In the radioactive material fraction of active material remaining after time t is \frac{9}{16}. The  fraction that was remaining after t/2 is
 
Option: 1 \frac{4}{5}
Option: 2 \frac{3}{5}
Option: 3 \frac{3}{4}  
Option: 4 \frac{7}{8} 

Answers (1)

\begin{array}{l} \frac{9}{16}=\left(\frac{1}{2}\right)^{\frac{t}{T}} \\ \\ \frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{\frac{t}{2 T}} \\ \\ \left(\frac{N}{N_{0}}\right)^{2}=\left(\frac{1}{2}\right)^{t / T} \\ \\ \text { or } \frac{{N}^2}{N_{0}^{2}}=\frac{9}{16} \text { or } \frac{N}{N_{0}}=\frac{3}{4} \end{array}

So, option 3 is correct.

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