WBJEE · Physics · Nuclear Physics
The number of atoms of a radioactive substance of half-life \(T\) is \(N_{0}\) at \(t=0 .\) The time necessary to decay from \(N_{0} / 2\) atoms to \(N_{0} / 10\) atoms will be
- A \(\frac{5}{2} T\)
- B \(\operatorname{tlog} 5\)
- C \(T \log \left[\frac{5}{2}\right]\)
- D \(\frac{T}{2} \log 5\)
Answer & Solution
Correct Answer
(C) \(T \log \left[\frac{5}{2}\right]\)
Step-by-step Solution
Detailed explanation
We have, \(\frac{N(t)}{N_{0}}=e^{-\lambda t}\) or \(N(t)=N_{0} e^{-\lambda t}\) \(\therefore\) For the given condition. \(\frac{N_{0}}{2}=N_{0} e^{-\lambda t_{1}}\) and \(\frac{N_{0}}{10}=N_{0} e^{-\lambda t_{2}}\) \(\Rightarrow \quad \frac{1}{2}=e^{-\lambda t_{1}}\) and…
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