Question 677: Atoms & Nuclei

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 nT years, then the value of n is

Accepted Answer

Half life of radioactive material = T years
Let amount of radioactive material as fuel at the beginning be N
0
and corresponding power produced by it be P
0
.
According to question,
Power requirement of the village
= 12.5% of $${P_0} = {{{P_0}} \over 8}$$
Since, after each T year, power will be half, i.e.,
$${P_0}\buildrel T \over
 \longrightarrow {{{P_0}} \over 2}\buildrel T \over
 \longrightarrow {{{P_0}} \over 4}\buildrel T \over
 \longrightarrow {{{P_0}} \over 8}$$
Total time upto which the plant can meet the village's need = 3T years = nT years
$$	herefore$$ n = 3

Atoms & Nuclei

Integer / Numeric Answer Type