Lecture6 radiometricdating
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Lecture6 radiometricdating

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    Lecture6 radiometricdating Lecture6 radiometricdating Presentation Transcript

    • Lithosphere: solid Earth
    • 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
    • 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
    • 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)
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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…
    • 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
    • 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
    • t = 3.96 Ga + 1 ln ∙ t = 1 k D P How old are the oldest rocks on Earth?
    • 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
    • Radiometric dating
      • = dating based on the steady decay of unstable isotopes
      • This is where we get the numbers on the following geologic time scale
    • Geologic Time
      • Earth ≈ 4.6 billion years old
      • Geological Time Scale
      • calendar of Earth history
      • divided into eons, eras, and periods
      Millions of years
    • This is just for your own edification; I don't expect you to memorize this!!
    • Geologic Time
      • Earth ≈ 4.6 billion years old
      • Geological Time Scale
      • calendar of Earth history
      • divided into eons, eras, and periods
      Millions of years
    • Geologic Time Millions of years End of the last ‘Ice Age’: ~12,000 yrs ago End of the dinosaurs: ~65 million yrs ago
    • 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?
    • 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?
    • 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
    • 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)
    • Scaling problem calculation
      • 4. X cm = (10 cm)(50 km)
      • 6400 km
      • 5. X = 0.078 cm
      • Unit conversion?
      • Significant figures?
    • 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)?
    • 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