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Lecture6 radiometricdating

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  • 1. Lithosphere: solid Earth
  • 2. Geologic time: dating
    • 2 types
    • Relative Dating = sequential age
      • based on positions of rocks relative to each other
      • e.g., rock layer B is older than A and younger than C
    • 2. Absolute Dating = actual age
      • based on radiometric dating
      • e.g., rock layer B is 50 million years old
  • 3. Radiometric dating
    • = dating based on the steady decay of unstable isotopes
    • Atoms = nucleus of protons & neutrons orbited by electrons
    • Isotopes = different forms of element w/ different numbers of neutrons
    • unstable (Mother or Parent) isotopes
    • stable (Daughter) isotopes
    decay
  • 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
  • 10. How old are the oldest rocks on Earth?
    • Given: Sample from Acasta Gneiss in Canada
    • It has crystals of zircon that
    • contain 238 U.
    • 238 U is unstable.
    • It decays into 206 Pb.
    • The half-life (H) of decay
    • of 238 U into 206 Pb = 4.47 billion years
    • We can measure how much 206 Pb (D) and 238 U (P) is in the rock and report it as a ratio…
  • 11. How old are the oldest rocks on Earth?
    • Given: Sample from Acasta Gneiss in Canada
    • H of 238 U into 206 Pb
    • = 4.47 billion years
    • D/P = 0.85
    where t = age D = amount of daughter (stable) isotope P = amount of mother (unstable) isotope k = 0.693/H H = half-life + 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?
  • 14. How old is the Earth?
    • oldest rocks = 3.96 billion years old
    • difficult to find older rocks because early crust destroyed
    • most meteorites = 4.5 - 4.6 Ga
    •  we presume that the
    • age of the Earth
    • ≈ 4.6 billion years
  • 15. Radiometric dating
    • = dating based on the steady decay of unstable isotopes
    • This is where we get the numbers on the following geologic time scale
  • 16. Geologic Time
    • Earth ≈ 4.6 billion years old
    • Geological Time Scale
    • calendar of Earth history
    • divided into eons, eras, and periods
    Millions of years
  • 17. This is just for your own edification; I don't expect you to memorize this!!
  • 18. Geologic Time
    • Earth ≈ 4.6 billion years old
    • Geological Time Scale
    • calendar of Earth history
    • divided into eons, eras, and periods
    Millions of years
  • 19. Geologic Time Millions of years End of the last ‘Ice Age’: ~12,000 yrs ago End of the dinosaurs: ~65 million yrs ago
  • 20. If the Earth were the age of the USA…
    • Let’s condense the ~4.6 billion years of the Earth down to the ~230 years of the Republic
    • How long ago (in Republic time) did the dinosaurs die out?
    • How long ago did the last ice age end?
  • 21. Scaling problem
    • Revisiting the concept of scale…
    • 99% of our atmosphere: 50 km thick
    • If you shrunk the Earth down to the size of a basketball, how thick would the atmosphere be?
  • 22. Scaling problem
    • Given
    • Earth’s radius = 6400 km
    • Thickness of the atmosphere = 50 km
    • Need to figure out
    • Basketball radius?
    • How thick the atmosphere would be if the Earth was the size of a basketball
  • 23. Scaling problem calculation
    • 1.
    • Thickness of mini atm = Radius of mini Earth
    • Thickness of atm Radius of Earth
    • 2. X cm = 10 cm
    • 50 km 6400 km
    • 3. (6400 km)(X cm) = (50 km)(10 cm)
  • 24. Scaling problem calculation
    • 4. X cm = (10 cm)(50 km)
    • 6400 km
    • 5. X = 0.078 cm
    • Unit conversion?
    • Significant figures?
  • 25. If the Earth were the age of the USA…
    • Let’s condense the ~4.6 billion years of the Earth down to the ~230 years of the Republic.
    • How long ago (in Republic time) did the dinosaurs die out (65 Ma)?
    • How long ago did the
    • last ice age end (12 ka)?
  • 26. If the Earth were the age of…
    • Pick some familiar time interval
      • Possibilities: a day, a week, your life, your time at W&M, etc.
    • Scale down Earth’s age to that time interval. How long is recorded history on your new time scale?
    • The Sumerians developed cuneiform writing in ~4000 B.C. (~6000 years ago)
    • Earth is ~4.6 billion years old