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(B) The amount of radioactive material remaining is given by the formula $N = N_0 \left(\frac{1}{2}\right)^n$,where $n$ is the number of half-lives.Gi

Vedclass · Accepted Answer

$8$

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(B) The amount of radioactive material remaining is given by the formula $N = N_0 \left(\frac{1}{2}ight)^n$,where $n$ is the number of half-lives.Given that $25 \%$ of the material remains,we have $\frac{N}{N_0} = 25 \% = \frac{25}{100} = \frac{1}{4}$.Substituting this into the formula: $\frac{1}{4} = \left(\frac{1}{2}ight)^n$.Since $\frac{1}{4} = \left(\frac{1}{2}ight)^2$,we get $n = 2$.This means $2$ half-lives have passed in $16$ days.Therefore,the duration of $1$ half-life is $T_{1/2} = \frac{16 	ext{ days}}{2} = 8 	ext{ days}$.

If a radioactive material remains $25 \%$ after $16$ days,then its half-life will be ......... days.

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