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. `1`
B. `2`
C. `3`
D. `4`

Answer

C

Explanation

Let E= power requirement of the village
E'=power of plant
`:. E=12.5/100xxE' :. E=(E')/8 or E=(E')/(2^(3))`
No. of half lives=3
So total time required `= 3xxTyrs=nTyrs`
`:. n=3`