Half-life of a substance is 10 years. In what | vedclass

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(C) The radioactive decay law is given by $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$,where $N$ is the remaining amount,$N_0$ is the initial amou

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$20$

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(C) The radioactive decay law is given by $N = N_0 \left( \frac{1}{2} ight)^{t/T_{1/2}}$,where $N$ is the remaining amount,$N_0$ is the initial amount,$t$ is the time elapsed,and $T_{1/2}$ is the half-life.Given $T_{1/2} = 10 	ext{ years}$ and $N = \frac{1}{4} N_0$.Substituting these values: $\frac{1}{4} N_0 = N_0 \left( \frac{1}{2} ight)^{t/10}$.$\frac{1}{4} = \left( \frac{1}{2} ight)^{t/10}$.Since $\frac{1}{4} = \left( \frac{1}{2} ight)^2$,we have $\left( \frac{1}{2} ight)^2 = \left( \frac{1}{2} ight)^{t/10}$.Comparing the exponents: $2 = \frac{t}{10}$.Therefore,$t = 20 	ext{ years}$.

Half-life of a substance is $10$ years. In what time,it becomes $\frac{1}{4}$ of the initial amount?

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