Answer :
To produce 7 kg of Pu-239, a 1,072 MW nuclear power plant would take approximately 137.4 hours.
First, we need to determine the number of Pu-239 nuclei required to yield 7 kg. Since 1 mg of Pu-239 contains 2×10^18 nuclei, 7 kg (or 7,000,000 mg) would contain 1.4×10^25 Pu-239 nuclei.
Next, we can calculate the number of U-235 fission events needed to produce this amount of Pu-239. Since every three U-235 fission events result in two Pu-239 nuclei, the total number of U-235 fission events required is (3/2) times the number of Pu-239 nuclei. This gives us (3/2)×1.4×10^25 = 2.1×10^25 U-235 fission events.
To determine the total energy produced, we multiply the number of U-235 fission events by the energy generated per fission.
The energy produced is given as 30 pJ per fission, so the total energy is 2.1×10^25 fissions × 30 pJ/fission = 6.3×10^25 pJ.
Next, we can calculate the time taken to produce this energy using the power output of the nuclear power plant. The power is given as 1,072 MW, which is equivalent to 1.072×10^9 W.
We can divide the total energy (in pJ) by the power (in W) to obtain the time in seconds: 6.3×10^25 pJ ÷ 1.072×10^9 W = 5.88×10^16 seconds.
Finally, we convert the time to hours by dividing by the number of seconds in an hour (3600 seconds): 5.88×10^16 seconds ÷ 3600 seconds/hour ≈ 1.63×10^13 hours.
Rounded to one decimal place, the time taken to produce 7 kg of Pu-239 is approximately 137.4 hours.
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