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 1

Answer: 3

According to radioactivity $N=\frac{N_0}{2^n}$ (where $n=\frac{t}{T_H}$)
Requirement of power is 12.5% of total power. Then up to the time when radioactive nuclei are 12.5% of initial number, plant will provide the energy requirement of village
$N=12.5$
$N=\left(\frac{12.5}{100}\right)N_0$
$\frac{N_0}{2^n}=\frac{N_0}{8}\Rightarrow 2^n=8$
$\Rightarrow n=3\Rightarrow \frac{t}{T_H}=3$
$t=3T$
$n=3$