How is the age of a rock estimated using radioactive decay?

• A. Number of half-lives of the isotope multiplied by the length of one half-life.
• B. The current amount of parent isotope alone.
• C. The ratio of daughter to parent isotopes only.
• D. The total number of daughter isotopes remaining.

Answer: (A)

Radioactive decay proceeds at a constant rate, and the time it takes for half the parent atoms to decay is the half-life. To estimate how long ago a rock formed, you figure out how many half-lives have passed and multiply by the length of one half-life: age equals the number of half-lives times the half-life duration. This works because the amount of time elapsed is directly tied to how many times the parent population has been cut in half. You can infer how many half-lives have occurred by looking at the current amounts of parent and daughter isotopes and applying the decay equations, which connect the remaining parent to the elapsed time. Relying only on the current amount of the parent lacks information about the starting amount, so it doesn’t uniquely determine age. Using only the ratio of daughter to parent also requires knowing initial conditions about any daughter present at formation, so it isn’t a direct age measure on its own. Counting only the daughter isotopes ignores how long decay has been happening and can mislead about the true time elapsed.