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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
Step 1
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
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:
Since we know the decay constant , 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:
Step 3
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.
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