A-Level AQA Physics Work, Energy & Power: During a single fission event of

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

Question 31

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 from one fission event

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Answer

The energy released from a single fission event can be calculated using the equation:

$E = ext{mass loss} imes c^2$

Where:

ext{mass loss} = 0.23 ext{ u} = 0.23 imes 1.66 imes 10^{-27} ext{ kg} = 3.818 imes 10^{-28} ext{ kg}
c = 3 imes 10^8 ext{ m/s}

Thus,

$E = 3.818 imes 10^{-28} ext{ kg} imes (3 imes 10^8 ext{ m/s})^2 = 1.14 imes 10^{-11} ext{ J}$

Step 2

Determine the effective energy available due to efficiency

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Answer

Only 25% of the energy is utilized effectively due to the efficiency of the reactor:

$E_{ ext{effective}} = 0.25 imes 1.14 imes 10^{-11} ext{ J} = 2.85 imes 10^{-12} ext{ J}$

Step 3

Calculate the number of fission events required to generate 900 MW of power

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Answer

To find the number of events per second required, we use the formula:

$ext{Power} = ext{Energy per event} imes ext{Number of events per second}$

Given the reactor generates 900 MW, we convert it to watts:

$900 ext{ MW} = 900 imes 10^6 ext{ W}$

Setting up the equation:

$900 imes 10^6 = 2.85 imes 10^{-12} imes N$

Where N is the number of events per second. Solving for N:

$N = \frac{900 imes 10^6}{2.85 imes 10^{-12}} \approx 3.16 imes 10^{20}$

Step 4

Choose the closest answer

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Answer

The closest answer to the calculated result of approximately $3.16 imes 10^{20}$ events per second is option C: $1.1 imes 10^{20}$ .

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

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

Calculate the energy released from one fission event

Determine the effective energy available due to efficiency

Calculate the number of fission events required to generate 900 MW of power

Choose the closest answer

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