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The unstable uranium nuclide 238 92U has a half-life of 4.5 billion years and decays into the thorium nuclide 234 90Th . The th...Question
The unstable uranium nuclide 238 92 U has a half-life of 4.5 billion years and decays into the thorium nuclide 234 90 Th. The thorium daughter nuclide has a half-life
of 24.1 days and decays into the protactinium nuclide 234 91 Pa, which has a half-life of 6.75 hours and decays into 234 90 U, whose half-life is 245 thousand years.
In a sample of uranium-containing rock, of the four nuclides the most abundant will be blank.
Answers below:
238 92 U because the very long half-life means a very small rate of decay
234 90 U because it is the decay product of the other nuclides
234 90 Th because the decay rate of 238 92 U is so large and the decay rate of 234 91 Pa is small
234 91 Pa because it has the shortest half-life and therefore has the smallest rate of decay
of 24.1 days and decays into the protactinium nuclide 234 91 Pa, which has a half-life of 6.75 hours and decays into 234 90 U, whose half-life is 245 thousand years.
In a sample of uranium-containing rock, of the four nuclides the most abundant will be blank.
Answers below:
238 92 U because the very long half-life means a very small rate of decay
234 90 U because it is the decay product of the other nuclides
234 90 Th because the decay rate of 238 92 U is so large and the decay rate of 234 91 Pa is small
234 91 Pa because it has the shortest half-life and therefore has the smallest rate of decay
Answers
GPT-4o mini
In the given scenario, we're dealing with a decay series that starts with uranium-238 (238 \(^{92}\text{U}\)), which has a very long half-life of 4.5 billion years. As it decays, it produces thorium-234 (234 \(^{90}\text{Th}\)), which has a much shorter half-life of 24.1 days, and then this decays into protactinium-234 (234 \(^{91}\text{Pa}\)), which decays further into uranium-234 (234 \(^{90}\text{U}\)).
Considering the half-lives of each of the nuclides involved:
- Uranium-238 (238 \(^{92}\text{U}\)): 4.5 billion years (very long, thus it will be abundant)
- Thorium-234 (234 \(^{90}\text{Th}\)): 24.1 days (short, so less abundant than U-238)
- Protactinium-234 (234 \(^{91}\text{Pa}\)): 6.75 hours (very short, rapidly decays)
- Uranium-234 (234 \(^{90}\text{U}\)): 245 thousand years (longer than Th-234 and Pa-234 but shorter than U-238)
Since uranium-238 has such a long half-life, a significant amount of it would remain present in the rock sample. In contrast, the daughter products (Th-234, Pa-234, U-234) would be in much smaller amounts due to their relatively short half-lives, leading to faster decay.
Thus, the most abundant nuclide in the sample of uranium-containing rock will be:
**238 \(^{92}\text{U}\) because the very long half-life means a very small rate of decay.**
Considering the half-lives of each of the nuclides involved:
- Uranium-238 (238 \(^{92}\text{U}\)): 4.5 billion years (very long, thus it will be abundant)
- Thorium-234 (234 \(^{90}\text{Th}\)): 24.1 days (short, so less abundant than U-238)
- Protactinium-234 (234 \(^{91}\text{Pa}\)): 6.75 hours (very short, rapidly decays)
- Uranium-234 (234 \(^{90}\text{U}\)): 245 thousand years (longer than Th-234 and Pa-234 but shorter than U-238)
Since uranium-238 has such a long half-life, a significant amount of it would remain present in the rock sample. In contrast, the daughter products (Th-234, Pa-234, U-234) would be in much smaller amounts due to their relatively short half-lives, leading to faster decay.
Thus, the most abundant nuclide in the sample of uranium-containing rock will be:
**238 \(^{92}\text{U}\) because the very long half-life means a very small rate of decay.**