What happens to the half-life of a radioactive substance as it decays?

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BlackTom AI · Accepted Answer

Question restatement: What happens to the half-life of a radioactive substance as it decays?

Option A: It decreases at a constant rate. In other words, suggesting the half-life itself shortens steadily over time. This is not correct because the half-life is a characteristic of the substance, determined by the decay constant; the rate of decay can be constant in a differential sense, but the half-life itself does not shrink linearly.

Option B: It remains constant. This is the key concept: for a given radioactive isotope under fixed conditions, the time required for the quantity to reduce by half is fixed. The decay process follows an exponential law, but the half-life is a constant value (t1/2 = ln(2)/λ) that does not change as the substance decays.

Option C: It decreases at an exponential rate. While the number of undecayed nuclei decreases exponentially with time, the half-life itself does not decrease; rather, the remaining quantity follows an exponential decline with a constant half-life. Conflating the exponential decay of quantity with a changing half-life is a common misunderstanding.

Option D: It increases. This would imply that the time needed to halve the quantity grows over time, which contradicts the fundamental description of radioactive decay. The half-life does not increase during decay under normal, stable conditions.

Summary note: The half-life of a radioactive substance is a constant determined by the isotope’s decay constant, independent of how much material is present or how long it has been decaying. It is linked to the exponential decay law, but the intrinsic half-life value does not change as decay proceeds.

PHYSICS 1201 SU2025 (10585) Final Exam- Requires Respondus LockDown Browser

What happens to the half-life of a radioactive substance as it decays?

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