Nuclear/chemical kinetics – order of radioactive decay Radioactive decay processes follow which overall kinetic order?

Introduction / Context:Radioactive decay is a stochastic, unimolecular process in which unstable nuclei transform spontaneously. In chemical engineering and nuclear science, its time dependence is modeled as a kinetic rate law that is independent of concentration of other species.

Given Data / Assumptions:

• Each nucleus decays independently.
• No external reactant is required; decay probability per unit time is constant.

Concept / Approach:For first-order processes, the rate of decrease in the number of nuclei N is proportional to N itself: dN/dt = −λ N, where λ is the decay constant. Integration yields an exponential law and a constant half-life independent of initial amount, matching observed radionuclide behavior.

Step-by-Step Solution:

Verification / Alternative check:Measured activities (A = λ N) decay exponentially; plotting ln A vs. time gives a straight line with slope −λ, confirming first-order kinetics.

Why Other Options Are Wrong:Second- or third-order kinetics require bimolecular/termolecular interactions, which are not involved in spontaneous nuclear decay. Zero order would imply a constant decay rate independent of N, contrary to experiment.

Common Pitfalls:Confusing activity decay (A) with dose rate or detector counts affected by geometry and shielding; the underlying nuclear decay remains first order.

Final Answer:First order