α & β Decay Equations
Alpha Decay
- Alpha decay is common in large, unstable nuclei with too many protons
- The decay involves a nucleus emitting an alpha particle and decaying into a different nucleus
- An alpha particle consists of 2 protons and 2 neutrons (the nucleus of a Helium atom)
Alpha decay produces a daughter nucleus and an alpha particle (helium nucleus)
- When an unstable nucleus (the parent nucleus) emits radiation, the constitution of its nucleus changes
- As a result, the isotope will change into a different element (the daughter nucleus)
- Alpha decay can be represented by the following radioactive decay equation:
Alpha decay equation
- When an alpha particle is emitted from a nucleus:
- The nucleus loses 2 protons: proton number decreases by 2
- The nucleus loses 4 nucleons: nucleon number decreases by 4
Worked example
The radioactive nucleus 
undergoes alpha decay into a daughter nucleus Po.
(a)
Which letter in the diagram represents the daughter product?
(b)
What is the nucleon number and proton number of Po?
(a) Answer: C
- The number of neutrons in is 222 − 86 = 136
- In alpha decay, the parent nucleus loses a helium nucleus (2 protons, 2 neutrons)
- Proton number: 86 decreases to 84
- Neutron number: 136 decreases to 134
- Therefore, the correct answer is C
(b)
- The equation for alpha decay is as follows:
- Hence the daughter nucleus Po has
- Nucleon number = 222 − 4 = 218
- Proton number = 86 − 2 = 84
Beta-Minus Decay
- A beta-minus, β-, particle is a high energy electron emitted from the nucleus
- β- decay is when a neutron turns into a proton emitting an electron and an anti-electron neutrino
- When a β- particle is emitted from a nucleus:
- The number of protons increases by 1: proton number increases by 1
- The total number of nucleons stays the same: nucleon number remains the same
Equation for beta minus emission
- The new nucleus formed from the decay is called the “daughter” nucleus (nitrogen in the example above)
Beta-Plus Decay
- A beta-plus, β+, particle is a high energy positron emitted from the nucleus
- β+ decay is when a proton turns into a neutron emitting a positron (anti-electron) and an electron neutrino
- When a β+ particle is emitted from a nucleus:
- The number of protons decreases by 1: proton number decreases by 1
- The total number of nucleons stays the same: nucleon number remains the same
Equation for beta plus emission
Worked example
A radioactive substance with a nucleon number of 212 and a proton number of 82 decays by β-plus emission into a daughter product which further decays by β-plus emission into a granddaughter product.
Which letter in the diagram represents the granddaughter product?
Answer: A
- The number of neutrons in the parent nucleus is 212 − 82 = 130
- In beta-plus decay, a proton turns into a neutron
- Proton number: 82 decreases to 80
- Neutron number: 130 increases to 132
- Therefore, the correct answer is A
Exam Tip
Remember to avoid the common mistake of confusing the number of neutrons with the nucleon number. In alpha decay, the nucleon (protons and neutrons) number decreases by 4 but the number of neutrons only decreases by 2.
