Which statement about the relationship of the effective half-life is true?

Which statement about the relationship of the effective half-life is true?

• A. Always longer than both
• B. Equal to biological half-life
• C. Sometimes shorter than radiological half-life
• D. Always shorter than both

Answer: (D)

The relationship tested is how two first-order processes—physical decay and biological elimination—combine into an overall clearance, called the effective half-life. The key math is 1/T_eff = 1/T_p + 1/T_b, so T_eff = 1 / (1/T_p + 1/T_b). Because both T_p and T_b are positive, the sum 1/T_p + 1/T_b is larger than either 1/T_p or 1/T_b alone, and taking the reciprocal makes T_eff smaller than both T_p and T_b. In practical terms, when both processes occur, the overall half-life is shorter than either one by itself, meaning it clears faster than either the physical decay or the biological clearance alone. Note that if one process effectively doesn’t occur (an infinite half-life), the effective half-life equals the other process’s half-life rather than being shorter than both.

The relationship tested is how two first-order processes—physical decay and biological elimination—combine into an overall clearance, called the effective half-life. The key math is 1/T_eff = 1/T_p + 1/T_b, so T_eff = 1 / (1/T_p + 1/T_b). Because both T_p and T_b are positive, the sum 1/T_p + 1/T_b is larger than either 1/T_p or 1/T_b alone, and taking the reciprocal makes T_eff smaller than both T_p and T_b. In practical terms, when both processes occur, the overall half-life is shorter than either one by itself, meaning it clears faster than either the physical decay or the biological clearance alone. Note that if one process effectively doesn’t occur (an infinite half-life), the effective half-life equals the other process’s half-life rather than being shorter than both.