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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 C 222 g
Given:
One uranium-235 nucleus releases 190 MeV of energy during its fission.
1 MeV=1.6×1013 J

190 MeV=190×1.6×1013 J

=3.04×1011 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=7.2×10113.04×1011
=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 hr1×24 hr=221.78 g
222 g

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