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Half -life period of an isotope of Uranium is 2.5 \times 10^{5} years. In how much time the a mount of the isotope remaining be only 25 \% of the original amount?

Option: 1

2.5 \times 10^{4} \mathrm{yrs}


Option: 2

2.5 \times 10^{5}\mathrm{ yrs}


Option: 3

5 \times 10^{5}\mathrm{ yrs}


Option: 4

10^{7}\mathrm{ yrs}


Answers (1)

best_answer

\mathrm{\because \quad \lambda =\frac{1}{t} \ln \frac{N_{0}}{N} }

\mathrm{\frac{\ln 2}{t_{1 / 2}} =\frac{1}{t} \ln \frac{N_{0}}{N_{0} / 4} }
\mathrm{\frac{\ln 2}{2.5 \times 10^{5}} =\frac{1}{t} \ln 4 }

\mathrm{t =2 \times 2.5 \times 10^{5} }
\mathrm{t =5 \times 10^{5} \mathrm{yrs} }

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Divya Prakash Singh

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