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

Question

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

Answer:

3.00

Solution:

$12.5 % \to {(\frac{1}{8})}^{t h}$ of initial power
$∵$ After each T, P will be half
$P \overset{T}{\to} \frac{P}{2} \overset{T}{\to} \frac{P}{4} \overset{T}{\to} \frac{P}{8}$
$∴$ Total time $= 3 T$
$n = 3$

TestHub · Accepted Answer

12.5 % → 1 8 t h of initial power ∵ After each T, P will be half P → T P 2 → T P 4 → T P 8 ∴ Total time = 3 T n = 3

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