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  • The variation of the decay rate of two radioactive samples A and B with time is shown in the figure. Which of the following statements are true? (a) The decay constant of A is greater than that of B, hence A always decays faster than B (b) The decay cons

The variation of the decay rate of two radioactive samples A and B with time is shown in the figure. Which of the following statements are true?

(a) The decay constant of A is greater than that of B, hence A always decays faster than B

(b) The decay constant of B is greater than that of A but its decay rate is always smaller than that of A

(c) The decay constant of A is greater than that of B but it does not always decay faster than B

(d) The decay constant of B is smaller than that of A but still, its decay rate becomes equal to that of A at a later instant

Answers (1)

The correct answer of option (c,d).

Explanation:-

(c) The decay constant of A is greater than that of B but it does not always decay faster than B:-

However, due to the exponential nature of decay, as time progresses and the number of remaining atoms N decreases, sample B might catch up, and at certain times, the decay rate of B may become equal to or even greater than that of A. Therefore, A does not always decay faster than B.

(d) The decay constant of B is smaller than that of A but still, its decay rate becomes equal to that of A at a later instant:-

This can happen if the decay rate of A (with a larger decay constant) is initially higher but decreases more rapidly due to fewer remaining atoms. Meanwhile, sample B, although having a smaller decay constant, may have a larger number of atoms remaining for a longer period, so its decay rate could eventually match the decay rate of A at a later time.

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