Use decay equations, using nuclide notation, to show the emission of α-particles, β-particles and γ-radiation

5.2.3 Radioactive Decay

Learning Objective

Use decay equations, written in nuclide notation, to show the emission of α-particles, β-particles and γ-radiation.

Key Concepts

• Radioactive nuclei are unstable and transform to a more stable configuration.
• Three common types of nuclear radiation: α, β and γ.
• Nuclide notation: \$_{Z}^{A}\text{X}\$ where \$Z\$ is the atomic number, \$A\$ is the mass number and X is the chemical symbol.

Types of Radiation

Decay Equations in Nuclide Notation

General form of a decay equation:

\$\$

{Z}^{A}\text{X} \;\rightarrow\; {Z'}^{A'}\text{Y} \;+\; \text{radiation}

\$\$

α‑Decay

When an α‑particle is emitted, the mass number decreases by 4 and the atomic number decreases by 2.

\$\$

{Z}^{A}\text{X} \;\rightarrow\; {Z-2}^{A-4}\text{Y} \;+\; _{2}^{4}\text{He}

\$\$

Example: Decay of uranium‑238 to thorium‑234

\$\$

{92}^{238}\text{U} \;\rightarrow\; {90}^{234}\text{Th} \;+\; _{2}^{4}\text{He}

\$\$

β⁻‑Decay

A neutron transforms into a proton, emitting an electron (β⁻). The mass number remains unchanged, while the atomic number increases by 1.

\$\$

{Z}^{A}\text{X} \;\rightarrow\; {Z+1}^{A}\text{Y} \;+\; _{-1}^{0}\text{e}

\$\$

Example: Decay of carbon‑14 to nitrogen‑14

\$\$

{6}^{14}\text{C} \;\rightarrow\; {7}^{14}\text{N} \;+\; _{-1}^{0}\text{e}

\$\$

β⁺‑Decay (Positron Emission)

A proton converts into a neutron, emitting a positron (β⁺). The mass number stays the same, the atomic number decreases by 1.

\$\$

{Z}^{A}\text{X} \;\rightarrow\; {Z-1}^{A}\text{Y} \;+\; _{+1}^{0}\text{e}

\$\$

Example: Decay of fluorine‑18 to oxygen‑18

\$\$

{9}^{18}\text{F} \;\rightarrow\; {8}^{18}\text{O} \;+\; _{+1}^{0}\text{e}

\$\$

γ‑Radiation

γ‑radiation is emitted when an excited nucleus drops to a lower energy state. No change in \$A\$ or \$Z\$.

\$\$

{Z}^{A}\text{X}^{*} \;\rightarrow\; {Z}^{A}\text{X} \;+\; \gamma

\$\$

Example: De‑excitation of cobalt‑60 after β⁻‑decay

\$\$

{27}^{60}\text{Co}^{*} \;\rightarrow\; {27}^{60}\text{Co} \;+\; \gamma

\$\$

Step‑by‑Step Procedure for Writing a Decay Equation

1. Identify the type of radiation emitted (α, β⁻, β⁺, γ).
2. Write the parent nuclide in \$_{Z}^{A}\text{X}\$ form.
3. Apply the appropriate changes to \$A\$ and \$Z\$ according to the table above.
4. Write the daughter nuclide \$_{Z'}^{A'}\text{Y}\$ on the right‑hand side.
5. Add the emitted particle using its nuclide notation (or the symbol γ for gamma).
6. Check that both sides of the equation are balanced for mass number and atomic number.

Common Mistakes to Avoid

• Confusing the charge of the emitted particle with the change in atomic number.
• For β⁻‑decay, forgetting that the atomic number increases.
• For β⁺‑decay, forgetting that the atomic number decreases.
• Omitting the antineutrino or neutrino – they are not required in IGCSE equations but must be remembered conceptually.
• Treating γ‑radiation as a particle with mass; it carries no mass or charge.

Practice Questions

1. Write the decay equation for the α‑decay of \$^{226}_{88}\text{Ra}\$.
2. \$_{11}^{23}\text{Na}\$ undergoes β⁻‑decay. Identify the daughter nuclide.
3. A nucleus emits a positron and becomes \$^{55}_{26}\text{Fe}\$. What was the original nuclide?
4. Explain why the mass number does not change in γ‑radiation.

Suggested Diagram

Suggested diagram: A schematic showing a parent nucleus emitting an α‑particle, a β⁻‑particle, a β⁺‑particle and a γ‑photon, with arrows indicating the change in \$A\$ and \$Z\$ for each type of radiation.