If the amount of radioactive substance is increases three times, the number of disintegration per un — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - Law of Radioactive Decay The activity $A$ (disintegrations per unit time) of a radioactive sample is: $$A = \lambda N$$ where $\lambda$ = decay constant (property of the isotope) and $N$ = number of active nuclei present. Step 2 - Effect of Tripling the Amount Let initial amount $= N_1$, initial activity $= A_1 = \lambda N_1$. If amount is tripled: $N_2 = 3N_1$ $$A_2 = \lambda N_2 = \lambda (3N_1) = 3(\lambda N_1) = 3A_1$$ Step 3 - Analysis of Options - (A) doubled: incorrect — would require doubling the amount - (B) one-third: incorrect — would occur if amount were reduced to one-third - (C) triple: correct — $A \propto N$ (first-order kinetics), so $3 \times$ amount $\Rightarrow$ $3 \times$ activity - (D) unchanged: incorrect — activity depends directly on the number of nuclei present $$\boxed{C}$$