Question

If an isotope has a half-life of 4 million years, and a fossil is 16 million years old, how much of the original isotope will be found in the fossil?

A. one-half of the original amount
B. one-sixteenth of the original amount
C. one-quarter of the original amount
D. one-eighth of the original amount

Answer 1

For an isotope with a half-life of 4 million years, after 16 million years (or four half-lives), only (B) one-sixteenth of the original isotope amount would be found in the fossil.

Step-by-step explanation:

When dealing with radioactive isotopes and their half-lives, we are talking about the time it takes for half of the original amount of an isotope to decay into its more stable form. In this case, each half-life of 4 million years results in half of the isotope remaining.

After the first half-life, half of the original amount remains. After the second half-life (8 million years total), one quarter remains because half of the half is one quarter. Continuing this, after the third half-life (12 million years total), one eighth remains. Finally, after the fourth half-life (16 million years total), one sixteenth of the original amount remains. Therefore, the correct answer is B. one-sixteenth of the original amount.