Assuming that about 200g MeV energy is released per fission of `""_(92)U^(235)` nuclei. What would be the mass of `U^(235)` consumed per day in the fission of reactor of power 1 MW approximately?

Options

A. `10^(-2)g`
B. `1 g`
C. `100 g`
D. `10,000 g`

Answer

b

Explanation

Power `P` of fission reactor,
`p =10^(6)W=10^(6) J s^(-1)`
Time `= t= 1 day =24 xx 36 xx 10^(2) s`
Energy produced, `U=Pt`
or `U=10^(6) xx 24 xx 36 xx 10^(2)`
`=24 xx 36 xx 10^(8) J`
Energy released per fission of `U^(235)` is
`200 MeV = 32 xx 10^(-12) J`
Number of `U.^(235)` atoms used is
`(24 xx 36 xx 10^(8))/(32 xx 10^(-12))=27 xx 10^(20)`
Mass of `6 xx 10^(23)` atoms of `U.^(235) =235 g`
Mass of `27 xx 10^(20)` atoms `U.^(235)g`
`((235)/(6 xx 10^(23)))(27 xx 10^(20))=1.058 g=1g`.