Given below are two statements:
Statement-I: The law of radioactive decay states that the number of nuclei und

Question

Given below are two statements:
Statement-I: The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.
Statement-II: The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time t=0.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

1. **Analyze Statement-I:** The law of radioactive decay states that the rate of disintegration (number of nuclei decaying per unit time, $-\frac{dN}{dt}$) is **directly proportional** to the number of nuclei ($N$) present in the sample at that instant . The statement says 'inversely proportional', which is **incorrect**.
2. **Analyze Statement-II:** The quantity defined as the 'sum of lifetimes of all nuclei divided by the initial number of nuclei' is the **Mean Life** (or Average Life, $	au$), not the Half-life . The Half-life ($T_{1/2}$) is the time required for the number of radioactive nuclei to reduce to half of its initial value . Therefore, this statement is **incorrect**.
3. **Conclusion:** Both statements are incorrect.

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