This chapter of the video:
• presents an electron interference experiment using a double-slit.
• illustrates how the experiment provides evidence for both the particle nature and the wave nature of electrons.
• introduces de Broglie’s wave equation for matter.
WAVE-PARTICLE DUALITY
In classical physics, matter is modelled as a particle. However, in the subatomic world of quantum physics, things are different. The double-slit experiment with electrons highlights the dual nature of subatomic matter, illustrating both particle and wave behaviour, intrinsic to the quantum realm.
Dr. Herman Batelaan and his team at the University of Nebraska-Lincoln have successfully conducted an electron double-slit experiment. Dr. Batelaan’s team fired electrons at two tiny slits, only 100 nm wide. Their investigation is the most recent version of an electron double-slit experiment and provides a concrete look into the wave–particle duality of matter on quantum scales
HOW THE EXPERIMENT WORKS
In the experiment, a tungsten filament is heated to a few thousand degrees, causing electrons in the filament to be ejected at high speeds. The high-speed electrons pass through narrow apertures that collimate the beam. The beam of electrons is incident on a silicon nitride double-slit barrier. The slits are 100 nm wide and are separated by a distance of 200 nm. After passing through the slits each electron is detected by an electron multiplier that is used to generate a magnified image on a computer monitor. It is impossible to predict where an individual electron will hit the screen. After enough electrons have passed through the apparatus, however, a distinctive interference pattern emerges. Figure 2.3 is a simplified schematic diagram of the experimental set-up.
The intensity of the electron beam can be turned down so that there is only one electron in the apparatus at a time. Surprisingly, despite the fact that electrons are passing through the apparatus one electron at a time, an interference pattern will still develop over time. The interference pattern can be analyzed using the same equations used to investigate Young’s double-slit experiment for light.
where
The interference pattern result raises deep questions about what the electron is actually doing as it travels through the double-slit apparatus, and how seemingly particle-like objects are able to produce an interference pattern. The mathematical formalism of quantum mechanics predicts the interference, but it does not answer any questions about what a specific electron is actually doing inside the apparatus. This ambiguity is what leads to the various interpretations presented in Chapter 5.
MATTER EXHIBITS WAVE PROPERTIES
The wave–particle duality of an electron was part of de Broglie’s 1924 doctoral thesis, in which he derived his matter–wave equation (see equation 2.2). Interestingly, an electron interference experiment was not actually conducted until 1961 when Claus Jönsson of Tübingen, Germany finally verified the 1920s theoretical predictions. By then, the result was not at all surprising and received little fanfare. The wave nature of matter is mathematically expressed by the de Broglie equation
The variables contained in the de Broglie equation help illustrate the wave–particle duality of matter. The object’s wavelength, a wave property, is determined from the object’s mass and velocity (typically associated with a particle) and Planck’s constant. Planck’s constant is a common feature in equations dealing with quantum physics. The constant is extremely small and is related to the minimum size of the discrete units of energy, mass, spin, and other quantum descriptors.
It is important to emphasize that any quantum object exhibiting wave–particle duality only ever demonstrates one behaviour at a time. For example, in the double-slit experiment with electrons, the interference pattern is built up one electron at time and it is this pattern that provides the evidence for wave-like behaviour. However, the individual electrons that are emitted and strike the screen at localized spots provide evidence for particle-like behaviour. This dual nature is not observed in the macroscopic world, and it highlights a key difference between descriptions in classical physics and quantum physics. A classical particle always behaves as a particle, and never requires a classical wave model to describe its behaviour. A quantum object is not a classical particle or a classical wave. Careful use of language is required to correctly describe a quantum object. Phrases that describe the observed behaviour are preferred over statements about what a quantum object actually is. For example, it is safer to say that an electron “behaves like a particle” than an electron “is a particle.” Interpretations about what an electron “is” are discussed in the Chapter 5 Summary.
THE WAVEFUNCTION - A MATHEMATICAL DESCRIPTION
Quantum physics mathematically addresses wave–particle duality and the behaviour of an electron by using a mathematical wave called a wavefunction. A wavefunction gives the probabilities for finding an electron at all of the possible locations that it can be observed. If the amplitude of an electron’s wavefunction at a particular location is large, there is a high probability of finding the electron there. If the amplitude is small, there is a low probability of finding the electron there. The wavefunction is a mathematical description and, in the absence of a specific interpretation, does not answer the question about what an electron is.
