Final answer:
Isotopes such as 226Ra, 222Rn, and 210Po are found in a 3×109-year-old rock with uranium-238 because they are daughter products of the ongoing decay chain of 238U, being continuously regenerated. So, the correct answer is option c) These isotopes are daughters of 238U decay.
Step-by-step explanation:
In a 3×109-year-old rock that originally contained 238U (uranium-238), we would still expect to find some 238U remaining because its half-life is approximately 4.5×109 years. Despite their much shorter half-lives, isotopes such as 226Ra (radium-226), 222Rn (radon-222), and 210Po (polonium-210) are also found in the rock because they are continuously formed as daughter products in the decay chain of 238U.
This continues to occur over time as 238U undergoes radioactive decay, even if it happens over billions of years. This decay series produces various isotopes until a stable nuclide, 206Pb (lead-206), is finally formed.
Therefore, the presence of these isotopes despite their short half-lives is due to the fact that they are continuously regenerated as part of the decay process of the long-lived parent isotope 238U.
In a 3x109-year-old rock that originally contained some 238U, we expect to find 226Ra, 222Rn, and 210Po because they are daughters of the decay of 238U. These isotopes are produced continuously as a result of the radioactive decay of 238U, even though they have much shorter half-lives compared to 238U. So, the correct answer is option c) These isotopes are daughters of 238U decay.