Question
The unstable uranium nuclide 238 92U
has a half-life of 4.5 billion years and decays into the thorium nuclide 234 90Th
. The thorium daughter nuclide has a half-life of 24.1 days and decays into the protactinium nuclide 234 91Pa
, which has a half-life of 6.75 hours and decays into 234 90U
, whose half-life is 245 thousand years. In a sample of uranium-containing rock, of the four nuclides the most abundant will be __________.(1 point)
Responses
234 90U
because it is the decay product of the other nuclides
subscript 90 superscript 234 baseline upper U because it is the decay product of the other nuclides
234 90Th
because the decay rate of 238 92U
is so large and the decay rate of 234 91Pa
is small
subscript 90 superscript 234 baseline upper T h because the decay rate of subscript 92 superscript 238 baseline upper U is so large and the decay rate of subscript 91 superscript 234 baseline upper P a is small
234 91Pa
because it has the shortest half-life and therefore has the smallest rate of decay
subscript 91 superscript 234 baseline upper P a because it has the shortest half-life and therefore has the smallest rate of decay
238 92U
because the very long half-life means a very small rate of decay
has a half-life of 4.5 billion years and decays into the thorium nuclide 234 90Th
. The thorium daughter nuclide has a half-life of 24.1 days and decays into the protactinium nuclide 234 91Pa
, which has a half-life of 6.75 hours and decays into 234 90U
, whose half-life is 245 thousand years. In a sample of uranium-containing rock, of the four nuclides the most abundant will be __________.(1 point)
Responses
234 90U
because it is the decay product of the other nuclides
subscript 90 superscript 234 baseline upper U because it is the decay product of the other nuclides
234 90Th
because the decay rate of 238 92U
is so large and the decay rate of 234 91Pa
is small
subscript 90 superscript 234 baseline upper T h because the decay rate of subscript 92 superscript 238 baseline upper U is so large and the decay rate of subscript 91 superscript 234 baseline upper P a is small
234 91Pa
because it has the shortest half-life and therefore has the smallest rate of decay
subscript 91 superscript 234 baseline upper P a because it has the shortest half-life and therefore has the smallest rate of decay
238 92U
because the very long half-life means a very small rate of decay
Answers
GPT-4o mini
To determine which of the four nuclides is the most abundant in a sample of uranium-containing rock, we need to consider the half-lives and decay rates of each nuclide.
1. **Uranium-238 (238 92U)** has a half-life of 4.5 billion years, which means it decays very slowly. Therefore, it will still be present in significant amounts.
2. **Thorium-234 (234 90Th)**, the daughter nuclide of uranium-238, has a half-life of 24.1 days, which is relatively short compared to uranium-238. This means that while it is produced from uranium-238 decay, it will decay away relatively quickly.
3. **Protactinium-234 (234 91Pa)** has a half-life of 6.75 hours, making it even shorter-lived than thorium-234. As a result, it will decay very rapidly.
4. **Uranium-234 (234 90U)** has a half-life of 245 thousand years, which is longer than both thorium-234 and protactinium-234, but shorter than uranium-238.
Given this information, the most abundant nuclide in the sample will be **238 92U** because it has the longest half-life and will therefore still be present in significant amounts despite decay producing the other elements.
The correct response then is:
- **238 92U because the very long half-life means a very small rate of decay.**
1. **Uranium-238 (238 92U)** has a half-life of 4.5 billion years, which means it decays very slowly. Therefore, it will still be present in significant amounts.
2. **Thorium-234 (234 90Th)**, the daughter nuclide of uranium-238, has a half-life of 24.1 days, which is relatively short compared to uranium-238. This means that while it is produced from uranium-238 decay, it will decay away relatively quickly.
3. **Protactinium-234 (234 91Pa)** has a half-life of 6.75 hours, making it even shorter-lived than thorium-234. As a result, it will decay very rapidly.
4. **Uranium-234 (234 90U)** has a half-life of 245 thousand years, which is longer than both thorium-234 and protactinium-234, but shorter than uranium-238.
Given this information, the most abundant nuclide in the sample will be **238 92U** because it has the longest half-life and will therefore still be present in significant amounts despite decay producing the other elements.
The correct response then is:
- **238 92U because the very long half-life means a very small rate of decay.**