Some atoms are stable, while others appear to fall apart. Lead-208 will probably last forever, but the synthetic isotope Technetium-99 will be present for just a few hours. The difference lies in the structure of the nuclei of atoms, where a certain “magic number” of nuclear particles creates isotopes that are particularly resistant to radioactive decay.
So, what are these magical numbers and why are they so special?
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This stability appears to be partially connected to the mass of the atoms, and has proven to be less stable for heavier elements. However, in the 1940s and 1950s, scientists observed that many of the lighter elements also had radioisotopes. Both carbon-14 and potassium-40 undergo slow radioactive decay, causing much of the planet’s background radiation.
Interestingly, these scientists noticed that a very specific number of protons and neutrons appear to lead to an unusually stable nucleus, and these values have come to be known as magical numbers.
“The magic numbers are 2, 8, 20, 28, 50, 82, 126,” said David Jenkins, a nuclear physicist at York University in the UK.
Related: Why are the nuclei of atoms not round?
Shell Game
Helium nuclei, also known as alpha particles, are spontaneously released from heavier, unstable atoms when undergoing nuclear decay.
“If you think about it, it’s very strange,” Jenkins said. “If an atom decays, why don’t you lose one proton or neutron at a time? The reason is that the alpha particles are so stable that it relates to this magical idea of numbers.”
Other magical nuclei include oxygen-16 (8 protons and 8 neutrons), calcium-40 (20 protons and 20 neutrons), and lead 208 (82 protons and 126 neutrons).
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To understand these strange observations, physicists proposed the “nuclear shell model.” This is similar to the electron shell used to explain the chemical behavior of atoms.
“Protons and neutrons were a bit similar to electrons in atoms, and the excitation of the nucleus was accompanied by protons and neutrons jumping between their shells,” Jenkins explained.
Like their electron analogs, these nuclear shells have fixed energy values known as quantized states, and once these shells are fully filled, the system is most stable. The exact reason behind this is the complex combination of quantum mechanical factors, but the powerful force, the fundamental interaction that holds protons and neutrons together in the nucleus, is thought to be higher than expected per particle in the completed shell.
Therefore, the magical number is the number of particles needed to fill each of these nuclear shells, with separate levels of protons and neutrons. Individual isotopes are magical accordingly, either alone, with a magic number of protons or neutrons (e.g., primitive isotope iron 56), or double magic, with both positive and neutrons (e.g., oxygen-16 or Lead-208).
These double magical systems are rare, but they have some interesting quantum properties, Jenkins said.
“The double magic system has a spherical distribution of matter and charging,” he said – a completely round nucleus. “Most nuclei deform and rotate. They have very different structures.”
No one knows how far this model will grow. TIN-100 – the heaviest double magical nucleus with 50 protons and 50 neutrons – has a half-life of just 1.2 seconds, but the next magical element after lead, Unbihexium, has been synthesized. So whether this magical stability improvement is sufficient to allow scientists to add 8 columns to the cycle table remains an open question.
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