Atomic Orbitals: The Origin Story

Hi! Welcome to Science with Serena.

I’m Serena.

I write about concepts in quantum computing the way I would like to read about them. Today I’m taking a brief intermission from superconductors to talk about something just as exciting. So foundational we almost forget about them, if you’ve ever wondered how we know atoms exist, or why they behave the way they do — you’re in the right place.

Let’s get into it.

What are Atoms?

The existence of tiny, indivisible particles as the foundation of the universe was first thought up by Greek philosopher Democritus around 5th century BCE in ancient Greece. As thinking really hard was considered science back then (petition to bring this back?), Democritus’s position on matter was more a philosophical pondering than a concrete theory backed by evidence. Still, his way of understanding the universe gave atomic theory a strong start.

old time-y science when thinking really hard was peak performance.

The next evolution came about in 1897 when J.J. Thomson discovered a negatively charged particle, later named the electron, indicating atoms weren’t indivisible. He proposed the “plum pudding” model to explain what he saw, which modeled atoms as big balls of positive charge with little balls of negative electrons floating around in them.

Ernest Rutherford quickly refined this idea in 1911 with his experiment on gold foil, revealing atoms have a dense, positively charged nucleus, with electrons surrounding it.

Niels Bohr was then next person to take a stab at modeling the atomic structure of an atom. He approached the problem by trying to explain the hydrogen spectrum using quantum mechanics. Until then, there had been a mystery surrounding this spectrum because hydrogen emitted distinct spectral lines when exposed to light when it should have been a continuous band.

Each scientist’s attempt to match observable physical reality with atomic structure. Bohr’s model is what people are usually most familiar with, which is good, except it it’s not really accurate at all. Garbage, as my favorite chem professor used to say.

By combining the previous atomic model with quantization, Bohr was able to explain the spectral lines emitted by hydrogen with a re-imagined atomic structure. He found that by considering electrons only at specific energy levels (rather than just anywhere in the atom), he could explain the emission lines he saw. Electrons in orbit around the nucleus would absorb light energy, hop up to another energy level, and then release a wavelength as they relaxed back down to their original energy level. The wavelength released matched the lines perfectly!

This model gave us the image of an atom most of us know and love: electrons orbiting around a nucleus in specific energy levels. Yet when Bohr tried to apply this model more complex atoms, it fell apart.

As it turns out, he was thinking about atoms all wrong.

Schrödinger Saves the Day

Erwin Schrödinger was the one who developed a key component of the modern atomic model using a method he invented called wave mechanics. Unlike in regular mechanics where atoms are treated only like tiny particles, in wave mechanics the atoms are modeled as waves . To learn more about how and why that is, check out my previous article on particle-wave duality

In wave mechanics, a particle’s behavior is described by a mathematical function called a wavefunction. The wavefunction is the solution to Schrodinger’s wave equation, which describes how a particle’s wavefunction changes in time and space. We use the wave equation as a tool to get the wavefunction to tell us about the particle.

where. are. the. electrons.

The conceptually tricky part is that the wavefunction is not a description of reality itself — it has no physical equivalent. It does not “represent” the particle. Instead, we can think of it like a placeholder to get us to the information we do want: the probability of finding a particle at a particular location, called a probability density function. The probability density of a particle is the square of the wavefunction and what we can consider the particle to “be”.

How Schrödinger’s work influenced the atomic model. Instead of being particles, electrons are considered at their highest probability densities.

It’s a bit confusing, so you can think about it like this: imagine you are our particle, and I am trying to find you at 3 am on Monday night.

I don’t really know where you are (as you could be anywhere), but you are somewhere so there is going to be a certain place in the world that has the highest probability of your presence. If its 3 am on a Monday night, you’re going to most likely be in your bed sleeping, so instead of determining your exact location, I could consider “you” to be the location with the highest probability of finding you. So, instead of modeling you, I can model “you” as the probability of you being in your bed. This is a good approximation as every time I physically check on you, that is exactly where you are.

It’s the same for our electrons. If we wanted to find out where they are in our atom, we can consider them to be where we are most likely to find them, where their probability densities are highest.

The Schrödinger Equation

To do that for an electron, we need to employ the tool I mentioned earlier — the Schrödinger equation. The Schrödinger equation describes the quantum state of a system by solving it for a wavefunction. We just pick our system, define its potential energy, and set some boundary conditions. Once we do that, our wavefunction will give us the position the particle is most likely to have and its allowed energy levels.

Using this method to solve for the position of an atom’s electrons gave Schrodinger the accurate atomic model. He found the most likely locations of electrons were called orbitals and came in different shapes depending on their energies.

The s orbital is the lowest energy level and is a spherical region around the nucleus. The p orbital comes next and is shaped like a dumbbell, with the density regions on either side, appearing in three orientations.

Visualization of the first three orbitals (s, p, d). Fun fact, these were actually named for how they appeared on a hydrogen spectra — sharp, principle, diffuse. Sorry not sorry for the lack of f orbital drawings; I am not God.

There are five d orbitals, each with a complex, clover-like shape made up of four lobes. The trend continues with the next orbital, the f orbital, and so on and so forth. These orbitals, combined with Pauli’s Exclusion Principle (which stated how electrons could fit into each energy level) gave us the atomic model we use now: a positive nucleus with surrounding electron density clouds called orbitals.

Join me next time as I look at the final boss of superconductivity — superconducting qubits and how they use the principles discussed in my previous articles to perform quantum computing.

Until then, science needs me.

Gotta go!

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