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Two radioactive substances have decay constants 5 \lambda  and \lambda  respectively. At time \mathrm{t=0}, they have the same number of nuclei. The ratio of number of nuclei of substance A to that B will be \left (\frac{ 1}{e} \right )^2 after time interval -
 

Option: 1

\frac{1}{2 \lambda}


Option: 2

\frac{1}{4 \lambda}


Option: 3

4 \lambda


Option: 4

2 \lambda


Answers (1)

best_answer

\begin{aligned} &\mathrm{Use, \quad N=N_0 e^{-\lambda t}}\\ &\mathrm{\frac{N_A}{N_B}=\frac{N_0 e^{-5 \lambda t}}{N_0 e^{-\lambda t}}}\\ &\mathrm{but ~\frac{N_A}{N_B}=(1 / e)^2 \text{ them equation 0 become-}}\\ &\mathrm{ \left(\frac{1}{e}\right)^2=e^{-4 \lambda t} }\\ &\mathrm{ \frac{1}{e^2}=e^{-4 \lambda t} }\\ &\mathrm{ e^{-2}=e^{-4 \lambda t} }\\ &\mathrm{ -2=-4 \lambda t \Rightarrow t=\frac{1}{2 \lambda} }\\ \end{aligned}

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seema garhwal

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