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   Blaise Pabón - controlpl4n3 (blaise@hachyderm.io)'s status on Thursday, 10-Apr-2025 23:52:41 JST Blaise Pabón - controlpl4n3

   in reply to

   • John Carlos Baez

   @johncarlosbaez
   In highschool (1981) we only learned s, p, d, f, with the mnemonic Sopa Pura De Fideos.

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 10-Apr-2025 23:52:42 JST John Carlos Baez

     in reply to

     In nuclear physics, the magic numbers are

       2
       8 = 2+6
      20 = 2+6+12
      28 = 2+6+12+8
      50 = 2+6+12+8+22
      82 = 2+6+12+8+22+32
     126 = 2+6+12+8+22+32+44

     What's the big deal about this? I could explain it to you, but I'm just learning this stuff, so I'd basically be repeating the explanation here:

     https://en.wikipedia.org/wiki/Nuclear_shell_model

     The basic idea is this: neutrons and protons in nuclei form 'shells' somewhat like how electrons form shells in atoms... so a lot of the same math applies, namely the representation theory of the rotation group. But protons and neutrons interact so strongly that the patterns get complicated, even for fairly small nuclei. For the electrons in atoms, we can do surprisingly well at predicting the patterns in the periodic table by pretending they don't interact, until we reach rather large atoms.

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     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.

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