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t years after death
•
•
•
•
NO CO2 exchange with atmosphere
C12 is stable
C14 decays
Ratio at time t is reduced to Rt with
Rt = C14/C12 at time t
= R0 (1/2)t/T
(T = T1/2)
= R0 e-t/T
(T = Tm)
• t = T1/2 log2(R0/Rt)= Tm ln(R0/Rt)
with T1/2 = 5568 years
or Tm = 8033 years
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How to measure Rt = C14/C12 ratio
• Use chemistry to convert sample to known compound
of carbon of high purity
• Weight gives quantity of C12 (and a little C13)
– NC12 = 6 x 1023 x (weight of carbon in grams)/12
• Radioactivity gives quantity of C14
– Carbon compound dissolved in liquid scintillator
– Decay electron stimulates light emission by scintillator
– Light pulses converted to electrical pulses by
photomultipliers and counted at rate D per minute
• NC14 = D x Tm(in minutes) = D x (Tm x 365 x 24 x 60)
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Counting C14 activity
C14
Electron
path
Photons
(light)
photomultiplier
photomultiplier
Sample
cell
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****Critical for naïve approach****
• Work from: t = T1/2 log2(R0/Rt)= Tm ln(R0/Rt)
• R0 = C14/C12 at death is known
– C14 production independent of time
– C12 content of reservoir independent of time
– Mixing adequate to give SAME C14/C12 everywhere
• C14/C12 in organism same as in environment
• Rt = C14/C12 at time of dating is known
• T1/2 is known
• LET’S BRAINSTORM! HERE COME QUESTIONS:
NOT STATEMENTS OF WHAT’S IMPORTANT!!
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*C14/C12 ratio independent of time?*
• Both changes in earth’s magnetic field and changes in
magnetic field at the earth due to solar activity change
the magnitude of the cosmic rate intensity, hence
generation rate of C14
• Nuclear bomb testing in ‘50s doubled C14 concentration
in atmosphere
• How much release of C14 from nuclear reactors?
• Fossil fuel burning releases ONLY C12 into the
atmosphere: lowered C14/C12 ratio by ~1% by 1950
• Volcanic release of carbon species might do the same
• Effect of global climate change (e.g., ice age)?
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*C14/C12 ratio everywhere the same?*
• Is mixing between the stratosphere (where C14 is
produced) and the troposhere really fast enough?
• Is mixing equally efficient at all latitudes
• If nutritional cycling of carbon is important mixing
mechanism, polar regions may be poorly mixed
• Mixing of deep with shallow ocean water is NOT all that
fast. (Deep water may be “1500 years old” in C14 time.)
• Surface waters (ponds and streams) containing CaCO3
leached from limestone (in which any original C14 will
have long since decayed) will have anomalously low
C14/C12 ratio
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*****C14/C12 ratio in organism
same as local reservoir?*****
• Chemical fractionation? Chemical (and
biological) reaction rates ARE a little different
for different isotopes. Not important UNLESS
isotope ratio is critical issue
• Do all parts of the organism have the same
C14/C12 ratio? (E.g., trees)
• Which part of the reservoir, the air it breathes
or the water it drinks?
• How long does it take a tree to die?
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**t = T1/2 log2(R0/Rt)= Tm ln(R0/Rt)**
• Do we know R0? See last few slides.
• Have we measured Rt correctly? More
next Wednesday.
• Is the decay really exponential? Yes, to
the best we can measure.
• Does T 1/2 depend on chemical
environment? Not in any significant way.
• Is T 1/2 = 5568 years? (= Libby half-life)
NO! Better is T 1/2 = 5730 years
(= Cambridge half-life)
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Calibration graph
Calibration graph to convert from conventional
radiocarbon age to calibrated calendar date.
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Implications
• NOT that method is invalid
• Ideas point to where care is required
– Care in technique
– Care in interpretation
• Need for knowledge of other disciplines
• YOU HAVE TO KNOW WHAT’S
BEHIND THE KNOBS
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