Radioactive decay | IGCSE Physics Revision Notes

1. Overview

Radioactive decay is the process by which an unstable nucleus releases radiation to become more stable. This fundamental process explains how certain elements change into others over time and is the basis for understanding nuclear energy, medical imaging, and carbon dating.

Key Definitions

Radioactive Decay: The process in which an unstable atomic nucleus loses energy by emitting radiation.
Spontaneous: A process that is not affected by external factors (such as temperature, pressure, or chemical environment).
Random: It is impossible to predict exactly which individual nucleus will decay next, or exactly when a specific nucleus will decay.
Nuclide: A distinct kind of atom or nucleus characterized by its specific number of protons and neutrons.
Isotope: Atoms of the same element with the same number of protons but different numbers of neutrons.

Core Content

The Nature of Decay

Unstable nuclei do not stay unstable forever. To reach a stable state, they undergo a change called radioactive decay. During this process, the nucleus emits one or more types of radiation:

Alpha ($\alpha$) particles: Helium nuclei ($2$ protons, $2$ neutrons).
Beta ($\beta$) particles: High-speed electrons.
Gamma ($\gamma$) radiation: High-frequency electromagnetic waves.

Random and Spontaneous Process

Spontaneous: You cannot "speed up" or "slow down" decay by heating a sample or changing the pressure.
Random: While we can predict how many nuclei in a large sample will decay over time, we cannot point to one specific nucleus and say when it will explode.

Changing Elements

When a nucleus emits an alpha or beta particle, the number of protons in the nucleus changes. Because the atomic number defines the element, the nucleus changes into a different element.

Alpha decay: The nucleus loses 2 protons; it "moves back" two places in the Periodic Table.
Beta decay: The nucleus gains 1 proton; it "moves forward" one place in the Periodic Table.
Gamma emission: This is just energy being released; the element stays the same.

📊A large unstable nucleus "Parent" splitting into a smaller "Daughter" nucleus and an emitted particle (Alpha or Beta), showing the change in identity.

Extended Content (Extended Curriculum Only)

Why are some isotopes radioactive?

Isotopes are usually unstable (and therefore radioactive) for two main reasons:

Too many neutrons: The ratio of neutrons to protons is too high, making the nucleus "unbalanced."
Too heavy: The nucleus is simply too large for the strong nuclear force to hold it together (usually elements with an atomic number greater than 82).

Effects of Decay on the Nucleus

The goal of decay is to increase the stability of the nucleus.

Alpha ($\alpha$) decay: Reduces the mass of the nucleus significantly. Both the number of protons and neutrons decrease.
Beta ($\beta$) decay: Reduces the number of excess neutrons. A neutron in the nucleus actually transforms into a proton and an electron. The proton stays in the nucleus, and the electron is shot out as a $\beta$-particle.
- Equation of change: $\text{neutron} \rightarrow \text{proton} + \text{electron}$
Gamma ($\gamma$) emission: Occurs when a nucleus has "surplus" energy after alpha or beta decay. It releases this energy as a wave to reach its lowest energy state.

Decay Equations using Nuclide Notation

In these equations, the total mass number (top) and atomic number (bottom) must be equal on both sides.

1. Alpha Decay Example: $$^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + ^4_2\alpha$$ (Note: Mass decreases by 4, Atomic number decreases by 2)

2. Beta Decay Example: $$^{14}{6}\text{C} \rightarrow ^{14}{7}\text{N} + ^0_{-1}\beta$$ (Note: Mass stays the same, Atomic number increases by 1)

3. Gamma Decay Example: $$^{60}{27}\text{Co} \rightarrow ^{60}{27}\text{Co} + \gamma$$ (Note: No change to mass or atomic number)

Key Equations

Nuclide Notation: $^A_Z X$
- $A$ = Nucleon number (mass)
- $Z$ = Proton number (atomic number)
- $X$ = Chemical symbol
Alpha Particle: $^4_2\alpha$ or $^4_2\text{He}$
Beta Particle: $^0_{-1}\beta$ or $^0_{-1}e$

Common Mistakes to Avoid

❌ Wrong: Thinking that the probability of a single nucleus decaying decreases over time.
✅ Right: The total activity of the sample decreases, but the probability for any individual nucleus to decay remains constant.
❌ Wrong: Decreasing the mass number during Beta decay.
✅ Right: In Beta decay, a neutron turns into a proton. The total number of nucleons (mass) stays the same, but the atomic number increases by 1.
❌ Wrong: Thinking that shielding (like lead) stops the decay process.
✅ Right: Lead shields the environment from the radiation, but the internal decay inside the source continues at its own natural rate.
❌ Wrong: Thinking an alpha particle is just a "proton."
✅ Right: An alpha particle is a helium nucleus (2 protons AND 2 neutrons).

Exam Tips

Conservation Check: When completing decay equations, always check that the numbers on the top (left vs right) and the numbers on the bottom (left vs right) add up to the same total.
Terminology: Use the words "spontaneous" and "random" specifically when asked to describe the nature of radioactive decay; examiners look for these exact keywords.
Identify the Particle: If the atomic number increases by 1 but the mass stays the same, it is always Beta decay. If the mass drops by 4 and the atomic number drops by 2, it is always Alpha decay.