Learning Objectives: What is half-life How does half-life allow scientists to tell how old a fossil is BE able to solve basic half-life problems

Radiometric Dating: Absolute Time Half-Life (λ) : The time it takes radioactive elements to to partially (50%) decay to a more stable form Ex: Carbon-14 (C14) decays to Nitrogen-14 and has λ = 5,730 years Potassium-40 (K40) decays to Argon -40 λ = 1.3 Billon years (1,300,000,000 years) Uranium 238 (U238) decays to Lead-206 λ = 4.4 Billon years (4,400,000,000 years)

So after 20 days (4 x λ) there is 2 grams of radioactive Half-life Practice Problem: If you start with 32 grams of radioactive element “A” how much is left after 20 days? “A”  “B” λ = 5 days A B 16g λ 5 days 5 days A B 8g 24g λ λ 5 days A 4g B 28g 5 days A 2g B 30g λ A 32g So after 20 days (4 x λ) there is 2 grams of radioactive element “A” left

Half-life Practice Problem: “C”  “D” λ = 7 days If you start with 80 grams of “C” how much is left after 35 days 35 days = 5 half-lives (λ =7 days) 7 days C = 80g D = 0g C = 5 g D = 75g λ λ λ C = 20g D = 60g λ C = 10g D = 70g C = 40g D = 40g C = 2.5 g D = 77.5g λ

Half-life Practice Problem: “X”  “Y” λ = 4 years If you start with 60 grams of “X” How much “Y” is created after 12 years? 12 years = 3 half-lives (λ =4 years) λ X = 60g Y = 0g X = 30g Y = 30g λ X = 15g Y = 45g λ X = 7.5g Y = 52.5g

A Real Half-life Problem: C14  N14 λ = 5,730 years A bone fossil of animal has 75g of N14 and 25g of C14. Assuming there was 0g of N14 when the animal died. Estimate the age of the fossil C14 = 100g N14 = 0g Animal Died λ 5,730 λ C14 = 50g N14 = 50g 5,730 C14 = 25g N14 = 75g Fossil Found 11,460 years old 2 x λ (5,730 years) =