Which of the following statements about the half-life of a radioactive isotope is true?

• A. After two half-lives, one quarter of the original radioactive nuclei remain.
• B. The half-life of a radioactive isotope increases as the amount of the isotope decreases.
• C. The half-life depends on the initial amount of the radioactive isotope present.
• D. The half-life is the time required for half of the radioactive nuclei in a sample to decay.

Answer: (D)

Verified step by step guidance

1. Understand the definition of half-life: The half-life of a radioactive isotope is the time required for half of the radioactive nuclei in a sample to decay. This is a fundamental property of the isotope and does not depend on the amount of the isotope present.
2. Analyze the statement 'After two half-lives, one quarter of the original radioactive nuclei remain': After one half-life, half of the nuclei remain. After the second half-life, half of that half remains, which is one quarter. This statement correctly describes the exponential decay process.
3. Evaluate the statement 'The half-life of a radioactive isotope increases as the amount of the isotope decreases': The half-life is independent of the amount of isotope present; it is a constant characteristic of each isotope. Therefore, this statement is false.
4. Evaluate the statement 'The half-life depends on the initial amount of the radioactive isotope present': Since half-life is a constant property of the isotope, it does not depend on the initial quantity. This statement is false.
5. Summarize: The true statements are that the half-life is the time for half the nuclei to decay, and that after two half-lives, one quarter of the original nuclei remain. The other statements about half-life changing with amount are incorrect.