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  • A sample contains  each of two substances A and B with half lives 4 s and 8 s respectively. The rat

A sample contains 10^{-2}kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1:2. The ratio of the amounts of A and B after 16 s is \frac{x}{100} . The value of x is______

Option: 1

50


Option: 2

--


Option: 3

--


Option: 4

--


Answers (1)

best_answer

\begin{aligned} m_{A} &=m_{B}=10^{-2} \mathrm{~kg} \\ \text { At time }t=0 \\ \frac{\left(N_{A}\right)_{0}}{\left(N_{B}\right)_{0}} &=\frac{m_{A} / M_{A}}{m_{B} / M_{B}}=\frac{M_{B}}{M_{A}}=\frac{2}{1} \\ \left(T_{A}\right)_{1 / 2} &=4s \\ \left(T_{B}\right)_{1 / 2} &=8 \mathrm{~s} \end{aligned}

\begin{aligned} N_{A} &=\left(N_{A}\right)_{0} 2^{-t /\left(T_{1 / 2}\right)_{A}} \\ N_{B} &=\left(N_{B}\right)_{0} 2^{-t /\left(T_{1 / 2}\right)_{B}} \\ \frac{N_{A}}{N_{B}} &=\frac{\left(N_{A}\right)_{0}}{\left(N_{B}\right)_{0}} \times \frac{2^{-t /\left(T_{1 / 2}\right)_{A} }}{2^{-t /\/\left(T_{1 / 2}\right)_{B}}} \\ &=2 \times \frac{2^{-16 / 4}}{2^{-16 / 8}} \\ &=2 \times \frac{2^{-4}}{2^{-2}} \\ \frac{N_{A}}{N_{B}} &=\frac{1}{2}=\frac{50}{100} \\ & x=50 \end{aligned}

 

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Rishabh

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