The Mass-5 Roadblock

Protons can combine to form alpha particles in proton-proton fusion. This can be presumed to have created alpha particles in the early universe, but the existence of the present universe depends upon the fact that alpha particles didn't combine to make heavier elements, clumping all the matter into heavy nuclei.

The alpha particle is extraordinarily tightly bound, with a particle binding energy of 28.3 MeV. It could form a mass-5 nucleus by adding a neutron to form 5He or a proton to form 5Li, but neither of these nuclides is stable. If you use the Weizsaecker formula to estimate the binding energy

Eb(5He) = 20.3 MeV

Eb(5Li) = 18.2 MeV

Both of these binding energies is much less than the binding energy of the alpha particle. If you look at the energetics of adding a proton or a neutron to an alpha particle:

Mass-5 nuclide
α + nucleon
Anticipated mass of 5He (MeV)
3(939.565) + 2(938.273) - 20.3 = 4674.9
α + n
3727.4 + 939.565 = 4667.0 MeV
Anticipated mass of 5Li (MeV)
2(939.565) + 3(938.273) - 18.2 = 4675.7
α + p
3727.4 + 938.273 = 4665.7 MeV

So an alpha particle plus either a free neutron or proton would have higher stability (lower mass) than either of these mass-5 nuclides. This mass-5 roadblock is an important part of the history of the universe. If the combination of protons and neutrons had been allowed to continue with the formation of all the heavier elements, there would have been no star and galaxy formation and no universe as we know it.

Mass-5 roadblock in the big bang model
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