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  • The activity of a radioactive material is curie. Its half life is 5 days. The a

The activity of a radioactive material is 6.4 \times 10^{-4} curie. Its half life is 5 days. The activity will become 5 \times 10^{-6} curie after :
 

Option: 1

7 days

 


Option: 2

15 days
 


Option: 3

25 days
 


Option: 4

35 days


Answers (1)

best_answer

The activity at time t

\mathrm{A_t= A_0 \: 2^{-t / T_{1 / 2}} }

             OR

\mathrm{A_t= A_0 \: \epsilon^{-\lambda t} }

\mathrm{A_t= 5 \times 10^{-6}=6.4 \times 10^{-4} 2^{-t/5}}

\mathrm{\frac{5}{6.4} \times 10^{-2}=2^{-t / 5}}

\mathrm{\frac{1}{128}=\frac{1}{2^{t/5}}}

\mathrm{t/5=7}

\mathrm{t=35\: days}

The activity will become \mathrm{5\times 10^{-6}}  curie after 35 days

Hence 4 is correct option


 

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