If a rock has experienced 2 half-lives for a particular isotope, its age is:

• A. Two times the length of one half-life
• B. Equal to the current amount of parent isotope
• C. Two times the initial number of parent isotopes
• D. The total of parent and daughter isotopes remaining

Answer: (A)

Half-life is the time required for half of a radioactive sample to decay. After two half-lives have passed, the elapsed time equals two durations of the half-life, so the age is two times the length of one half-life. In other words, t = 2 × t_half.

The remaining amount of parent after two half-lives is only one-quarter of the original, since (1/2)² = 1/4, so the current quantity is not the age. While the total number of atoms (parent plus daughter) stays equal to the initial amount if you count both types, the age itself is about how long decay has occurred, not the current count of nuclei.