Dr. Christopher S. Baird

# What is the shape of an electron?

Category: Physics      Published: February 7, 2014

By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and Associate Professor of Physics at West Texas A&M University

When interacting like a particle, an electron is exactly a single point in space and has no shape according to the Standard Model, as shown in this illustration. Public Domain Image, source: Christopher S. Baird.

Depending on how you define "shape", an electron either has no shape, or an electron can take on various wave shapes. The shape of an electron is never statically round like an orange. The reason for this is that an electron is not a solid little ball, despite being so often portrayed this way in the popular media and in elementary-level science texts. Rather, electrons are quantum objects. Along with all other quantum objects, an electron is partly a wave and partly a particle. To be more accurate, an electron is neither literally a traditional wave nor a traditional particle, but is instead a quantized fluctuating probability wavefunction. This wavefunction looks in certain ways like a wave and in other ways like a particle.

An electron looks like a particle when it interacts with other objects in certain ways (such as in high-speed collisions). When an electron looks more like a particle it has no shape, according to the Standard Model. In this context, physicists call an electron a "point particle," meaning that it interacts as if it is entirely located at a single point in space and does not spread out to fill a three-dimensional volume. If you find the concept of a fixed amount of mass being contained in the infinitely small volume of a single point illogical, then you should. But you have to realize that the electron is not literally a solid ball. This means that the electron's mass is not literally squeezed into an infinitely small volume. Rather, in certain cases where the electron looks somewhat like a particle, it interacts as if it were completely located at a single point. Therefore, in the sense of particle-like interactions, an electron has no shape.

An electron bound in a hydrogen atom takes on various shapes depending on its energy, such as shown here in this physically-accurate mathematical plot. Note that this image shows a single electron. Each of the white spots is one of the peaks of the electron's wavefunction. Public Domain Image, source: Christopher S. Baird.

Note that an electron is a fundamental particle; it is not made out of anything else (according to our current experiments and theories). All fundamental particles interact as shapeless points when acting like particles. But not all quantum objects are fundamental, and therefore not all quantum objects are point particles. The proton, for instance, is not fundamental, but is instead composed of three quarks. The existence of particles inside a proton means that a proton must spread out to fill a certain space and have a certain shape. A proton is not a point particle, but is in fact a sphere with a radius of 8.8 × 10-16 meters. (Note that as a quantum object, a proton is not a solid sphere with a hard surface, but is really a quantized wave function that interacts in particle-like collisions as if it were a cloud-like sphere.) If the electron was composed of other particles, it could indeed have a shape when interacting like a particle. But it doesn't. The electron is a point particle.

When an electron is behaving more like a wave, it can have all sorts of shapes, as long as its shape obeys the electron wave equation. An electron's wave equation, and therefore its shape, is a function of its energy and the shape of the potential well trapping it. For instance, when an electron is bound in a simple hydrogen atom, an electron can take on the familiar orbitals taught in elementary physics and chemistry classes, such as the shape shown on the right. In fact, the word "orbital" in this context really just means "the shape of an electron when acting as a wave bound in an atom". Each atomic orbital is not some mathematical average of where the electron has been, or some average forecast of where the electron may be. Each orbital is the electron, spread out in the quantum wavefunction state.

Electrons trapped in the wells of a quantum cascade laser take on wavefunction shapes that look more like our traditional notion of a wave, shown in this computationally-determined plot as the black and colored horizontal squiggles. Public Domain Image, source: Christopher S. Baird.

In the sense of its wave-like state, an electron in a hydrogen atom can have the shape of layered spheres (the "s" states), layered dumbbells (the "p" states), layered four-leaf clovers (the "d" states), and other shapes at higher energies. In other atoms and molecules, an electron can take on even more complex shapes.

An electron can also be trapped by other objects besides atoms. For instance, electrons trapped in the potential wells of a quantum cascade laser take on shapes that look more like traditional waves. An example of electron wavefunction shapes in a quantum cascade laser is shown on the right.

Note that when scientists or journalists say "the shape of an electron is round," they are not talking about the literal shape. They are talking about the electric field distribution created by a free electron, which is entirely different from the actual shape.