JEE Mains · Physics · STD 12 - 13. Nuclei
Two radioactive materials \(A\) and \(B\) 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 a to that of \(B\) will be \(1/e\) after a time
- A \(\frac{1}{{11\lambda }}\)
- B \(\frac{1}{{10\lambda }}\)
- C \(\frac{1}{{9\lambda }}\)
- D \(\frac{11}{{10\lambda }}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{{9\lambda }}\)
Step-by-step Solution
Detailed explanation
\({{\text{N}}_1} = {{\text{N}}_0}{{\text{e}}^{ - 10\lambda t}}\) ; \(\mathrm{N}_{2}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}}\) \(\frac{1}{e}=\frac{N_{1}}{N_{2}}=e^{-9 \lambda t}\) \(\Rightarrow 9 \lambda t=1\) \(\Rightarrow t=\frac{1}{9 \lambda}\)
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