1987) postulated that because photons have both wave and particle characteristics, perhaps particles also have wave characteristics. From the energy of the photon,
the momentum of a photon can be derived:
De Broglie hypothesized that material particles with momentum p should have a wave nature and a corresponding wavelength given by his equation:
Note that the de Broglie wavelength is directly proportional to h, which is a constant to the –34 power. With the relatively large masses and velocities of ordinary life, the de Broglie wavelengths are so small that they are virtually undetectable.
The Heisenberg uncertainty principle
The Heisenberg uncertainty principle, formulated by Werner Heisenberg (1901–1976), states that it is impossible to simultaneously measure a particle's position and velocity exactly. Specifically, the uncertainty in the measurements are given by
Another form of the expression refers to the uncertainty in measurements of energy and time
In principle, it is possible to make exact measurements in classical physics; however, even in principle making exact measurements is not possible in quantum mechanics. Consider finding the exact position of a charged particle that produces a spot of light when hitting a phosphor. The exact position is known, but information about the particle's momentum has changed. Or consider viewing an object under a microscope. In order to see the object, some photons must reflect off it to the eye of a viewer. These incident photons will cause uncertainties in the measurement. In other words, the very act of the measurement procedure in quantum mechanics introduces uncertainty into the data collected.