Which factors determine the effective half-life?

• A. Biological half-life only
• B. Radiological half-life only
• C. The combination of biological and radiological half-lives
• D. Neither

Answer: (C)

The effective half-life reflects how long the activity stays in the body when both radioactive decay and biological elimination are at work. Both processes act simultaneously, so their rates add. Since each process has its own decay constant, the combined rate is lambda_eff = lambda_phys + lambda_bio, where lambda = ln(2) divided by the respective half-life. This leads to Teff = ln(2) / (lambda_phys + lambda_bio) = 1 / (1/Tphys + 1/Tbio) = (Tphys * Tbio) / (Tphys + Tbio).

In other words, the effective half-life is determined by the combination of the radiological (physical) half-life and the biological half-life. If the radiological half-life is short, Teff is dominated by that short decay; if the biological clearance is rapid, Teff is shortened accordingly. If one process is very slow, Teff approaches the other half-life.

Example: if the physical half-life is 8 days and the biological half-life is 24 days, Teff ≈ (8 * 24) / (8 + 24) ≈ 6 days.