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(B) The number of radioactive nuclei remaining after time $t$ is given by the formula $N = N_0 \left( \frac{1}{2} \right)^n$,where $n = \frac{t}{T_{1/

Vedclass · Accepted Answer

$20$

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(B) The number of radioactive nuclei remaining after time $t$ is given by the formula $N = N_0 \left( \frac{1}{2} ight)^n$,where $n = \frac{t}{T_{1/2}}$ is the number of half-lives.Given $N_0 = 1.414 	imes 10^6$,$N = 10^6$,and $t = 10 	ext{ min}$.Substituting the values: $10^6 = 1.414 	imes 10^6 	imes \left( \frac{1}{2} ight)^n$.$\frac{1}{1.414} = \left( \frac{1}{2} ight)^n$.Since $1.414 \approx \sqrt{2}$,we have $\frac{1}{\sqrt{2}} = \left( \frac{1}{2} ight)^n$.$(2)^{-1/2} = (2)^{-n}$.Therefore,$n = 1/2$.Since $n = \frac{t}{T_{1/2}}$,we have $1/2 = \frac{10}{T_{1/2}}$.$T_{1/2} = 20 	ext{ min}$.

In a radioactive sample,there are $1.414 \times 10^6$ active nuclei. If they reduce to $10^6$ within $10 \text{ min}$,then the half-life of this sample will be ....... $\text{min}$.

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