Which statement about the effective half-life is true?

Which statement about the effective half-life is true?

• A. Gamma dose rate constant is independent of distance.
• B. Attenuation coefficient μ only applies to gamma rays.
• C. The effective half-life is computed from both physical and biological half-lives.
• D. The Geiger-Müller counter is used for spectroscopy.

Answer: (C)

Effective half-life is the combined time it takes for both radioactive decay and biological clearance to reduce the activity in the body by half. It ties together the physical half-life (how quickly the radionuclide decays) and the biological half-life (how quickly the body eliminates the substance). The relationship is 1/te = 1/tp + 1/tb. This means te is always influenced by both processes and is typically shorter than either tp or tb unless one of them is infinite. For example, if the physical half-life is 6 hours and the biological half-life is 24 hours, then 1/te = 1/6 + 1/24 = 5/24, giving te ≈ 4.8 hours. That’s why the effective half-life matters for estimating how long radiation exposure lasts in a patient. The other statements aren’t correct in this context. The gamma dose rate constant is not truly independent of distance; dose rate from a source changes with distance, roughly following the inverse-square law for point sources. The attenuation coefficient μ describes how photons are attenuated by material and applies to photons in general, not only gamma rays. And a Geiger–Müller counter measures counts but does not provide energy resolution for spectroscopy; spectroscopy relies on detectors that can resolve energy, such as scintillation counters or semiconductor detectors.

Effective half-life is the combined time it takes for both radioactive decay and biological clearance to reduce the activity in the body by half. It ties together the physical half-life (how quickly the radionuclide decays) and the biological half-life (how quickly the body eliminates the substance). The relationship is 1/te = 1/tp + 1/tb. This means te is always influenced by both processes and is typically shorter than either tp or tb unless one of them is infinite. For example, if the physical half-life is 6 hours and the biological half-life is 24 hours, then 1/te = 1/6 + 1/24 = 5/24, giving te ≈ 4.8 hours. That’s why the effective half-life matters for estimating how long radiation exposure lasts in a patient.

The other statements aren’t correct in this context. The gamma dose rate constant is not truly independent of distance; dose rate from a source changes with distance, roughly following the inverse-square law for point sources. The attenuation coefficient μ describes how photons are attenuated by material and applies to photons in general, not only gamma rays. And a Geiger–Müller counter measures counts but does not provide energy resolution for spectroscopy; spectroscopy relies on detectors that can resolve energy, such as scintillation counters or semiconductor detectors.