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  • Two radioactive elements A and Bhave half lives T and 2 Trespectively. In the beginning the number of atoms in both samples is same. After A T time the ratio of remaining atom of An

Two radioactive elements A and Bhave half lives T and 2 Trespectively. In the beginning the number of atoms in both samples is same. After A T time the ratio of remaining atom of A and B wire be-

Option: 1

1 / 2


Option: 2

1 / 8


Option: 3

1 / 4


Option: 4

1 / 16


Answers (1)

best_answer

Here,
\mathrm{ \begin{aligned} & N_1=N_0 e^{-\lambda_1 t}-(1) \\ & N_2=N_0 e^{-\lambda_2 t}-(2) \\ & \end{aligned} }
\mathrm{\begin{aligned} \frac{N_1}{N_2} & =\frac{N_0 e^{-\lambda_1 t}}{N_0 e^{-\lambda_2 t}} \\ & =e^{-\left(\lambda_1-\lambda_2\right) t} \\ & =e^{-\left[0.693\left(\frac{1}{T}-\frac{1}{2 T}\right) \times 4 T\right]} \\ & =e^{-\left[0.693 \times \frac{1}{2 T} \times 4 T\right]} \\ \frac{N_1}{N_2} & =\frac{1}{4} \text { Ans. } \end{aligned} }

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