1. Lithosphere: solid Earth

4. Radiometric Dating Half-life = time required for ½ of the unstable isotopes in a sample to decay into stable isotopes Decay is a perfectly random process; every atom has a 50/50 chance of decaying in a given time period (i.e., the half-life)

5. time (My) Proportion of unstable isotopes 1.0 Half-life = 1 My Radiometric Dating 1 2 3 4 0 0 5 0.5 0.25 0.125 0.0625

6. Radiometric Dating P = P 0 e - kt P = # unstable isotopes (parent) at time t P 0 = # unstable isotopes (parent) at time 0 (the initial # of isotopes) e = 2.718… k = decay constant = 0.693/H (to be precise, -k = ln(½)/H = -0.693/H) H = half-life t = time

7. Radiometric Dating P = P 0 e - kt To find the age of a rock, solve this eq. for t: But we don’t know how many parent isotopes we started with!! ln ∙ t = 1 k P 0 P

8. Radiometric Dating P = P 0 e - kt To find the age of a rock, solve this eq. for t: ln ∙ t = 1 k P 0 P P 0 - P = # stable (daughter) isotopes at time t! Let’s call this D. + 1 ln ∙ t = 1 k P 0 - P P ln ∙ t = 1 k P 0 - P + P P

9. Radiometric Dating P = P 0 e - kt To find the age of a rock, solve this eq. for t: This is the equations we’ll use. ln ∙ t = 1 k P 0 P + 1 ln ∙ t = 1 k D P

12. How old are the oldest rocks on Earth? t = 6.45 Ga · ln(1.85) t = 6.45 Ga · 0.615 + 1 ln ∙ t = 1 k D P + 1 ln ∙ t = H 0.693 D P 0.85 + 1 ln ∙ t = 4.47 Ga 0.693 G = giga = billion a = annum = years

13. t = 3.96 Ga + 1 ln ∙ t = 1 k D P How old are the oldest rocks on Earth?

17. This is just for your own edification; I don't expect you to memorize this!!

19. Geologic Time Millions of years End of the last ‘Ice Age’: ~12,000 yrs ago End of the dinosaurs: ~65 million yrs ago