To determine which isotope scientists would avoid using for dating a fossil, we need to consider the half-lives of each isotope provided:
- Carbon-14: 5.7 x 10^3 years (approximately 5,700 years)
- Potassium-40: 1.3 x 10^9 years (approximately 1.3 billion years)
- Radon-222: 1.0 x 10^4 seconds (which is a very short half-life)
- Thorium-232: 1.4 x 10^10 years (approximately 14 billion years)
For dating fossils, we generally want to use isotopes with half-lives that are suitable for the age range of the fossils. Carbon-14 is commonly used for dating relatively young fossils (up to about 50,000 years), while potassium-40 and thorium-232 are more suitable for dating much older geological formations. Radon-222, with its short half-life, would decay too quickly to be effective for dating fossils and is primarily used for other applications.
Based on this analysis, the isotope Radon-222 would be avoided for dating a fossil due to its very short half-life.