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JEE Mains · Physics · STD 12 - 13. Nuclei
The half-life of a radioactive element \(A\) is the same as the mean-life of another radioactive element \(B.\) Initially both substances have the same number of atoms, then
- A \(A\) and \(B\) decay at the same rate always .
- B \(A\) and \(B\) decay at the same rate initially.
- C \(A\) will decay at a faster rate than \(B.\)
- D \(B\) will decay at a faster rate than \(A\)
Answer & Solution
Correct Answer
(D) \(B\) will decay at a faster rate than \(A\)
Step-by-step Solution
Detailed explanation
\({\left( {{{\text{T}}_{1/2}}} \right)_{\text{A}}} = {\left( {{{\text{t}}_{{\text{mean}}}}} \right)_{\text{B}}}\) \( \Rightarrow \frac{{0.693}}{{{\lambda _A}}} = \frac{1}{{{\lambda _B}}}\) \( \Rightarrow {\lambda _A} = 0.693{\lambda _B}\) or \(\quad \lambda_{A} < \lambda_{B}\)…
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