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For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is
Explanation
One-quarter remaining means two half-lives have elapsed.
Detailed Solution
Number of nuclei remaining $= 600 - 450 = 150$
$\frac{N}{N_0} = \left(\frac{1}{2}\right)^{n}$, where $n = \frac{t}{t_{1/2}}$
$\frac{150}{600} = \left(\frac{1}{2}\right)^{t/t_{1/2}}$
$\left(\frac{1}{2}\right)^{2} = \left(\frac{1}{2}\right)^{t/t_{1/2}}$
$t = 2t_{1/2} = 2 \times 10 = 20$ minutes