Modern Physics 5 Question 30
33. 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 from 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
(2015 Adv.)
Analytical & Descriptive Questions
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Solution:
- Let initial power available from the plant is $P _0$. After time $t=n T$ or $n$ half lives, this will become $\frac{1}{2}{ }^{n} P _0$. Now, it is
given that, $\frac{1}{2}{ }^{n} P _0=12.5 %$ of $P _0=(0.125) P _0$
Solving this equation we get, $n=3$
