Q. 10

The variation of decay rate of two radioactive samples A and B with time is shown in Fig. 13.1. Which of the following statements are true?

A. Decay constant of A is greater than that of B, hence A always decays faster than B.

B. Decay constant of B is greater than that of A but its decay rate is always smaller than that of A.

C. Decay constant of A is greater than that of B but it does not always decay faster than B.

D. 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.

Answer :

A decay rate graph is given which shows radioactive decay of 2 substances A and B against time t. According to the formula of Rutherford and Soddy the decay rate constant is proportional to the total activity or the number of radioactive decay happening per unit time. Thereby, seeing the graph we can come to a conclusion that the decay rate of A is greater than B at the start of time but as time goes on the decay rate decreases similarly to the decay rate of B. Hence, due to a larger decay rate constant of the substance A, the substance decay faster with time whereas decay rate of B is lower than time hence, stays a bit longer than A. Therefore, although decay constant of A is greater than that of B but slower in nature and decay constant of B is lesser than that of A which helps it in staying longer but will at a certain and specific time be equal to that of A.

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