5.2.3 Radioactive decay
- Syllabus
- 0625–2026–2027
- Topic
- 5.2.3
- Level
- —
Learning objectives
5.2.3.1Radioactive decay is a change in an• Know: radioactive decay is a change in an unstable nucleus that can result in the emission of α-particles or β-particles and/or γ-radiation; know: these changes are spontaneous and random5.2.3.2During α-decay or β-decay, the nucleus• State: during α-decay or β-decay, the nucleus changes to that of a different element5.2.3.3Isotopes of an element may be• Know: isotopes of an element may be radioactive due to an excess of neutrons in the nucleus and/or the nucleus being too heavy5.2.3.4Effect of α-decay, β-decay and• Describe the effect of α-decay, β-decay and γ-emissions on the nucleus, including an increase in stability and a reduction in the number of excess neutrons; the following change in the nucleus occurs during β-emission neutron → proton + electron5.2.3.5Decay equations, using nuclide• Use decay equations, using nuclide notation, to show the emission of α-particles, β-particles and γ-radiation
Define radioactive decay
Radioactive decay is a change in an unstable nucleus that can result in the emission of an alpha particle, a beta-minus particle and/or gamma radiation.
The change is spontaneous: it occurs without an external trigger. Heating, cooling, pressure and chemical reactions do not select when a nucleus decays.
The change is random: it is impossible to predict which particular nucleus will decay next or the exact time at which it will decay.
For a large sample, the behaviour of many nuclei can form a statistical pattern even though each individual event remains unpredictable.
A lead container may absorb emitted radiation, but it does not stop the nuclei inside from decaying. Random detector readings are therefore expected, not proof that the detector is faulty.
Relate alpha and beta decay to a new element
An element is identified by its proton number. If a decay changes the number of protons in the nucleus, the product nucleus belongs to a different element.
| Decay | Change in proton number | Result |
|---|---|---|
| alpha | decreases by 2 | a nucleus of a different element |
| beta-minus | increases by 1 | a nucleus of a different element |
Alpha emission removes two protons as part of the alpha particle. In beta-minus decay, a neutron changes into a proton and an electron, and the electron is emitted, so the nucleus gains one proton.
The daughter can be an isotope, but it is an isotope of the new element, not another isotope of the original element. Gamma emission alone does not change proton number and therefore does not change the element.
Explain why some isotopes are radioactive
An isotope may be radioactive because its nucleus is unstable. Two syllabus reasons are an excess of neutrons and a nucleus that is too heavy.
Isotopes of one element have the same proton number but different neutron numbers. An isotope with too many neutrons for a stable arrangement can reduce that neutron excess through radioactive change.
A very heavy nucleus contains a large total number of nucleons. The balance of forces can be unstable, so the nucleus may emit radiation and move towards a more stable arrangement.
Do not infer that every isotope with more neutrons is radioactive or that physical size alone determines stability. The required statements are that neutron excess and/or excessive nuclear mass may cause instability.
Describe how each emission changes the nucleus
| Emission | Change inside or from nucleus | Change in A | Change in Z |
|---|---|---|---|
| alpha | 2 protons and 2 neutrons leave | −4 | −2 |
| beta-minus | neutron → proton + electron; electron leaves | 0 | +1 |
| gamma | nucleus loses energy as electromagnetic radiation | 0 | 0 |
Radioactive emission moves an unstable nucleus towards greater stability. Alpha emission removes two neutrons as well as two protons; beta-minus emission converts one excess neutron into a proton; gamma emission removes excess nuclear energy without changing the numbers of protons or neutrons.
The electron emitted in beta-minus decay is created by the nuclear change; it is not an orbital electron. Nucleon number stays constant because one nucleon changes type.
Gamma emission can increase stability without reducing the neutron number. Alpha and beta-minus change the element; gamma alone does not.
Write and balance nuclear decay equations
Write a nuclide as ᴬ_ZX, where A is the nucleon number and Z is the proton number. In every decay equation, the totals of A and Z must balance on both sides.
| Emission | Emitted term | Daughter change |
|---|---|---|
| alpha | ⁴₂He (or ⁴₂α) | A − 4, Z − 2 |
| beta-minus | ⁰₋₁e (or ⁰₋₁β) | A unchanged, Z + 1 |
| gamma | ⁰₀γ | A unchanged, Z unchanged |
Alpha example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Both nucleon numbers balance, 238 = 234 + 4, and both proton numbers balance, 92 = 90 + 2.
Beta-minus example: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e. The nucleon number remains 14 and the proton-number total balances because 6 = 7 + (−1).
Gamma example: ᴬ_ZX* → ᴬ_ZX + ⁰₀γ. The asterisk indicates a higher-energy nucleus; emission changes neither A nor Z.
Method: identify the emission, write its A and Z values, conserve both columns, then use the daughter proton number to identify the new element.
For beta-minus decay, do not subtract one from the daughter proton number: the daughter has one more proton. For gamma emission, do not invent a new element because both numbers are unchanged.