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  • A radioactive isotope has a, half-life of 5 years. After how much time it its activity reduced to 3.125 % of its original activity?Option: 1 20 years

A radioactive isotope has a, half-life of 5 years. After how much time it its activity reduced to 3.125 % of its original activity?

Option: 1

20 years 


Option: 2

40 years 


Option: 3

25 years 


Option: 4

24 years 


Answers (1)

best_answer

\mathrm{we \ know, \left(\frac{R}{R_0}\right)=\left(\frac{1}{2}\right)^n } \\ {Given, \frac{R}{R_0}=3.125 \%=3.125 \times \frac{1}{100} }
\mathrm{\begin{aligned} & \frac{3 \cdot 125}{100}=\left(\frac{1}{2}\right)^n \text { or } \frac{1}{32}=\left(\frac{1}{2}\right)^n \\ & \left(\frac{1}{2}\right)^5=\left(\frac{1}{2}\right)^n \end{aligned} }
Given, n=5 years

As, n=t/T=5

t=25 years

 

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