Atoms And Nuclei Question 382

Question: A radioactive nucleus can decay by two different processes. The half-life for the first process is $ t_{1} $ and that for the second process is $ t_{2} $ . If effective half-life is t, then

Options:

A) $ t=t_{1}+t_{2} $

B) $ \frac{1}{t}=\frac{1}{t_{1}}+\frac{1}{t_{2}} $

C) $ t=\frac{2t_{1}t_{2}}{t_{1}+t_{2}} $

D) $ t=\frac{t_{1}+t_{2}}{2} $

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Answer:

Correct Answer: B

Solution:

  • $ \frac{dN}{dt}=-N,({\lambda_{1}}+{\lambda_{2}})=-N\lambda $
    $ \Rightarrow ,\lambda ={\lambda_{1}}+{\lambda_{2}} $ so $ \frac{1}{t}=\frac{1}{t_{1}}+\frac{1}{t_{2}},[ as,\lambda =\frac{0.693}{t} ] $


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