JEE Mains · Physics · STD 12 - 13. Nuclei
Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_A\) and \(\lambda_B\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.
- A \(\lambda_{ A }=\lambda_{ B }\)
- B \(\lambda_{ A }=2 \lambda_{ B }\)
- C \(\lambda_{ A }=\lambda_{ B } \ln 2\)
- D \(\lambda_{ A } \ln 2=\lambda_{ B }\)
Answer & Solution
Correct Answer
(C) \(\lambda_{ A }=\lambda_{ B } \ln 2\)
Step-by-step Solution
Detailed explanation
\(T_{1 / 2}(A)=T_{w N}(B)\) \(\frac{\ln 2}{\lambda_{ A }}=\frac{1}{\lambda_{ B }}\) \(\lambda_{ A }=\lambda_{ B } \ell 2\)
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