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 naturally-occurring ore. 1. Describe what happens when neutrons interact with U-235 and U-238 nuclei in a thermal nuclear reactor. 2. The amounts of U-235 and U-238 in the ore decrease due to radioactive decay at different rates. A sample of uranium ore today contains 993 g of U-238. The mass of U-238 in this sample was greater 2.00 × 10² years ago. Show that the mass of U-238 in this sample at that time was about 1.4 kg. decay constant of U-238 = 1.54 × 10⁻¹⁰ year⁻¹ 3. A thermal nuclear reactor requires a minimum of 3.0% of its uranium mass to be U-235. The ratio of U-235 to U-238 in the ore has changed over time. 2.00 × 10² years ago, the sample in Question 06.2 contained 52 g of U-235. 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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A thermal nuclear reactor uses enriched uranium as its fuel - AQA - A-Level Physics - Question 6 - 2020 - Paper 2

Question 6

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:

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.
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.
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:

$N_t$ is the current amount of substance (993 g),
$N_0$ is the initial amount,
$au$ is the time elapsed (200 years), and
$au_{1/2}$ is the half-life of U-238 (about $4.5 imes 10^9$ years).

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

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

The total mass of the sample at that time was 993 g of U-238 and 52 g of U-235.
Calculate the percentage of U-235: $ext{Percentage } = rac{m_{U-235}}{m_{total}} imes 100 = rac{52}{993 + 52} imes 100\ \ ext{Mass of U-235} = 52 g ; \ \ ext{Total mass} = 993 + 52 = 1045 g$ $ext{Percentage } = rac{52}{1045} imes 100 \\ ext{ (approximately }5 ext{.0 ext{%})}$
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.

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

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

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

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

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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