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

Published by Patrick Mutisya · 14 days ago

IGCSE Physics 0625 – Half‑life and Applications

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 a characteristic property of each isotope and determines how quickly the activity (decays per second) decreases:

\$\$

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

\$\$

where \$N_0\$ is the initial number of nuclei and \$N(t)\$ is the number remaining after time \$t\$.

Why half‑life matters for practical uses

  • Activity level: Short half‑lives give high activity but decay quickly; long half‑lives give low, steady activity.
  • Safety and handling: Isotopes with very short half‑lives may become harmless quickly, while those with very long half‑lives remain hazardous for years.
  • Radiation type: The emitted particle or photon (α, β, γ, X‑ray) determines penetration power and suitability for a given application.

Key radiation types

RadiationChargePenetrationTypical shielding
Alpha (α)+2Very low – stopped by a sheet of paper or skinPaper, plastic
Beta (β)−1 (electron) or +1 (positron)Moderate – a few millimetres of aluminiumAluminium, acrylic
Gamma (γ) / X‑ray0 (photon)High – many centimetres of lead or several metres of concreteLead, concrete, steel

Isotopes commonly used in the applications below

IsotopeRadiationHalf‑lifeTypical activity (Ci or Bq)Reason for selection
Americium‑241α (with some γ)432 years\overline{37} kBq (1 µCi) per alarmLong half‑life gives a stable source for decades; α particles ionise air but are stopped by the alarm’s detector window.
Cobalt‑60γ (1.17 MeV & 1.33 MeV)5.27 years10⁴–10⁶ Ci for industrial irradiatorsHigh‑energy γ rays penetrate food and medical equipment but are easily shielded for safety.
Cobalt‑60 (again)γ5.27 years10⁴–10⁶ Ci for sterilisationSame as above – sufficient penetration to sterilise packed items.
Iridium‑192γ (0.3–1.4 MeV)73.8 days\overline{10} Ci for industrial radiographyShort half‑life gives high activity for brief inspections; γ energy suitable for thickness measurement.
Cobalt‑60 (again)γ5.27 yearsTherapeutic beams of 1–2 MeVPenetrates deep tumours while allowing precise dose control.

Application (a): Household fire (smoke) alarms

Smoke detectors use a small sealed source of Americium‑241. The α particles ionise the air in a chamber, creating a small electric current. When smoke enters, it attaches to the ions, reducing the current and triggering the alarm.

  • Half‑life of 432 years → the alarm works for decades without source replacement.
  • α radiation is ideal because it has very low penetration; it cannot escape the sealed chamber, making the device safe for household use.

Suggested diagram: Schematic of an ionisation‑type smoke detector showing the Am‑241 source, ionisation chamber, electrodes, and smoke entry path.

Application (b): Irradiating food to kill bacteria

Food irradiation employs high‑energy γ rays, most commonly from Cobalt‑60. The photons penetrate the food pack, breaking DNA bonds in bacteria and other microorganisms, rendering them inactive.

  • Half‑life of 5.27 years provides a balance: the source remains active for several years, yet its activity decays enough that the source can be replaced on a practical schedule.
  • γ rays have high penetration, allowing uniform dose throughout bulk food items.
  • Shielding (lead or concrete) protects workers, while the food itself receives the intended dose.

Suggested diagram: Cross‑section of a food irradiation tunnel showing a Co‑60 source, lead shielding, conveyor belt, and dose distribution.

Application (c): Sterilisation of equipment using gamma rays

Medical and laboratory equipment are sterilised in “gamma chambers” using the same Cobalt‑60 source. The high‑energy photons destroy bacterial spores without heating the items, preserving heat‑sensitive materials.

  • Half‑life ensures a predictable, long‑term supply of radiation.
  • γ radiation penetrates dense packaging, allowing sterilisation of pre‑packed instruments.
  • Dosimetry is critical: the required dose is typically 25 kGy for bacterial spore kill.

Application (d): Measuring and controlling thicknesses of materials

Industrial radiography uses isotopes that emit γ rays of suitable energy to assess material thickness. The principle is based on exponential attenuation:

\$\$

I = I_0 e^{-\mu x}

\$\$

where \$I\$ is the transmitted intensity, \$I_0\$ the initial intensity, \$\mu\$ the linear attenuation coefficient, and \$x\$ the thickness.

  • Iridium‑192 (half‑life 73.8 days) emits γ rays of 0.3–1.4 MeV, ideal for moderate‑thickness steel, concrete, and pipe walls.
  • Shorter half‑life gives high activity, producing a strong beam for quick measurements.
  • Selection of radiation energy is matched to the material’s attenuation properties: higher‑energy γ rays for thicker or denser materials, lower‑energy for thin sections.

Suggested diagram: Radiographic setup with an Ir‑192 source, collimator, test piece, detector film or digital sensor, illustrating how varying thickness changes image darkness.

Application (e): Diagnosis and treatment of cancer using gamma rays

In radiotherapy, external beam machines (e.g., linear accelerators) generate high‑energy photons, but in some facilities sealed sources of Cobalt‑60 are used (Cobalt‑60 teletherapy units). The γ rays deposit energy in tumour tissue, damaging DNA and killing cancer cells.

  • Half‑life of 5.27 years provides a stable, long‑lasting source for a treatment centre.
  • γ photons of 1.17 Me \cdot and 1.33 Me \cdot have sufficient penetration to treat deep‑lying tumours while allowing dose shaping with collimators.
  • Safety protocols rely on the predictable decay rate to schedule source replacement and waste disposal.

Suggested diagram: Cross‑section of a Co‑60 radiotherapy unit showing the source, shielding, collimator, patient positioning, and dose distribution within a tumour.

Summary table – Matching isotope, half‑life and radiation to application

ApplicationIsotope (radiation)Half‑lifeKey reason for choice
Smoke alarmAmericium‑241 (α)432 yearsVery long life, α particles safe inside sealed chamber
Food irradiationCobalt‑60 (γ 1.17 & 1.33 MeV)5.27 yearsHigh‑energy γ penetrates bulk food; manageable decay rate
Equipment sterilisationCobalt‑60 (γ)5.27 yearsUniform dose, deep penetration, long service life
Thickness measurement (radiography)Iridium‑192 (γ 0.3–1.4 MeV)73.8 daysHigh activity for quick imaging; energy suited to moderate thicknesses
Cancer radiotherapyCobalt‑60 (γ)5.27 yearsStable, high‑energy photons for deep tumours; well‑understood dosimetry

Key take‑away points

  1. The half‑life determines how long a source remains useful and how its activity changes over time.
  2. The type of radiation (α, β, γ) dictates penetration ability and shielding requirements.
  3. For each practical use we select an isotope whose half‑life and radiation type give the optimum balance of safety, effectiveness, and economic lifespan.
  4. Understanding the exponential decay law and attenuation equation allows us to predict dose delivery and design appropriate shielding.