Question

# A nuclear power plant generates electric power of 200 MW using the nuclear fusion of U-235. How much uranium is consumed in a day to produce the electric power, if one U-235 nucleus produces 190 MeV of energy?

A
444 g
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B
235 g
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C
222 g
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D
105 g
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Solution

## The correct option is B 222 gGiven: One uranium-235 nucleus releases 190 MeV of energy during its fission. 1 MeV=1.6×10−13 J ⟹190 MeV=190×1.6×10−13 J =3.04×10−11 J Electric power generated, P=200 MW Electric energy generated in an hour, E=200×106×3600=7.2×1011 J The number of U-235 nuclei needed to release an energy of 7.2×1011 J=7.2×10113.04×10−11 =2.3684×1022 nuclei Mass of 6.023×1023 uranium nuclei = 235 g Mass of 2.3684×1022 uranium nuclei = 2356.023×1023×2.3684×1022 =9.2408 g per hour For a day, the uranium consumed = 9.2408 g hr−1×24 hr=221.78 g ≈222 g

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