The Uncertainty Principle

An electron is a subatomic particle with mass, m. But it also behaves as a wave, with velocity v, as demonstrated by the de Broglie relation. So, an electron has both wave- and particle-like characteristics.

Unfortunately, it is not possible to witness the electron being both a particle, with a defined location, and a wave, with a known velocity or momentum, at the same time. What happens when an experiment is set up to observe the dual nature of an electron?

First, reconsider the double-slit experiment where there are two closely-spaced apertures. When a beam of electrons passes through the slits, an interference pattern is produced. This is a unique property of waves.

When electrons pass through one by one, the same pattern is observed. Since an electron is a particle, it should be possible to monitor which slit or slits it travels through.

To study this, a laser beam is arranged directly behind the slits. When an electron travels through a slit, it produces a small flash — indicating the slit it just passed through.

During the experiment, flashes are observed at only one of the slits at a time, but never both slits simultaneously. Moreover, the interference pattern is no longer observed; instead, two bright lines are seen. In trying to observe the particle-nature of the electron, its wave nature is lost.

In other words, the electron is observed as either a particle or a wave, but never both at the same time. The particle-nature and wave-nature of an electron, and by extension its position and momentum, are therefore complementary properties. This means that it is also impossible to simultaneously observe the accurate position and velocity of an electron.

Werner Heisenberg related that the uncertainty in these properties, represented by Δx and mΔv, must be greater than or equal to a finite quantity — Planck’s constant over 4π. This is known as Heisenberg’s Uncertainty Principle.

The more accurately the position of the electron is known, and the smaller the Δx, the less certain the velocity of the electron is known and larger the Δv, and vice versa.

Now, consider a golf ball resting on a tee. According to classical physics, the path or trajectory of the golf ball can be predicted by knowing its initial position, the force with which it is hit, and the effect of other factors, such as gravity, wind, and air resistance.

With these data, the golf ball’s position and velocity can be determined at any moment.

However, if only the golf ball’s initial location is known, it is not possible to deduce its final position.

Similarly, for an electron, because its position and velocity can not be known at the same time, its trajectory can also not be predicted. This is known as the indeterminacy behavior of an electron. Its present location can not determine its future position.

Because of this, instead of describing a precise position for an electron, the likelihood, or probability, of finding it within a certain region of the atom is used. This is known as a probability density, where each dot represents the potential location of an electron within an atom.

The density of dots is proportional to the probability of finding an electron. So, an electron is more likely to be found closer to the atom’s nucleus than very far away. Thus, a more accurate representation of the atom is depicted by the nucleus surrounded by its electron probability density, which is also known as the electron cloud model.