Answer :
Final answer:
The duration required to produce 5 kg of Pu-239 in a 1,366 MW power plant fissioning U-235 can be calculated using Avogadro's number, the known ratio of Pu-239 nuclei produced per U-235 fission events, and the energy produced per fission event. Factors such as the ease of fission of U-235 and Pu-239, and breeder reactor technology that produces Pu-239 from absorbed fast neutrons in U-238, contribute to the actual energy production.
Explanation:
The question is asking how long a 1,366 MW nuclear power plant which fissions U-235 would take to produce 5 kg of Pu-239 if each 3 U-235 fission events produce 2 Pu-239 nuclei. To calculate this, we first need to know how many Pu-239 atomic nuclei are in 5 kg which can be achieved using Avogadro's number. We then calculate the number of U-235 fission events required to produce this amount, followed by how much energy each fission event produces. We can then find out the total energy required to generate 5kg of Pu-239 and calculate the duration the plant needs to operate at a power of 1366 MW to produce this amount of energy.
U-235 undergoes fission converting lost mass into a large amount of energy which is significantly larger than energy from chemical reactions. U-235 and Pu-239 are easier to fission making them key in energy production. In breeder reactors fast neutrons from U-235 fission get absorbed by U-238 resulting in the production of Pu-239, allowing for the expansion of earth's supply of fissionable material.
It's important to note that due to the complexity of the problem, a lot of factors are not accounted for including efficiency losses in the practical process within a reactor, conversion of heat into electricity and operational breaks of the power plant.
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