gen-define-radiometric-dating-and-give-one-short-worked-example-f47c

Define radiometric dating and give one short worked example.

# Radiometric Dating **Definition:** Radiometric dating is a method of determining the age of materials (rocks, fossils, artifacts) by measuring the abundance of radioactive isotopes and their decay products. It relies on the predictable rate at which unstable radioactive "parent" isotopes decay into stable "daughter" isotopes, characterized by their half-life. ## Worked Example: Carbon-14 Dating **Problem:** A wooden artifact contains 25% of the original Carbon-14 compared to a living tree. How old is the artifact? (Half-life of C-14 = 5,730 years) **Solution:** After each half-life, 50% of the parent isotope remains: - Start: 100% C-14 - After 1 half-life: 50% C-14 - After 2 half-lives: 25% C-14 Since the artifact has 25% remaining, **2 half-lives** have passed. **Age = 2 × 5,730 years = 11,460 years old** Alternatively, using the formula: N = N₀(½)^(t/t½) - 0.25 = 1(½)^(t/5730) - log(0.25) = (t/5730)log(0.5) - t = 11,460 years