Nucleon Mass Problem

-I thought this was due to some rounding error. But no-

Back then, my naive mind doesn't know what E=mc^2 is. In this case, they aren't supposed to be directly added up. Mass-energy equivalence plays its part.

I searched up the mass of the proton and neutron and both turned about to be a teeeeeny tiiiiny bit bigger than 1 amu. I assumed that the fact that 12 nucleons add up to be heavier than 12 amu is a technical issue. How could 12 numbers bigger than 1 add up to 12?

From the internet, the mass of:

And the atomic mass unit is an accurate 1/12 the mass of a carbon-12 atom. Consisting of 6 neutrons, 6 protons and 6 electrons.

Now when you add the nucleon's masses together, you get -

Why is it bigger than 12.0989 amu? And I'm ignoring the electrons (which does have mass) so in fact it should be even heavier. Why is that?

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My answer for now...

There's this thing called a mass defect - the difference between the actual atomic mass and the predicted mass from adding the components' masses up.

The actual mass would always be smaller than the predicted mass. The difference is accounted for by the binding energy: the energy required to break a nucleus into its component nucleons, or the energy released when nucleons "fuse" together into a nucleus.

Wait what - are you saying that somehow, the nucleons' mass turned into energy? Yes! Remember what Einstein said? Mass can be transformed into energy, and vice versa, with a simple relation:

It's all clear then. The small bits of mass above 1 amu for protons and neutrons turned into energy and is released when they fuse into carbon-12 (side note: they're not fused together directly). Mystery solved!

Bonus: this is also how nuclear fusion in stars work. When nuclei fuse together to form a larger nucleus, energy is released (and mass is lost) because the larger nucleus has a larger average binding energy.

Nucleus fission (splitting a large nucleus into smaller ones), on the other hand, occurs when smaller nuclei have a collective higher average binding energy than the bigger nucleus. These smaller nuclei require less energy to exist thus the larger nucleus breaks into them.

Iron-56 has the highest average binding energy across all the nuclei, thus when conditions are established, nature always want to join smaller nuclei or break a larger nucleus to form iron-56.

NUCLEAR FISSION - Scientific Figure on ResearchGate. Available from: https://www.researchgate.net/figure/the-graph-of-binding-energy-per-nucleon_fig1_358738740 [accessed 5 Apr, 2024]