Modern Physics Ques 205
- 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.)
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Answer:
Correct Answer: 205.$(3)$
Solution:
Formula:
- 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, $n=3$
BETA
