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13.Nuclei
medium
A nuclear power plant supplying electrical power to a village uses a radioactive material of half life $T$ years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is $12.5 \%$ of the electrical power available form the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of $n T$ years, then the value of $n$ is
A
$1$
B
$2$
C
$3$
D
$4$
(IIT-2015)
Solution
$\frac{A}{A_0}=\left(\frac{1}{2}\right)^{\frac{t}{T}}$
Where, $A_0$ is the initial activity of the radioactive material and $A$ is the activity at $t$.
So, $\frac{12.5}{100}=\left(\frac{1}{2}\right)^{\frac{t}{T}}$
$\therefore t =3 T \text {. }$
Standard 12
Physics
