1. A product is detectable (THE CLOCK)
    2. The rate of production of that product is know (THE TICKING CLOCK)
    3. Product amount is 0 (or known) at age 0 of sample (CLOCK SET TO ZERO)

    Product / Rate = Time
        mushrooms grow 0.5g/yr
        how old is a 10g mushroom?
    10g / 0.5g/yr = 20 years
        mushrooms grow at a rate of Wt = W0e0.69t
        how old is a 10g mushroom?
        (weighed 0.1g at birth)
    ln(Wt/W0) / 0.69 = 6.67 years

Isotopes: elements with the same atomic number but different atomic mass.
    atomic number: number of protons in nucleus, e.g., 6-Carbon 7-Nitrogen, 19-Potassium
    atomic mass: number of protons + neutrons, e.g., Carbon 12, 13, 14; Potassium 39, 40
    Written 126C to distinguish from ion charge C+4
Some isotopes unstable 40K, 14C; while others are stable 39K, 41K, 12C, 13C
Unstable isotopes decay to another stable or unstable Isotope
    Expressed as "half-life" (T½)" time in which ½ of radioisotopes to decay:
      14C       5730 yr (5570, Libby)
      40K       1.31 X 109 yr
      210Pb     22 yr

Radiocarbon half-lifes

K - Ar & Ar - Ar Dating
    K/Ar dates are based on ratio of 40K / 40Ar trapped in sample,
    heating drives off argon gas, re-setting clock.
    half-life (T½) 1,250,000,000 years

    40Ar/39Ar relies on artificial production of 39Ar from 39K, which (using constant ratio of 40K/39K)
       gives 40K / 40Ar ratio from same part of rock
       avoids "leaky rocks" problem

210Pb DATING: radiometric dates for the last 100 year
    Origin of 210Pb: Uranium Decay Series
      α decay
      Β decay

    Sources of 210Pb
      supported 210Pb produced by radioactive decay of sediments (autochthonous)
      unsupported 210Pb transported to lake from watershed (allochthonous)

    Models for 210Pb decay in sediment
      CRS - Constant rate of Supply
      CIC - Constant Initial Concentration
    low precision
    high precision

Uranium Thorium Dating 230Th/238U

T½ 4.5 billion years (α, β, β, α particle emissions)
Based on the detection of the parent (238U) and daughter (230Th) isotopes
Material: carbonate sediments, bones, teeth (closed system)
Range: 1000 - 500,000 yr.
example: Bull Lake Glaciation 150,000±8300 yr (Sharp et al., 2003)
  • Berkeley Radiometric Dating


    Carbon Isotope Ratios
      14C/12C = 10-12
      13C/12C = 10-2
    1. isotopes (and products) must be detectable
      n,p (production of neutrons in atm. by cosmic rays)
      147N + n -> 146C + H+
      146C -> 147N + Β(Beta) + neutrino
      1. measure rate of Beta decay, find position on T½ chart
      2. measure amounts of 14C & 12C (AMS technique)

    2. beginning of decay must be related to age of sample
        Living organisms incorporate 14C/12C at near atmospheric ratio.
        Death starts the clock, no new 14C incorporated, only decay back to 147N.

      Precision: statistical uncertainty "±" of radiocarbon date = standard deviation of multiple counts

      Maximum Determinable Age, and Precision depends on size of sample.
    Global production of 14C: cosmic ray bombardment produces free neutrons
      2 n sec-1 cm-2     in equilibrium, so     2 decays sec-1 cm-2 (dps)
      2 dps / 8.5 g C cm-2 X 60 sec min-1 =   13.56 14C decays min-1 g-1 carbon = Actmod

    Organic matter is about ½ carbon: a 2 gm sample would contain about 1 gm carbon

  • Actsample
    AGE (yr) = - [ 8033 x ln --------- ]

    Fractionation: organism incorporate carbon isotopes differentially, 13C & 14C proportionally

    13C/12C ratiospl - 13C/12C ratioPD
    δ 13C =
    x 1000 ‰
    13C/12C ratiospl

    Material 13C ‰ Correction
    wood -25 0 yr
    marine -14 179 yr
    atm. CO2 -8 280 yr

    2 ( 25 + δ 13C ‰)
    Actcorrected = Actsample ( 1 - ----------------------------)

    example: material has -12 δ 13C ‰ and 7 dpm g C -1
    Actcorrected = 6.818 dpm = 5523 yr

    Reservoir Effect: ratio of 14C/12C different in oceans, caves, some lakes
      oceans ca. 400 yrs younger than terrestrial, differences due to deep circulation
      example: Gulf of California 500 yr, coastal California 200 yr

    Anthropogenic Effect:
      12C enrichment due to industrial revolution (negative 14C anomaly [too old])
      Suess Effect (Suess, 1955; Levin et al., 1989)

      14C enrichment due to proton production by atmospheric A-Bomb testing
        bomb anomaly used as tracer in oceanic circulation, groundwater circulation

    Calibration: using the relationship between radiocarbon ages and dates from tree rings, varves, and U/Th dates to calibrate the radiocarbon dates.
      The 12C/14C atmospheric ratio is effected by
      (Beck et al., 2001)
    • geomagnetic strength - cosmic rays
    • solar variability (sunspots) - cosmic rays
    • carbon budget
        Delta 14C

        Calibration Software Probability Density Function

        Tree rings and other calibration records

    Wiggle-Matching: Using fluctuations in calibration curve to obtain precise ages relatively-dated series.



    Rb-Sr, K-Ar and Ar-Ar Dating notes UIUC

    Calibration Programs
    Calib 4.2