For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time tak

Question

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

Accepted Answer

Number of nuclei remaining = $600 - 450 = 150$. Using the formula $\frac{N}{N_0} = (\frac{1}{2})^n$, where $n = \frac{t}{t_{1/2}}$, we get $\frac{150}{600} = (\frac{1}{2})^{\frac{t}{10}}$. Thus, $\frac{1}{4} = (\frac{1}{2})^{\frac{t}{10}}$, which implies $(\frac{1}{2})^2 = (\frac{1}{2})^{\frac{t}{10}}$. Therefore, $\frac{t}{10} = 2$, so $t = 20$ minutes.

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