Elements: A Visual Exploration of Every Known Atom in the Universe
Book Preface
Hang on tight, we’re going to explain quantum mechanics in one page. (If you find this section too technical, feel free to skim it— there isn’t going to be a quiz at the end.) Every element is defined by its atomic number, the number of positively charged protons in the nucleus of every atom of that element. These protons are matched by an equal number of negatively charged electrons, found in “orbits” around the nucleus. I say “orbits” in quotes because the electrons are not actually moving around their orbits like planets around a star. In fact, you can’t really speak of them as moving at all.
Instead, each electron exists as a probability cloud, more likely to be in one place than another, but not actually in any one place at any given time. The figures below show the various threedimensional shapes of the probability clouds of electrons around a nucleus.
The first type, called an “s” orbital, is totally symmetrical—the electron is not any more likely to be in one direction than another. The second type, called a “p” orbital, has two lobes, meaning the electron is more likely to be found on one side or the other of the nucleus, and less likely to be found in any direction in between.
While there is only one “s”type orbital, there are three “p” types, with lobes pointing in the three orthogonal directions (x, y, z) of space. Similarly there are five different types of “d” orbitals and seven different types of “f” orbitals, with increasing numbers of lobes. (You may think of these shapes as a bit like threedimensional standing waves.) Each shape of orbital can exist in multiple sizes, for example the 1s orbital is a small sphere, 2s is a larger sphere, 3s is larger still, and so forth. The energy required for an electron to be in any given orbital increases as the orbit becomes bigger. And all else being equal, electrons will always settle into the smallest, lowestenergy orbit.
So do all the electrons in an atom normally sit together in the lowestenergy 1s orbital? No, and here we come to one of the most fundamental discoveries in the early history of quantum mechanics: No two particles can ever exist in exactly the same quantum state. Because electrons have an internal state known as “spin,” which can be either up or down, it turns out that exactly two electrons can reside in a given orbital— one with spin up and one with spin down. Hydrogen has only one electron, so it sits in the 1s orbital. Helium has two, and they both fit into 1s, filling it to its capacity of two. Lithium has three, and since there is no room in 1s anymore, the third electron is forced to sit in the higherenergy 2s orbital. And so on— the orbitals are filled one at a time in order of increasing energy.
Look at the Electron Filling Order diagram on the right side of any element page in this book, and you’ll see a graph of the possible orbitals from 1s to 7p, with a red bar indicating which ones are filled with electrons (7p is the orbital of highest energy occupied by electrons of any known element). The exact order in which orbitals are filled turns out to be surprisingly subtle and complex, but you can watch it happen as you flip through the pages of this book. Pay particular attention around gadolinium (64)—if you think you’ve got it figured out, your confidence might be shaken by what happens there.
It is this filling order that determines the shape of the periodic table. The first two columns represent electrons filling “s” orbitals. The next ten columns are electrons filling the five “d” orbitals. The final six columns are electrons filling the three “p” orbitals. And last but not least, the fourteen rare earths are electrons filling the seven “f” orbitals. (If you’re asking yourself why helium, element 2, is not above beryllium, element 4, congratulations—you’re thinking like a chemist rather than a physicist. Eric Scerri’s book, referenced in the bibliography, is a good start toward answering such questions.)
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May 21, 2021 
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