If the half life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on the \(3^{\text {rd }}\) day? (Given that \(\sqrt[3]{0.25} \approx 0.63\) )

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If the half life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on the \(3^{\text {rd }}\) day? (Given that \(\sqrt[3]{0.25} \approx 0.63\) )

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kritika · Answer 1 · 2021-12-15T12:34:15+0000

Ans: (D)
\(: \mathrm{N}=\frac{\mathrm{N}_{0}}{2^{\mathrm{t} / \mathrm{w}_{12}}} \quad \therefore \mathrm{t}_{1 / 2}=3\) days
At \(t=2\) days; \(\quad N_{1}=\frac{N_{0}}{2^{2 / 3}}=\frac{N_{0}}{4^{1 / 3}}=0.63 N\)
At \(t=3\) day, \(N_{2}=\frac{N_{0}}{2}\), Fraction disintegrated \(=\frac{N_{1}-N_{2}}{N_{0}}=\frac{(0.63-0.5) N_{0}}{N_{0}}=0.13\)

If the half life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on the \(3^{\text {rd }}\) day? (Given that \(\sqrt[3]{0.25} \approx 0.63\) )

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