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  • A radioactive sample decays   times its original quantity in 15 minutes. The half life of t

A radioactive sample decays \frac{7}{8}  times its original quantity in 15 minutes. The half life of the sample is
 

Option: 1

5 \mathrm{~min}


Option: 2

7.5 \mathrm{~min}


Option: 3

15 \mathrm{~min}


Option: 4

30 \mathrm{~min}


Answers (1)

Amount of radioactive sample remaining at time \mathrm{t=15\: mins}

\mathrm{N_{t}=N_{o}-\frac{7N_{o}}{8}=\frac{N_{o}}{8}}

\mathrm{N_{o}\rightarrow Original\: quantity}

By the law of radioactive decay

\mathrm{N_t=N_0 2^{-t / T_{1 / 2}} }

\mathrm{\frac{N_0}{8}=N_0 \: 2^{-t / T_{1 / 2}} }

\mathrm{\frac{t}{T_{1 / 2}}=3 }

\mathrm{\frac{15}{T_{1 / 2}}=3 }

\mathrm{T_{1 / 2}=5 \mathrm{~min}}
The half life of the sample is \mathrm{5 \mathrm{~min}}

Hence 1 is correct option




 

Posted by

Ramraj Saini

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