in a nucleri reactor `U^(235)` undergoes fission releasing energy 100 MeV , the reactor has 20% efficiency and the power produces is 2000 MW . If the reactor is to fuction for 5 yr , find the total mass of uranium required .

Explanation

Given , output power ,`P _(0) =2000 MW =22210^(9) W`
Efficiency , `eta =("Output power"P_(0))/("input power"P_(i))`
`implies (20)/(100)=(2xx10^(9))/(P_(i))implies p_(i) =10^(10)W`
consider the mass of uranium ne be m.
Number of fision =Number of atoms
`("Given mass") /("Atomic mass")xx`Avogardro number
`(m)/(A) xxN_(A)=(m)/(235)xx6.023xx10^(23)`
Enary produced ,E=Number of fissions `xx` Energy per fission
`=(m)/(235)xx6.023xx10^(23)xx200 MeV `
`=(m)/(235)xx6.023xx10^(23)xx100xx1.6xx10^(-13)J`
`(:' 1 MeV =1.6xx10^(-13) J)`
`=mxx0.041xx10^(12)J = xx4.1xx10^(10)J`
Power `=("Energy )/("time ")implies 10^(10)=(mxx4.1xx10^(10))/(5xx365xx24xx3600)`
`m=3.84xx10^(7)g=38.4xx10^(3)kg`