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. 3
B. 4
C. 2
D. 1

Answer

C

Explanation

At `t=0`
`P_("required")=P_("available")xx(12.5//100)=P_("available"//8)`
`:. P_("available")=8P_("required")`
`:.` After first half life, `P_("available")=4P_("required")`
After second life, `P_("available")=2P_("required")`
After third life, `P_("available")=P_("required")`
`:.` Power required by the village can be met upto 3 half lives.
`:. n=3`.