JEE Mains · Physics · STD 12 - 13. Nuclei
Activities of three radioactive substances \(A , B\) and \(C\) are represented by the curves \(A, B\) and \(C,\) in the figure. Then their half-lives \(T _{\frac{1}{2}}( A ): T _{\frac{1}{2}}( B ): T _{\frac{1}{2}}( C )\) are in the ratio
- A \(3: 2: 1\)
- B \(4: 3: 1\)
- C \(2: 1: 3\)
- D \(2: 1: 1\)
Answer & Solution
Correct Answer
(C) \(2: 1: 3\)
Step-by-step Solution
Detailed explanation
\(R = R _{0} e ^{-\lambda t}\) ln \(R =\ln R _{0}-\lambda t\) \(\lambda_{ A }=\frac{6}{10} \Rightarrow T _{ A }=\frac{10}{6}\) ln \(2\) \(\lambda_{ B }=\frac{6}{5} \Rightarrow T _{ B }=\frac{5 \ln 2}{6}\) \(\lambda_{ C }=\frac{2}{5} \Rightarrow T _{ C }=\frac{5 \ln 2}{2}\)…
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