Potassium-40 decays to argon-40 with a half-life of 1.27 × 10⁹ yr.The age of a mineral sample that has a mass ratio of ⁴⁰Ar to ⁴⁰K of 3.60 is ________ yr.

Question

Quizplus · Accepted Answer

The age of the mineral can be calculated using the formula for radioactive decay: t = (t₁/₂ / ln(2)) * ln(1 + (N_daughter/N_parent)). Here, t₁/₂ is the half-life, N_daughter/N_parent is the ratio of Argon-40 to Potassium-40, and ln is the natural logarithm. Substituting the given values, t = (1.27 × 10⁹ / ln(2)) * ln(1 + 3.60) ≈ 2.80 × 10⁹ years.

Potassium-40 Decays to Argon-40 with a Half-Life of 1