Final answer:
The fraction of Potassium-40 (40K) that was on Earth 4.5 billion years ago and remains today is 1/8, as three half-lives have approximately passed since the formation of Earth.
Step-by-step explanation:
The question asks what fraction of the isotope Potassium-40 (40K) that was present on Earth when it formed, approximately 4.5 billion years ago, remains today. Potassium-40 has a half-life of 1.277 billion years. We can use the concept of half-lives to determine how many half-lives have passed in 4.5 billion years and subsequently what fraction remains.
To calculate the number of half-lives that have passed, we divide the total time by the half-life of 40K:
- Total time = 4.5 × 109 years
- Half-life of 40K = 1.277 × 109 years
- Number of half-lives = 4.5 × 109 / 1.277 × 109 ≈ 3.52
After approximately three half-lives, the fraction of the original amount that remains would be (1/2)3 = 1/8. Therefore, the correct answer to the question is (d) 1/8.