There are \(10^{10}\) radioactive nuclei in a given radioactive element, Its half-life time is \(1\, minute.\) How many nuclei will remain after \(30\, seconds?\) \((\sqrt{2}=1.414)\)

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Correct Answer

(B) \(7 \times 10^{9}\)

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Detailed explanation

\(\frac{{N}}{{N}_{0}}=\left(\frac{1}{2}\right)^{\frac{{t}}{t_{\frac{1}{2}}}}\)

\(\frac{{N}}{10^{10}}=\left(\frac{1}{2}\right)^{\frac{30}{60}}\)

\({N}=10^{10} \times\left(\frac{1}{2}\right)^{\frac{1}{2}}=\frac{10^{10}}{\sqrt{2}} \approx 7 \times 10^{9}\)

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