Know that isotopes of an element may be radioactive due to an excess of neutrons in the nucleus and/or the nucleus being too heavy

5.2.3 Radioactive Decay

What makes an isotope radioactive? ⚛️

An isotope can be unstable if its nucleus has either:

  • an excess of neutrons compared to protons, or
  • too many nucleons overall, making the nucleus too heavy.

Think of the nucleus as a balance scale – if one side (neutrons) is too heavy, the scale tips and the nucleus seeks stability by emitting particles.

Common Decay Modes

Decay TypeParticle EmittedTypical Example
Alpha (α)\$^4_2\text{He}\$ nucleus\$^{238}\text{U} \rightarrow ^{234}\text{Th} + \alpha\$
Beta minus (β⁻)\$e^-\$ (electron)\$^{14}\text{C} \rightarrow ^{14}\text{N} + \beta^- + \bar{\nu}_e\$
Beta plus (β⁺)\$e^+\$ (positron)\$^{22}\text{Na} \rightarrow ^{22}\text{Ne} + \beta^+ + \nu_e\$
Gamma (γ)High‑energy photonOften follows any other decay to release excess energy.

Half‑Life and Decay Law

The number of undecayed nuclei after time \$t\$ is given by:

\$N(t) = N0 \left(\frac{1}{2}\right)^{t/T{1/2}}\$

where \$N0\$ is the initial amount and \$T{1/2}\$ is the half‑life.

Exam Tip 💡

• When a question asks for the type of radiation, look for clues in the change of atomic number (\$Z\$) and mass number (\$A\$).

• If \$Z\$ decreases by 1 and \$A\$ stays the same, it’s a β⁻ decay.

• If \$Z\$ increases by 1, it’s a β⁺ decay.

• If \$A\$ decreases by 4 and \$Z\$ decreases by 2, it’s an α decay.

• Remember that γ rays do not change \$Z\$ or \$A\$.

Real‑World Example: Carbon‑14 Dating

  1. Carbon‑14 (\$^{14}\text{C}\$) is produced in the atmosphere by cosmic rays.
  2. Living organisms absorb \$^{14}\text{C}\$; when they die, the isotope starts to decay.
  3. Its half‑life is about 5,730 years, so after that time half of the original \$^{14}\text{C}\$ remains.
  4. By measuring the remaining \$^{14}\text{C}\$ in a sample, we can estimate its age.

Key Points to Remember 📚

  • Radioactive isotopes are unstable due to neutron‑proton imbalance or excessive mass.
  • Decay is spontaneous and follows the exponential law with a characteristic half‑life.
  • Identify decay type by changes in \$Z\$ and \$A\$.
  • Half‑life calculations often involve the formula \$N(t)=N0(1/2)^{t/T{1/2}}\$.
  • Use the decay equation to check conservation of mass number and atomic number.