Final answer:
The age of the granite is calculated by multiplying the number of half-lives that have passed (3) by the half-life of uranium-235 (704 million years), resulting in an age of approximately 2.112 billion years for the granite rock.
Step-by-step explanation:
The question involves calculating the age of a granite rock using uranium-235 to lead-206 ratios in zircon crystals. Given that the parent (uranium-235) to daughter (lead-206) ratio is 25% to 75%, we can understand that three half-lives of uranium-235 have passed because the amount of parent isotope is halved with each half-life. Since the half-life of uranium-235 is 704 million years, the calculation would be 3 half-lives × 704 million years per half-life, giving us the age of the granite rock.
To perform the calculation:
- Determine the number of half-lives that have passed which is 3 (since the ratio has halved three times from 100% to 50%, to 25%).
- Multiply this by the half-life of uranium-235 (704 million years).
Age of granite = 3 half-lives × 704 million years/half-life = 2112 million years or 2.112 billion years.
Therefore, the granite is approximately 2.112 billion years old.