Radioactive decay of a substance follows which kinetic order in chemical-reaction terms (i.e., rate proportional to the amount remaining)?

Introduction / Context:
Radioactive decay is a spontaneous nuclear process, but its time dependence can be described using the same mathematics as chemical reaction kinetics. Examinations often ask which “order” of reaction best models the decay law that leads to exponential decrease and the concept of half-life.

Given Data / Assumptions:

• Nuclei decay independently and randomly.
• Decay probability per nucleus per unit time is constant (decay constant = lambda).
• No external forcing or replenishment of the parent nuclide.

Concept / Approach:
The defining kinetic equation is dN/dt = −lambda * N, where N is the number of undecayed nuclei. This is identical in form to a first-order rate law used in chemistry, where rate is directly proportional to the amount (or concentration) of the reactant present.

Step-by-Step Solution:
Start with: dN/dt = −lambda * N.Separate variables and integrate: ∫ dN/N = −∫ lambda dt.Obtain: ln(N) = −lambda t + constant ⇒ N = N0 * exp(−lambda * t).Define half-life t_1/2 from N/N0 = 1/2 ⇒ t_1/2 = 0.693 / lambda.

Verification / Alternative check:
First-order systems always produce a constant half-life regardless of starting amount, exactly as observed for radionuclides. Plotting ln(N) versus time gives a straight line with slope −lambda, a classic first-order test.

Why Other Options Are Wrong:
Zero order: would give linear decrease, not exponential.Second/Third order: rates would scale with higher powers of amount, not supported by decay statistics.Mixed order: unnecessary; a single first-order constant captures the behavior.

Common Pitfalls:
Confusing nuclear decay (first order) with surface or diffusion-limited processes.Thinking half-life depends on the initial quantity; it does not for first-order processes.

Final Answer:
First order