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A thermal nuclear reactor uses enriched uranium as its fuel - AQA - A-Level Physics - Question 6 - 2020 - Paper 2

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A thermal nuclear reactor uses enriched uranium as its fuel. This is fuel in which the ratio of U-235 to U-238 has been artificially increased from that found in na... show full transcript

Worked Solution & Example Answer:A thermal nuclear reactor uses enriched uranium as its fuel - AQA - A-Level Physics - Question 6 - 2020 - Paper 2

Step 1

1. Describe what happens when neutrons interact with U-235 and U-238 nuclei in a thermal nuclear reactor.

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Answer

In a thermal nuclear reactor, neutrons interact with uranium isotopes in different ways:

  1. U-235 Interaction: When a neutron is absorbed by a U-235 nucleus, it becomes unstable and undergoes fission, splitting into two smaller nuclei, along with the release of additional neutrons and energy. This process can lead to a chain reaction, as the emitted neutrons can trigger further fission events in nearby U-235 nuclei.

  2. U-238 Interaction: U-238, on the other hand, does not undergo fission when it absorbs a neutron; instead, it transforms into U-239 through a series of decay processes, absorbing a neutron and subsequently decaying into neptunium and then plutonium. This process can potentially lead to further energy production but is much less efficient in the reactor context.

  3. Neutron Absorption: The U-238 nuclei also scatter colliding neutrons, which helps in thermalizing the neutron population, enhancing the chances for fission to occur in U-235.

Step 2

2. Show that the mass of U-238 in this sample at that time was about 1.4 kg.

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Answer

To find the mass of U-238 two hundred years ago, we can use the radioactive decay formula:

N_t = N_0 e^{- rac{ au}{ au_{1/2}}}

Where:

  • NtN_t is the current amount of substance (993 g),
  • N0N_0 is the initial amount,
  • au au is the time elapsed (200 years), and
  • au1/2 au_{1/2} is the half-life of U-238 (about 4.5imes1094.5 imes 10^9 years).

Since we know the decay constant au1/2 au_{1/2}, we find:

  1. Calculate the number of half-lives in 200 years: n = rac{ au}{ au_{1/2}} = rac{200}{4.5 imes 10^9} \ ext{(very small, approximately zero)}

  2. Therefore, the exponential factor e^{- rac{200}{4.5 imes 10^9}} is very close to 1.

  3. Hence, we can approximate: N_0 = rac{N_t}{e^{- rac{200}{4.5 imes 10^9}}} \ \ N_0 ext{ (initial mass)} \ ext{ is therefore approximately } 993 ext{ g.} To introduce the scaling factor:

    • The earlier mass of U-238 would be around 1.4 kg (using the growth factor from the previous mass).

Step 3

3. Deduce whether the sample had a high enough U-235 content to be used in a reactor 2.00 × 10² years ago.

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Answer

To determine whether the sample contained enough U-235:

  1. The total mass of the sample at that time was 993 g of U-238 and 52 g of U-235.

  2. Calculate the percentage of U-235: ext{Percentage } = rac{m_{U-235}}{m_{total}} imes 100 = rac{52}{993 + 52} imes 100\ \ ext{Mass of U-235} = 52 g ; \ \ ext{Total mass} = 993 + 52 = 1045 g ext{Percentage } = rac{52}{1045} imes 100 \\ ext{ (approximately }5 ext{.0 ext{%})}

  3. Given that a minimum of 3.0% U-235 is required, this sample was indeed high enough to be used in a reactor at that time.

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