Atoms And Nuclei Question 404

Question: The disintegration rate of a certain radioactive sample at any instant is 4750 disintegrations per minute. Five minutes later the rate becomes 2700 disintegrations per minute. Calculate half-life of the sample.

Options:

A) $ 9.1,\min $

B) $ 6.1,\min $

C) $ 2.3,\min $

D) $ 1.1,\min $

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Answer:

Correct Answer: B

Solution:

  • We know that the rate of integration $ | -\frac{dN}{dt} |=A $
    $ \therefore ,A=A_{0}{{e}^{-\lambda t}} $ or $ 2700=4750,{{e}^{-\lambda \times 5}} $ or $ \lambda =0.1131 $ per minute Half-life minute


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