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GATE-2017 (72)

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72) The number of half-lives (T1/2) required for a certain amount of radioactive isotopes in a rock to reduce to 3% of its original amount is_____

 

(Thanks to Chandrasekhar, ANU)


Solution:

 

We know that the \frac{N}{N_{0}}=e^{-\lambda t}---------------(1)

 

  Given that \frac{N}{N_{0}}=3% = 0.03

 

 By substituting the above value in equation (1) w get

 

\frac{N}{N_{0}}=e^{-\lambda t}

 

0.03=e^{-\lambda t}

 

\ln(0.03)=-\lambda t

 

\lambda t=3.506

 

\frac{0.693}{t_{1/2}} \times t=3.506

 

t=\frac{3.506}{0.693}t_{1/2}

 

t=5.059t_{1/2}

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