Beta decay in unstable nuclei

1. A nucleus is held together by the balance between the strong nuclear force pulling all the nucleons together and the electrostatic repulsion pushing the protons apart.
2. When a nucleus holds too many neutrons or too many protons for that balance to hold, it is unstable and it will eventually decay.
3. Beta decay is the route an unstable nucleus takes when its problem is the ratio of neutrons to protons rather than its total size, so no nucleons are thrown out of the nucleus at all.
4. Instead, one nucleon changes identity inside the nucleus, and a small light particle is created and thrown out to carry away the charge.
5. There are two versions of this, and which one happens depends on which nucleon the nucleus has too many of.
   1. A nucleus with too many neutrons turns a neutron into a proton and emits an electron, which is called beta-minus decay and written ${\beta }^{-}$ decay.
   2. A nucleus with too many protons turns a proton into a neutron and emits a positron, which is called beta-plus decay and written ${\beta }^{+}$ decay.
6. The two emitted particles are antiparticles of each other, so they have the same very small relative mass but opposite relative charge.

Beta-minus decay

1. Inside a neutron-rich nucleus, a single neutron changes into a proton and an electron, and the electron is immediately expelled from the nucleus.
2. In words, the change to the nucleon is $neutron\to proton+electron$.
3. Using particle symbols, the same change is $n\to p+e^{-}$.
4. Written with mass numbers and charges, so that both quantities can be seen to balance, the change is ${}_0^{1}n{\to }_1^{1}p{+}_{-1}^{0}e$.
5. The emitted electron is the beta-minus particle, and in a nuclear equation it is written as ${}_{-1}^{0}e$ or ${}_{-1}^0\beta$.
6. Both symbols carry the same information: a mass number of $0$, because an electron contains no protons or neutrons, and a charge of $-1$, because it carries one electron charge.
7. The electron that leaves is created in the nucleus at the moment of decay, and it is not one of the electrons that was orbiting the atom beforehand.
8. Beta-minus emitters are common among the heavy nuclei produced in reactors and among the daughter products of long decay chains, because those nuclei are typically left neutron-rich.

Beta-plus decay

1. Inside a proton-rich nucleus, a single proton changes into a neutron and a positron, and the positron is immediately expelled from the nucleus.
2. In words, the change to the nucleon is $proton\to neutron+positron$.
3. Using particle symbols, the same change is $p\to n+e^{+}$.
4. Written with mass numbers and charges, the change is ${}_1^{1}p{\to }_0^{1}n{+}_{+1}^{0}e$.
5. The emitted positron is written ${}_{+1}^{0}e$ or ${}_{+1}^0\beta$, with a mass number of $0$ and a charge of $+1$.
6. A positron is a form of antimatter, so once it has left the nucleus it travels only a very short distance through matter before it meets an ordinary electron and the pair is annihilated.
7. Because a positron is destroyed so quickly, beta-plus emitters are much harder to keep and store than beta-minus emitters, and they are usually made artificially.

Comparing the two beta decays

1. Both decays start with an unstable nucleus, change one nucleon into the other kind of nucleon, and emit one light particle from the nucleus.
2. The differences all follow from which nucleon changes.
   1. In ${\beta }^{-}$ decay a neutron is the nucleon that changes, so the neutron count falls by one and the proton count rises by one.
   2. In ${\beta }^{+}$ decay a proton is the nucleon that changes, so the proton count falls by one and the neutron count rises by one.
3. The emitted particles differ only in the sign of their charge, which is what the minus and plus in the two names record.
4. Neither decay ejects a nucleon from the nucleus, which is what separates beta decay from alpha decay and from neutron emission.
5. Neither decay can be triggered or prevented, because which nucleus decays and when is settled by chance alone.