Atoms And Nuclei Question 392

Question: Starting with a sample $ ^{66}Cu,\frac{7}{8} $ of pure decays into Zn in 15 minutes. The corresponding half-life is

Options:

A) 15 minutes

B) 10 minutes

C) $ 7\frac{1}{2} $ minutes

D) 5 minutes

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Answer:

Correct Answer: D

Solution:

  • $ \frac{7}{8} $ of $ Cu $ decays in 15 minutes.
    $ \therefore $ $ Cu $ undecayed $ =N=1-\frac{7}{8}=\frac{1}{8}={{( \frac{1}{2} )}^{3}} $
    $ \therefore $ No. of half lifes = 3 $ n=\frac{t}{T} $ or $ 3=\frac{15}{T} $
    $ \Rightarrow $ T = half-life period $ =\frac{15}{3}=5 $ minutes


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