If a reactor produces an average power of 1000 MW for a year, how much ²³⁵U is used up assuming 200 MeV are released per fission?

Question

Quizplus · Accepted Answer

First, we need to calculate the number of fissions that occur in the reactor in one year. We can use the following formula to do this:

Number of fissions = (Average power output × 1 year) ÷ (Energy released per fission)

We are given that the average power output is 1000 MW, which we can convert to joules per year by multiplying by the number of seconds in a year (31,536,000):

Average power output = 1000 MW = 1 × 10^9 W
Energy produced per year = 1 × 10^9 W × 31,536,000 s = 3.1536 × 10^16 J

We are also given that 200 MeV are released per fission, which we can convert to joules by using the conversion factor 1 MeV = 1.602 × 10^-13 J:

Energy released per fission = 200 MeV × 1.602 × 10^-13 J/MeV = 3.204 × 10^-11 J

Now we can use the formula to calculate the number of fissions:

Number of fissions = (3.1536 × 10^16 J) ÷ (3.204 × 10^-11 J/fission) = 9.845 × 10^26 fissions

Finally, to calculate the amount of uranium-235 used up, we need to use the following formula:

Amount of uranium-235 = (Number of fissions) ÷ (Number of atoms per mole) ÷ (Mass per mole)

The mass per mole of uranium-235 is 235 g/mol, and the number of atoms per mole can be calculated from Avogadro's number (6.022 × 10^23 atoms/mol):

Amount of uranium-235 = (9.845 × 10^26 fissions) ÷ (6.022 × 10^23 atoms/mol) ÷ (235 g/mol) = 384 kg

Therefore, the answer is (C) 384 kg.

If a Reactor Produces an Average Power of 1000 MW