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Radioactive Decays

The three types of nuclear radioactive decay are alpha, beta and gamma emission.

  1. An alpha particle is a Helium 4 nucleus (two protons and two neutrons). It is produced by nuclear fission in which a massive nucleus breaks apart into two less-massive nuclei (one of them the alpha particle). This is a strong interaction process.

    Diagram of a typical alpha decay

  2. A beta particle is an electron. It emerges from a weak decay process in which one of the neutrons inside an atom decays to produce a proton, the beta electron and an anti-electron-type neutrino. Some nuclei instead undergo beta plus decay, in which a proton decays to become a neutron plus a positron (anti-electron or beta-plus particle) and an electron-type neutrino.

    Diagram of typical Beta Plus and Beta Minus Decays

  3. A gamma particle is a photon. It is produced as a step in a radioactive decay chain when a massive nucleus produced by fission relaxes from the excited state in which it first formed towards its lowest energy or ground-state configuration.

    Diagram of Gamma Decays

Stability and Instability in Nuclei

Why are some nuclei stable while others decay radioactively?

The answer lies in conservation of energy. A nucleus will decay if there is a set of particles with lower total mass that can be reached by any of the above types of decay process or simply by fission, a process in which a massive nucleus splits into two less massive ones.  Alpha decay is also a type of fission, common because the alpha particle is a particularly low energy arrangement of two protons and two neutrons.

The mass of a nucleus is determined by the sum of the energies of all its constituents. The energies of the constituents depend on their masses, their motion, and their interactions.

In chemistry we talk of the energy levels, or states of electrons, in an atom. Electrons fill energy levels because there is a rule of electron behavior (derivable from the quantum theory) known as the Pauli Exclusion Principle. This principle applies to all fermions. The principle states that only one electron can occupy any possible state in an atom. Each energy level has only a fixed number of states in it -- and can contain no more than that number of electrons.

Example -- Helium 4

Let us consider a Helium 4 nucleus. The two protons occupy the two lowest possible energy states for protons and the two neutrons occupy the two lowest energy states for neutrons. This fills the lowest energy levels for both types of particles.

Their interactions are such that the mass of this nucleus is less than the mass of a helium three nucleus plus a free neutron, so it cannot decay into that combination.

If one of the neutrons could beta decay it would produce a Lithium 4 nucleus (3 protons and one neutron) plus an electron and an anti-electron type neutrino. But the sum of these masses is greater than the Helium 4 mass so this decay is forbidden too.

But why is Lithium 4 more massive than Helium 4 even though a free neutron is more massive than a free proton?

The reason is that a third proton cannot be put into as low an energy state in the nucleus as occupied by the second neutron.  Just as for electrons in an atom, the lowest energy level in the nucleus has only two states for protons and two states for neutrons.

The pattern of stable nuclides thus consists of nuclei with roughly equal numbers of protons and neutrons (or a few extra neutrons because electrical repulsion between protons makes the energy levels for protons slightly higher than the equivalent levels for neutrons).  Nuclei with excess protons decay via beta-plus emission while nuclei with too many neutrons decay by beta-minus or electron emission.

Beta  decay and gamma decay  often occur as steps in a chain of radioactive decays that begins with the fission of some heavy element. The fragments which appear after this fission have the right number of neutrons and protons to be some nucleus, but they are not arranged in the right energy levels because they just split off in whatever arrangement they happened to find themselves in.  Secondary transitions in which a proton moves from a higher level to a lower one with emission of a photon are then common, as are beta-emission  transitions in which  either a proton or a neutron moves to lower energy level (and changes type). Only when all the fragments have settled down to their lowest mass (energy) forms does the decay chain end. Different steps in the chain may have very different half-lives.

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