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During a single fission event of uranium-235 in a nuclear reactor the total mass lost is 0.23 u - AQA - A-Level Physics - Question 31 - 2018 - Paper 2

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During a single fission event of uranium-235 in a nuclear reactor the total mass lost is 0.23 u. The reactor is 25% efficient. How many events per second are requir... show full transcript

Worked Solution & Example Answer:During a single fission event of uranium-235 in a nuclear reactor the total mass lost is 0.23 u - AQA - A-Level Physics - Question 31 - 2018 - Paper 2

Step 1

Calculate the energy released per fission event

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Answer

The energy released per fission event can be calculated using the mass-energy equivalence formula: E=rianglemc2E = riangle mc^2. Given that the mass lost is 0.23 u and using the conversion factor of 1 u = 931.5 MeV:

E=0.23imes931.5extMeV=214.24extMeVE = 0.23 imes 931.5 ext{ MeV} = 214.24 ext{ MeV}.

To convert this energy into joules (since 1 MeV = 1.602 imes 10^{-13} J):

E=214.24imes1.602imes1013J=3.43imes1011JE = 214.24 imes 1.602 imes 10^{-13} J = 3.43 imes 10^{-11} J.

Step 2

Determine the useful energy output per fission event considering efficiency

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Answer

Since the reactor is 25% efficient, the useful energy output per fission event is:

Euseful=0.25imesE=0.25imes3.43imes1011J=8.575imes1012JE_{useful} = 0.25 imes E = 0.25 imes 3.43 imes 10^{-11} J = 8.575 imes 10^{-12} J.

Step 3

Calculate the total energy required per second to generate 900 MW of power

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Answer

Power is defined as energy per unit time. Therefore, the total energy required per second to generate 900 MW is:

P=900extMW=900imes106extW=900imes106extJ/sP = 900 ext{ MW} = 900 imes 10^6 ext{ W} = 900 imes 10^6 ext{ J/s}.

Step 4

Determine the number of fission events required per second

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Answer

To find the number of fission events per second, we can divide the total power by the useful energy per fission event:

N=PEuseful=900imes106extJ/s8.575imes1012J1.05×1020N = \frac{P}{E_{useful}} = \frac{900 imes 10^6 ext{ J/s}}{8.575 imes 10^{-12} J} \approx 1.05 \times 10^{20} events per second.

Step 5

Select the correct answer

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Answer

Based on our calculations, the answer approximates to 1.1×10201.1 \times 10^{20} events per second, which corresponds to option C.

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