For IB Physics SL and HL, write a radioactive decay equation by identifying the emitted radiation and balancing both the nucleon number and proton number . The totals of and must be equal on both sides.
Write the parent nucleus using nuclear notation:
Here, is the total number of protons and neutrons, while is the number of protons. Then apply the changes caused by the type of decay.
| Decay type | General equation | Change to daughter nucleus |
|---|---|---|
| Alpha | , | |
| Beta-minus | ||
| Beta-plus | ||
| Gamma |
These changes follow conservation laws. In alpha decay, the nucleus ejects two protons and two neutrons, so both numbers decrease. In beta-minus decay, a neutron changes into a proton, an electron, and an electron antineutrino. In beta-plus decay, a proton changes into a neutron, a positron, and an electron neutrino. Gamma decay only removes excess nuclear energy, so the nuclide does not change.
A second check is electric charge conservation: proton number balancing already accounts for the charges of alpha particles, electrons, and positrons. Beta decay also conserves lepton number; this is why the electron neutrino or antineutrino appears even though its nucleon and proton numbers are zero.
For example, carbon-14 undergoes beta-minus decay:
Check the nucleon numbers: . Check the proton numbers: . The equation is therefore balanced.
For comparison, uranium-238 alpha decay produces thorium-234:
The daughter element is fixed by , not by . Checking gives and .
A common misconception is that beta-minus emission removes an electron already inside the nucleus. Instead, the electron is produced during the neutron-to-proton transformation.
In Topic E.3, an examiner may ask you to determine a missing daughter nuclide or emitted particle. Balance and separately, include the neutrino or antineutrino in beta decay, and use the periodic table to identify the element from its final proton number.
| unchanged, |
| unchanged, |
| Both unchanged |
