Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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:

Both Statement-I and Statement-II are correct.

Both Statement-I and Statement-II are incorrect.

Statement-I is correct but Statement-II is incorrect.

Statement-I is incorrect but Statement-II is correct.

Step-by-Step Solution

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.
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, $\tau$ ), 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.
Conclusion: Both statements are incorrect.

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