AP EAMCET · PHYSICS · Nuclear Physics
The half-life of a radioactive sample is \(T\). The fraction of the initial mass of the sample that decays in an interval \(T / 2\) is
- A \(\frac{1}{\sqrt{2}}\)
- B \(\sqrt{2}\)
- C \(\frac{(\sqrt{2}-1)}{\sqrt{2}}\)
- D \(\frac{(\sqrt{2}+1)}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Fraction remains after \(n\) half-lives is given as \(\frac{N}{N_0}=\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^{t / T} \quad\) [where, \(T\) is half-life] \(\Rightarrow \quad \frac{N}{N_0}=\left(\frac{1}{2}\right)^{\frac{t}{T}}\) Given, \(\quad t=\frac{T}{2}\)…
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