Question

The half-life for \(\alpha\)-decay of uranium \( U^{228} \) is 4.47 × 10\(^8\) yr. If a rock contains 60% of the original \( U^{228} \) atoms, then its age is

• A. 1.2 × 10\(^7\) yr
• B. 3.3 × 10\(^8\) yr
• C. 4.2 × 10\(^9\) yr
• D. 6.5 × 10\(^9\) yr

Hint:

The age of a rock can be determined by using the half-life formula based on the fraction of original isotopes remaining.

Answer 1

The Correct Option is C

Using the formula for half-life, we can calculate the age of the rock. The fraction of original \( U^{228} \) left is 60%. This corresponds to the decay equation, and we can calculate the time by taking the logarithm of the fraction and dividing by the decay constant.