​​Alpha and beta decay

​​In a nutshell

Unstable nuclei become more stable through radioactive decay, the most common types being alpha, beta and gamma decay. Alpha decay is a process where a nucleus emits an alpha particle. Beta decay is a process where a neutron decays into a proton and emits a beta particle and an antineutrino. The antineutrino was predicted due to the observation of an energy imbalance.

Radioactivity

An atom is said to be unstable when the forces that hold its nucleus together are unbalanced. Most of the known isotopes are unstable and to become more stable they spontaneously undergo radioactive decay. A nucleus before the decay is called the parent nucleus while a nucleus after the decay is called the daughter nucleus. There are many types of radioactive decay but the most common types are alpha, beta and gamma decay.

Gamma radiation consists of photons $$\gamma$$​ being emitted by a nucleus to lose energy. It is usually a product of alpha and beta radiation as, after decaying, the nucleus might still have too much energy left which it will release as a photon.

Alpha decay

Alpha decay is a process where a nucleus emits an alpha particle. This consists of two protons and two neutrons and is essentially a helium nucleus. Since those four particles are emitted, the element of the nucleus changes as the atomic number $$Z$$ decreases by two and the nucleon number $$A$$ decreases by four. A general nuclear equation for alpha decay is:

$$^A_ZX\rightarrow ^{A-4}_{Z-2}Y+^4_2\alpha$$​​

Below is an example of the decay of uranium-$$238$$​:

Beta decay

Beta decay is a process where a neutron in a nucleus decays into a proton and emits an electron and an antineutrino. The electron emitted is also known as a beta particle. Since the neutron decays into a proton the element of the nucleus changes as the atomic number $$Z$$​ increases by one while the nucleon number $$A$$​ stays the same. A general equation for beta decay is:

​$$^A_ZX\rightarrow^{\quad A}_{Z+1}Y+\beta^-+\overline{\nu}$$​​

Below is an example of the decay of radium-$$228$$:

There are two types of beta decay, the one discussed above is beta minus $$\beta^-$$. The other is called beta plus $$\beta^+$$ and it involves a proton decaying into a neutron and emitting a beta particle (a positron in this case) and a neutrino. A general equation for it is:

$$^A_ZX\rightarrow^{\quad A}_{Z-1}Y+\beta^++\nu$$​​

Beta decays are also often shown with protons and neutrons instead of the atoms.

Neutrinos and conservation of energy

Neutrinos are particles that have no charge and an extremely small mass which makes them very elusive. There are three types of neutrinos: electron neutrino $$\nu_e$$​, muon neutrino $$\nu_{\mu}$$​ and tau neutrino $$\nu_{\tau}$$. Each of them has its own antiparticle and is only affected by the weak nuclear force and the gravitational force.

In all radioactive decays, charge and energy are always conserved. This fact led to the prediction of neutrinos in the $$1930$$s when, by using energy measurements from beta decays, physicist Wolfgang Pauli found a surplus of energy which could not be accounted for by the beta particle or the daughter nucleus. He therefore hypothesized the existence of a very elusive particle known today as the neutrino. ​

Note: at this level you don't need to worry too much about the different types of neutrino, just remember they can all generally be represented by $$\nu$$.

Example

An atom of plutonium-$$239$$ undergoes alpha decay. Write down the correct nuclear equation for this interaction, including the atomic and nucleon number as well as the element of the daughter nucleus.

Firstly, you need to identify the symbol and the atomic number of plutonium. To do this you can use a periodic table:

$$^{239}_{\ \ 94}Pu$$​​

Next, write down the general equation for alpha decay:

​$$^A_ZX\rightarrow ^{A-4}_{Z-2}Y+^4_2\alpha$$​​

You now need to calculate the atomic and the nucleon number of the daughter nucleus:

$$A=239-4=235\newline Z=94-2=92$$​​

Using a periodic table you need to identify which element has this new atomic number, for $$Z=92$$ it's uranium $$U$$. You can then write the full nuclear equation:

​$$^{239}_{\ \ 94}Pu\rightarrow^{235}_{\ \ 92}U+^4_2\alpha$$​​

Exam tip: you don't need to remember the periodic table as you will be given enough information to deduce the elements from the numbers given.