Explain how the type of radiation emitted and the half-life of an isotope determine which isotope is used for applications including: (a) household fire (smoke) alarms (b) irradiating food to kill bacteria (c) sterilisation of equipment using gamma r

5.2.4 Half‑life

The half‑life (\$t_{1/2}\$) of a radioactive isotope is the time required for half of the original nuclei to decay. It is related to the decay constant (\$\lambda\$) by

\$t_{1/2} = \frac{\ln 2}{\lambda}\$

The number of undecayed nuclei (\$N\$) after a time \$t\$ is given by the exponential decay law

\$N = N_{0}\,e^{-\lambda t}\$

Different isotopes emit different types of radiation (alpha, beta, gamma) and have characteristic half‑lives. Both the radiation type and the half‑life determine the suitability of an isotope for a particular application.

Key properties of common isotopes

Applications and the role of half‑life & radiation type

1. Household fire (smoke) alarms

   Smoke detectors use a small amount of \$^{241}\$Am. The alpha particles ionise the air in a chamber; when smoke enters, ionisation is reduced and the alarm triggers.

   • Radiation type: Alpha particles have very low penetration; they are safely contained within the sealed detector.
   • Half‑life: 5.5 years provides a stable source for many years without frequent replacement, yet the activity decays slowly enough to maintain reliable sensitivity.

2. Irradiating food to kill bacteria

   Gamma rays from \$^{60}\$Co are used because they penetrate deeply and can uniformly sterilise packed food.

   • Radiation type: High‑energy gamma photons have high penetration, allowing treatment of thick or densely packed foods.
   • Half‑life: 5.27 years offers a balance between a strong, consistent dose rate and manageable source replacement intervals for commercial facilities.

3. Sterilisation of equipment using gamma rays

   Medical and laboratory equipment are sterilised in gamma chambers using \$^{60}\$Co or \$^{137}\$Cs sources.

   • Radiation type: Gamma rays penetrate metal casings and packaging, ensuring the interior of complex instruments receives an adequate dose.
   • Half‑life: A few‑year half‑life (e.g., \$^{60}\$Co) provides a high dose‑rate initially, which gradually declines, allowing predictable scheduling of source replacement.

4. Measuring and controlling thicknesses of materials

   Industrial radiography uses gamma or beta sources to assess material thickness. The attenuation of radiation follows \$I = I_{0}e^{-\mu x}\$, where \$x\$ is thickness.

   • Radiation type: Choice depends on required penetration:

     • Beta particles (e.g., from \$^{90}\$Sr) for thin sheets (a few mm) – limited penetration.
     • Gamma rays (e.g., from \$^{137}\$Cs or \$^{60}\$Co) for thicker metals – high penetration.

   • Half‑life: Longer half‑lives (decades) are preferred to minimise source replacement in continuous production lines.

5. Diagnosis and treatment of cancer using gamma rays

   External beam radiotherapy commonly employs \$^{60}\$Co gamma rays; brachytherapy may use \$^{192}\$Ir or \$^{125}\$I seeds.

   • Radiation type: Gamma rays have sufficient energy to reach deep‑seated tumours while sparing surrounding tissue when collimated.
   • Half‑life: For external machines, a half‑life of \overline{5} years (e.g., \$^{60}\$Co) provides a stable, high‑intensity beam for several years before source replacement is required. For implanted seeds, shorter half‑lives (e.g., \$^{125}\$I, \$t_{1/2}=60\$ days) deliver a high dose locally and then decay, reducing long‑term exposure.

Why half‑life matters for each application

Choosing an isotope involves balancing three factors:

• Radiation penetration: Determines whether the radiation can reach the target (e.g., deep tissue vs. surface contamination).
• Activity decay rate: A short half‑life gives a high initial activity but requires frequent replacement; a long half‑life provides steadier output but may require larger source mass to achieve the same dose rate.
• Safety and regulatory considerations: Short‑lived isotopes reduce long‑term waste, while long‑lived isotopes demand secure storage after use.