Question

Why does the binding energy per nucleon suddenly decrease between helium and lithium?

Answer 1

I think this is best described by shell theory - the idea that nucleons (as well as electrons) occupy quantised shells.

Explanation:

As both protons and neutrons are fermions they also obey the Pauli exclusion principle so cannot occupy identical quantum states, but exist in energy ‘shells’.

The lowest energy state allows for two nucleons but, as protons and neutrons have different quantum numbers, two of each can occupy this state (hence a mass of 4 amu.) This explains why `alpha` particles are readily emitted from massive, unstable nuclei as a “blob”. They are the single most stable unit in the nucleus, thus prone to be emitted together.

The theory thus provides a good explanation for the effect you describe, but also explains the ‘unreasonable’ stability of calcium and other nuclei. I’m teaching this next week and found a good video here (though it is quite long for teaching, so maybe a h/wk for my students!)

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