A nuclear power supplying electrical power to a villages uses a radioactive material of half life `T` year 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

Options

A. 5
B. 4
C. 3
D. 2

Answer

C

Explanation

`N_(0)` = amount of radioactive material as fuel at the beginning and `P_(0)` = power produced by the material at the beginning.
`therefore` Power required by the village = 12.5% of `P_(0) = (P_(0))/(8)`, Half-life period of the radioactive material = T years
`therefore` After T years, material will be `(N_(0))/(2)` and power produced will be `(P_(0))/(2)`.
`therefore` Then after 2T years, power will be `(P_(0))/(4)` and after 3T years power will be `(P_(0))/(8)`
After this the power produced will be `lt (P_(0))/(8)` and it will not be sufficient for the village.
`therefore` The total time upto which the power plant can sypply the necessary power to the village = 3T
But it is given that this time = nT
`therefore n = 3`.