1. 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

2. 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)

3. 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

4. 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

5. 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

6. 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) =