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

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
$N = 12.5 % \,of\, N_0$
$N = \left(\frac{12.5}{100}\right)\,N_{0}$
$\frac{N_{0}}{2^{n}} = \frac{N_{0}}{8} \Rightarrow 2^{n} = 8$
$\Rightarrow n = 3 \Rightarrow \frac{t}{T_{H}} = 3$
$t = 3T$
$n = 3$