WBJEE · Physics · Nuclear Physics
If the half-life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on the third day? (Given, \(\sqrt[3]{0.25} \approx 0.63)\)
- A 0.63
- B 0.5
- C 0.37
- D 0.13
Answer & Solution
Correct Answer
(D) 0.13
Step-by-step Solution
Detailed explanation
Given, \(t_{1 / 2}=3\) days Number of active nuclei remaining after time \(t\), \(N=N_{0}\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}\) After \(t=2\) days, \(N_{1}=N_{0}\left(\frac{1}{2}\right)^{2 / 3}=\frac{N_{0}}{2^{2 / 3}}=\frac{N_{0}}{4^{1 / 3}}=0.63 \mathrm{N}_{0}\)…
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