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 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 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 238 92U because the very long half-life means a very small rate of decay
GPT-4o mini
In the decay series starting from uranium-238 (U-238) to thorium-234 (Th-234) to protactinium-234 (Pa-234) to uranium-234 (U-234), let's analyze the stability and abundance of these nuclides.

- **Uranium-238 (U-238)** has a very long half-life of 4.5 billion years, which means it decays very slowly. It will be present in significant amounts because of its stability over such a long time.

- **Thorium-234 (Th-234)** has a half-life of only 24.1 days, meaning it decays relatively quickly compared to U-238. While Th-234 is the direct decay product of U-238, its abundance will not be high due to its short half-life.

- **Protactinium-234 (Pa-234)** has an even shorter half-life of 6.75 hours. Therefore, its abundance will be very low in comparison to the other longer-lived isotopes.

- **Uranium-234 (U-234)** has a half-life of 245,000 years, which is still much shorter than U-238 but longer than both Th-234 and Pa-234.

Considering all these points, since U-238 has such a long half-life, it will be the most abundant nuclide in the sample of uranium-containing rock.

Therefore, the most abundant nuclide in the sample will be **238 92U** because the very long half-life means a very small rate of decay.