AP EAMCET · PHYSICS · Nuclear Physics
Two radioactive materials \(X_1\) and \(X_2\) have decay constants \(10 \lambda\) and \(\lambda\) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \(X_1\) to that of \(X_2\) will be \(1 / e\) after a time
- A \((1 / 10 \lambda)\)
- B \(1 /(11 \lambda)\)
- C \(11 /(10 \lambda)\)
- D \(1 /(9 \lambda)\)
Answer & Solution
Correct Answer
(C) \(11 /(10 \lambda)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & N_1=N_0 e^{-10 \lambda t} \\ & N_2=N_0 e^{-\lambda t}\end{aligned}\) \(\begin{aligned} & \Rightarrow \quad \frac{N_1}{N_2}=\frac{1}{e}=e^{-1}=e^{(-10 \lambda+\lambda) t} \\ & =e^{-9 \lambda t} \\ & \Rightarrow \quad t=\frac{1}{9 \lambda} \\ & \end{aligned}\)
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