Atoms And Nuclei Question 394

Question: A sample of radioactive substance has $ 10^{6} $ nuclei. If half-life is 20 seconds, the number of nuclei left in the sample after 10 second is

Options:

A) $ 10^{4} $

B) $ 2\times 10^{5} $

C) $ 7\times 10^{5} $

D) $ 11\times 10^{5} $

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Answer:

Correct Answer: C

Solution:

  • $ N=N_{0}{{e}^{-\lambda /t}}=10^{6}{{e}^{-[ \frac{In2}{20}\times 10 ]}} $ $ =10^{6}{{e}^{-In\sqrt{2}}}=\frac{10^{6}}{\sqrt{2}}=\approx 7.07\times 10^{5} $


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