Assuming that about `200 MeV` of energy is released per fission of `._(92)U^(235)` nuceli, the mass of `U^(235)` consumed per day in a fission ractor of power `1` megawatt will be approximately .

Options

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

Answer

B

Explanation

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