Radiometric dating of a rock reveals an age of 1.52 billion years. Given that the half-life of the parent isotope used is 14.0 billion years, what percentage of the parent isotope is still present in the rock?

Question

Quizplus · Accepted Answer

The percentage of the parent isotope still present in the rock can be calculated using the formula for radioactive decay, which is: $$ \text{Remaining percentage} = 100 \times \left( \frac{1}{2} \right)^{\frac{\text{age of rock}}{\text{half-life of isotope}}} $$ Substituting the given values: $$ \text{Remaining percentage} = 100 \times \left( \frac{1}{2} \right)^{\frac{1.52}{14.0}} \approx 92.8\% $$ This calculation shows that approximately 92.8% of the parent isotope remains in the rock, indicating that only a small fraction has decayed over the 1.52 billion years.

Radiometric Dating of a Rock Reveals an Age of 1