Amount of electric power to generated , `P=2xx10^(5)MW`
10% of this amount has to be obtained from nuclear power plants.
`therefore` Amount of nuclear power, `P_(1)=(10)/(100)xx2xx10^(5)`
`=2xx10^(4)MW`
`=2xx10^(4)xx10^(6)J//s`
`2xx10^(10)xx60xx60xx24xx365J//y`
Heat energy released per fission of a `""^(235)U` nucleus, E=200 MeV
Efficienty of a reactor `=25 %`
Hence, the amount of energy converted into the electrical energy per fission is calculated as:
`(25)/(100)xx200=-50MeV`
`=50xx1.6xx10^(-19)xx10^(6)=8xx10^(-12)J`
Number of atoms required for fission per year:
`(2xx10^(10)xx60xx60xx24xx365)/(8xx10^(-12))=78840xx10^(24) " atoms"`
1 mole, i.e, 235 g of `U^(235)` contains `6.023xx10^(23)` atoms.
`therefore` Mass of `6.023xx10^(23)` atoms of `U^(235)=235g=235xx10^(-3)kg`
`therefore` Mass of `78840xx10^(24)` atoms of `U^(235)`
`=(235xx10^(-3))/(6.023xx10^(23))xx78840xx10^(24)`
`=3.076xx10^(4)kg`
Hence, the mass of uranium needed per year is `3.076xx10^(4) kg`.