Nuclear decays

The Pauli Exclusion Principle favors nuclei with N approximately equal to Z. Coulomb repulsion modifies this somewhat in favor of N larger than Z.

Coulomb repulsion makes very large nuclei unstable because as more and more nucleons are put into a nucleus, the Coulomb energy keeps going up, while the effect of the attractive nuclear force goes up less strongly because of its short-range nature. This is the reason that the periodic table contains only a limited number of entries.

The most energetically favorable nucleus is a middle-weight one: 56Fe. Nuclei much lighter than iron can undergo fusion to form more energetically favorable nuclei and release energy. (Due to Coulomb repulsion, special circumstances are needed to get nuclei close enough to one another to fuse; one way is through very high temperatures such as those in the sun or inside a nuclear bomb.) Nuclei that are much larger than iron can lower their energy through alpha decay in which they emit 2 protons and 2 neutrons packaged as a helium 4 nucleus, or by fission, in which the nucleus splits into two large fragments.

Although nuclei and other particles can change (e.g. beta decay of a neutron) the reactions must satisfy 3 conservation laws.

  1. Baryon number conservation: Protons and neutrons are examples of baryons. Electrons, photons and neutrinos have zero baryon number. The number of baryons must be the same before and after the reaction. Anti-protons and anti-neutrons have a negative baryon number. Therefore a proton and an anti-proton could annihilate each other and produce two photons.

  2. Lepton number conservation: Electrons and neutrinos are examples of leptons. Anti-electrons and anti-neutrinos are equivalent partices with negative lepton number. Photons, protons and neutrons have zero lepton number.

  3. Electric charge conservation:. Protons have a positive charge, electrons have a negative charge and neutrons, photons and neutrinos are neutral. An anti-proton has a negative charge and an anti-electron (positron) has a positve charge).

These three conservation laws can be illustrated in the beta decay of a neutron,

Baryon number is conserved by the presence of the proton on the right. The electron is necessary to conserve electric charge and the anti-neutrino (the 'anti" being noted by the overbar) ensures the conservation of lepton number. More about the conservation laws will be stated when we discuss particle physics.

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