The radioactive decay follows — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - The Rate Law for Radioactive Decay For radioactive decay, the number of nuclei disintegrating per unit time is directly proportional to the number of radioactive nuclei present at that instant: $$-\frac{dN}{dt} = \lambda N$$ where $\lambda$ is the decay constant. This is a **first-order rate law** because the rate is proportional to $N^1$. Step 2 - Integrated Form Confirms First Order $$N = N_0 e^{-\lambda t} = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}$$ This exponential decay is characteristic of first-order kinetics. Step 3 - Evaluate Options - **(A) zero order**: Zero-order rate = constant, independent of $N$. Not true for radioactive decay. Incorrect. - **(B) first order**: Rate $\propto N^1$. Defines all radioactive decay. **Correct.** - **(C) second order**: Would require rate $\propto N^2$. Not observed. Incorrect. - **(D) third order**: Rate $\propto N^3$. Not observed. Incorrect. $$\boxed{\text{Answer: B — First-order reaction}}$$