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Book Summary: Elemental

Author: Tim James

Substory: Schrödinger’s Quantum Equation

Quantum mechanics is infamous. Everyone has heard about it and its reputation for being weird (a reputation that is well deserved, by the way). However, in recent years, some of the vocabulary has been hijacked by spiritualists to mean all sorts of unrelated things, which sadly confuses the issue. Don’t misunderstand me; there’s nothing wrong with talking about spirituality but repurposing words from quantum mechanics to mean something else is unhelpful. So we’ll tread carefully.

The first thing to say is that quantum mechanics is not one idea but a sophisticated collection of theories that explain the world at its smallest level. The behavior of electrons, the nucleus, light, and their interactions are all explained by quantum mechanics so it is of great importance to chemistry.

Covering it in detail would take a separate book entirely so we’ll limit the discussion to the part, developed by Austrian physicist Erwin Schrödinger, that helped build the periodic table.

Schrödinger caused a lot of discomfort during his life and was politely asked to leave a number of universities and institutions. This wasn’t because of his academic achievements, which were outstanding. It was because he lived in a three-way relationship with his wife Annemarie and their girlfriend Hilde. He also wore a lot of bow ties. Scandalous.

Schrödinger’s most important contribution to science is called the Schrödinger wave equation. It’s the equation that tamed the periodic table and explains why elements behave the way they do. It looks like this:


I know equations can sometimes put people off but this one is vital to the story, so we can’t just brush it under a rug. I’ve included a short explanation of what it means in Appendix III if you’re feeling adventurous but don’t worry, we can still understand what the equation does without having to go into any mathematical detail.

Nobody is sure how Schrödinger came up with his equation because there are no clear records of him deriving it. Some claim he simply woke up one morning, went downstairs, and wrote it based on gut feeling. It was only later that it was tested and proven correct.

What the equation does is tell us where electrons are likely to be as they zip about the nucleus. You start by taking the electron’s properties (things like its mass, velocity, etc.) and then figure out how much attraction there is from the protons of whichever atom you want to describe.

By solving the equation for a given atom we can map out a three-dimensional region of where electrons are going to be and what patterns they will trace out in space.

When we do this, we find that electrons don’t move in circular orbits at all. They surround the nucleus in regions that come in a variety of shapes, the same way animals inhabit different-shaped enclosures at a zoo. We call these regions “orbitals” or sometimes when we’re being lazy, “electron clouds.”

Some electrons hang out in spherical orbitals while others occupy a dumbbell-shaped region protruding from the top and bottom of the atom. Each orbital can hold up to two electrons, so the more electrons you have on your atom the more orbitals end up being used and the more extravagant your atomic shape becomes.

The reason certain orbital shapes arise is because electron movements are sort of wavy. They don’t move in simple lines like marbles but seem to ripple as they travel from one point to another. Since ripples can only come in certain shapes (you can’t have half a wave, for example) so do the electron orbitals.