The decrease in the mass of Uranium in a nucl | vedclass

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(D) Given: Power $P = 12 	ext{ MW} = 12 	imes 10^6 	ext{ J/s}$.Time $t = 1 	ext{ day} = 24 	imes 3600 	ext{ s} = 86400 	ext{ s}$.Energy release

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$12.64 	ext{ g}$

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(D) Given: Power $P = 12 	ext{ MW} = 12 	imes 10^6 	ext{ J/s}$.Time $t = 1 	ext{ day} = 24 	imes 3600 	ext{ s} = 86400 	ext{ s}$.Energy released per fission $E = 200 	ext{ MeV} = 200 	imes 10^6 	imes 1.6 	imes 10^{-19} 	ext{ J} = 3.2 	imes 10^{-11} 	ext{ J}$.Total energy produced in one day $E_{total} = P 	imes t = 12 	imes 10^6 	imes 86400 	ext{ J} = 1.0368 	imes 10^{12} 	ext{ J}$.Number of fissions $n = \frac{E_{total}}{E} = \frac{1.0368 	imes 10^{12}}{3.2 	imes 10^{-11}} = 3.24 	imes 10^{22}$.Mass of one atom of ${}_{92}U^{235} = \frac{235}{6.023 	imes 10^{23}} 	ext{ g}$.Total mass consumed $m = n 	imes 	ext{mass of one atom} = \frac{3.24 	imes 10^{22} 	imes 235}{6.023 	imes 10^{23}} \approx 12.64 	ext{ g}$.

The decrease in the mass of Uranium in a nuclear reactor operating at a power of $12 \text{ MW}$ per day is (Energy released in one ${}_{92}U^{235}$ fission is about $200 \text{ MeV}$):

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