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Question
How much mass of 235U is required to undergo fission each day to provide 3000 MW of thermal power? Average energy per fission is 202.79 MeV.
Solution
Data: Power = 3000 MW = 3 x 109 J/s
∴ Energy to be produced each day
= 3 x 109 x 86400 J each day
= 2.592 x 1014 J each day
Energy per fission = 202.79 MeV
= 202.79 x 106 x 1.6 x 10-19 J = 3.245 x 10-11 J
∴ Number of fissions each day = `"Tatol Energy"/"Enery per Fussion"`
`= (2.592 xx 10^14)/(3.245 xx 10^-11)`
= `7.988 xx 10^24` each day
0.235 kg of 235U contains 6.02 x 1023 atoms
∴ Mass per Atom = `"Molar Mass"/"Avogadro's Number"`
= `(0.235)/(6.02 xx 10^23)`
= 0.039023 x 10-23kg
Total Mass = Number of Fissions × Mass per Atom
∴ M = 7.988 × 1024 × 0.039023 x 10-23
= 3.118 kg
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