If a nuclear fission reactor produces an average power of 1.0 GW over the course of a year,what mass of ²³⁵U is used up for a 365-day year if 200 MeV are released per fission reaction? (1 eV = 1.60 × 10^-19 J,m_neutron ≈ m_proton = 1.67 × 10-27 kg)

Question

Quizplus · Accepted Answer

First, we need to calculate the total energy produced over the year:
1.0 GW = 1.0 × 10^9 J/s
1 year = 365 days × 24 hours/day × 3600 s/hour = 3.15 × 10^7 s
Total energy produced = (1.0 × 10^9 J/s) × (3.15 × 10^7 s) = 3.15 × 10^16 J

Next, we need to calculate the total number of fissions that occurred:
Energy per fission = 200 MeV = 200 × 10^6 × 1.60 × 10^-19 J = 3.2 × 10^-11 J
Total fissions = (Total energy produced) / (Energy per fission) = (3.15 × 10^16 J) / (3.2 × 10^-11 J) = 9.84 × 10^26

Finally, we can calculate the mass of uranium consumed:
Each fission of uranium-235 produces two daughter nuclei and some neutrons. Assuming an average of 2.5 neutrons produced per fission, we have:
Mass of uranium consumed = (Total number of fissions) × (Mass per fission) = (9.84 × 10^26) × (235 + 2.5) × (1.67 × 10^-27 kg) = 390 kg

Therefore, the correct answer is C) 390 kg.

If a Nuclear Fission Reactor Produces an Average Power of 1.0