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Answer :
To produce 8 kg of Pu-239, which is enough for a bomb, from a 1,020 MW nuclear power plant, it would take approximately 20.7 hours.
To calculate the time required, we need to consider the energy generated by the nuclear power plant and the conversion efficiency of U-235 to Pu-239.
First, we calculate the energy produced by the power plant. The power output is given as 1,020 MW (mega watts), which is equivalent to 1,020 × 10^6 J/s (joules per second).
Next, we determine the number of U-235 fission events per second. Since each U-235 fission generates 30 pJ (picojoules) of energy, we can calculate the number of fission events by dividing the power output by the energy per fission event:
Number of fission events per second = Power output (J/s) / Energy per fission event (J)
Number of fission events per second = (1,020 × 10^6 J/s) / (30 × 10^-12 J)
Using this value, we can determine the rate of Pu-239 production. For every three U-235 fission events, two Pu-239 nuclei are produced. Therefore, the rate of Pu-239 production is two-thirds of the rate of U-235 fission events:
Rate of Pu-239 production = (2/3) × Number of fission events per second
Now, we can calculate the mass of Pu-239 produced per second. We know that 1 mg (milligram) of Pu-239 contains 2 × 10^18 Pu-239 nuclei. Therefore, the mass of Pu-239 produced per second is:
Mass of Pu-239 produced per second = (2 × 10^18 nuclei) × (1 mg / 2 × 10^18 nuclei)
Finally, we can determine the time required to produce 8 kg of Pu-239. Since we know the mass of Pu-239 produced per second, we divide 8 kg by this value and convert the result to hours:
Time required = (8 × 10^6 g) / (Mass of Pu-239 produced per second) / 3600 seconds/hour
Calculating this value, we find that it would take approximately 20.7 hours to produce 8 kg of Pu-239 from the given nuclear power plant.
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