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  • A. radioactive isotope has a half life of T years. How long will it take the activity to reduce 3.125 % of its original value?Option: 1 <img alt="t=5

A. radioactive isotope has a half life of T years. How long will it take the activity to reduce 3.125 % of its original value?

Option: 1

t=5 \mathrm{~T}


Option: 2

t=4 \mathrm{~T}


Option: 3

t= \mathrm{~T}


Option: 4

t=2 \mathrm{~T}


Answers (1)

best_answer

\mathrm{Use \frac{R}{R_0}=\left(\frac{1}{2}\right)^n} \\ {\begin{aligned} & \frac{R}{R_0}=\frac{3 \cdot 125}{100}=\frac{1}{32}=\left(\frac{1}{2}\right)^5 \\ & \frac{R}{R_0} \Rightarrow\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^5 \text {, or } \quad \begin{array}{l} n=5 \text { half lives. } \\ \frac{t}{T}=5 \end{array} \\ & \therefore t=5 \mathrm{~T} \text { Ans. } \end{aligned} }

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Devendra Khairwa

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