Nuclear Fission Mass Calculation

Question

A nuclear power plant produces $$1 	ext{ GW}$$ of thermal power for $$1$$ hour. Given that $$1 	ext{ GW} = 10^9 	ext{ W}$$ and $$1 	ext{ hour} = 3600 	ext{ s}$$, the total energy produced is $$3.6*10^{12} 	ext{ J}$$. If each fission of a U-235 nucleus releases approximately $$200 	ext{ MeV}$$ of energy (with $$1 	ext{ eV} = 1.602*10^{-19} 	ext{ J}$$), estimate the mass (in grams) of U-235 required to produce this energy. Assume that one mole of U-235 weighs approximately $$235 	ext{ g}$$ and contains $$6.022*10^{23}$$ nuclei.
 
Conversion Table:
| Quantity                | Value                                      |
|-------------------------|--------------------------------------------|
| 1 GW                    | $$10^9 	ext{ W}$$                         |
| 1 hour                  | $$3600 	ext{ s}$$                         |
| 1 eV                    | $$1.602*10^{-19} 	ext{ J}$$                |
| 1 mole                  | $$6.022*10^{23} 	ext{ nuclei}$$             |
| Molar mass of U-235     | $$235 	ext{ g/mol}$$                        |
| Energy per fission      | $$200 	ext{ MeV}$$ (1 MeV = $$10^6 	ext{ eV}$$) |

Accepted Answer

$$44 	ext{ g}$$

Answer

$$0.44 	ext{ g}$$

Answer

$$4.4 	ext{ g}$$

Answer

$$440 	ext{ g}$$

Quantity	Value
1 GW	$$10^9 \text{ W}$$
1 hour	$$3600 \text{ s}$$
1 eV	$$1.602*10^{-19} \text{ J}$$
1 mole	$$6.022*10^{23} \text{ nuclei}$$
Molar mass of U-235	$$235 \text{ g/mol}$$
Energy per fission	$$200 \text{ MeV}$$ (1 MeV = $$10^6 \text{ eV}$$)

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