Chart of nuclear shells and magic numbers from here: https://www.secretsofuniverse.in/magic-numbers-in-physics/

Notices where this attachment appears

1. Embed this notice
   John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 10-Apr-2025 23:52:43 JST John Carlos Baez

   Some atomic nuclei are round. Others are football-shaped. Some are even stranger. Some are pear-shaped! Some have a 'halo' of protons and neutrons orbiting a smaller core. They're all just minimizing energy - unless they're in a temporary 'excited state'. But the forces between protons and neutrons are so complex that this can make lots of things happen.

   Just as noble gases are exceptionally inert because they have a filled shell of electrons, the roundest and most stable nuclei are those with a filled shell of protons - and, separately, a filled shell of neutrons. Filled shells happen when we hit a 'magic number'. The magic numbers are

   2, 8, 20, 28, 50, 82, and 126.

   I want to show you some cool patterns in these numbers. But first, some examples:

   • Hydrogen, with just one proton, is perfectly round, but that's an exception.

   • Helium-4 has 2 protons and 2 neutrons, and that's the second most common element in the universe.

   • Oxygen-16 has 8 protons and 8 neutrons, and this is the most common form of oxygen.

   • Calcium-40 has 20 protons and 20 neutrons, and this is the most common form of calcium. It's also the heaviest stable nucleus that has the same number of protons and neutrons! Heavier nuclei need more neutrons to be stable, but calcium-40 is stabilized by the fact that 20 is a magic number.

   • Calcium-48 has 20 protons and 28 neutrons. It's not stable, because it has too many neutrons - but it has a half-life of 64 quintillion years, so it's damned close to being stable, thanks to the power of magic numbers.

   • Lead-208 has 82 protons and 126 neutrons. It's the most common form of lead.

   (1/2)