The burning of one gallon of gasoline releases about 2 $\times$ 10⁸ J. If each nuclear fission reaction in a nuclear power plant releases 173 MeV (1 MeV = 1.6 $\times$ 10^-13J), what quantity of Uranium-235 is used to produce the same amount of energy relased in burning a gallon of gasoline?

Question

Quizplus · Accepted Answer

First, we need to convert the energy released by burning a gallon of gasoline in joules:
2 x 10^18 J/gal ÷ 1 gal = 2 x 10^18 J

Next, we need to calculate how many MeV are in 2 x 10^18 J:
2 x 10^18 J ÷ (1.6 x 10^-13 J/MeV) ÷ (10^6 eV/MeV) = 1.25 x 10^13 MeV

Now we can calculate how many nuclear fission reactions are needed to release this much energy:
1.25 x 10^13 MeV ÷ 173 MeV/reaction = 7.23 x 10^10 reactions

Finally, we can calculate how much Uranium-235 is needed for this many fission reactions:
7.23 x 10^10 reactions x 1 nucleus/2 fission reactions x 235 g/mol ÷ (6.02 x 10^23 nuclei/mol) = 2.8 g of Uranium-235

Therefore, the answer is C) 2.8g of Uranium-235.

The Burning of One Gallon of Gasoline Releases About 2 ×\times×

The Burning of One Gallon of Gasoline Releases About 2 $\times$