1. AA&A-Spring 20021

2. 2 t years after death NO CO 2 exchange with atmosphere C12 is stable C14 decays Ratio at time t is reduced to R t with R t = C14/C12 at time t = R 0 (1/2) t/T (T = T 1/2 ) = R 0 e -t/T (T = T m ) t = T 1/2 log 2 (R 0 /R t )= T m ln(R 0 /R t ) with T 1/2 = 5568 years or T m = 8033 years

3. AA&A-Spring 20023 How to measure R t = 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) –N C12 = 6 x 10 23 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 N C14 = D x T m (in minutes) = D x (T m x 365 x 24 x 60)

4. AA&A-Spring 20024 Counting C14 activity C14 Electron path photomultiplier Photons (light) Sample cell photomultiplier

5. AA&A-Spring 20025 ****Critical for naïve approach**** Work from: t = T 1/2 log 2 (R 0 /R t )= T m ln(R 0 /R t ) R 0 = 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 T 1/2 is known LET’S BRAINSTORM! HERE COME QUESTIONS: NOT STATEMENTS OF WHAT’S IMPORTANT!!

6. AA&A-Spring 20026 Upper Atmosphere—Source of C-14 Cosmic ray junk neutron N-14 proton C-14 O2O2 CO 2 Nucleus of anything Production rate: 2 atoms/second-cm 2 7.5 kg/yr

7. AA&A-Spring 20027 *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)?

8. AA&A-Spring 20028 Atmospheric/oceanic mixing 2% 98%

9. AA&A-Spring 20029 *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 CaCO 3 leached from limestone (in which any original C14 will have long since decayed) will have anomalously low C14/C12 ratio

10. AA&A-Spring 200210 Steady state C14/C12 ratio generation decay New C14 Lost C14 atmosphere oceans C12 and C14 observed ratio R 0 = C14/C12 = 1.2 x 10 -12 Amount of C14 in reservoir adjusts until generation rate = decay rate: Amount of C12 in reservoir independent of time:

11. AA&A-Spring 200211 Living organisms C12 C14 Living organisms exchange with atmosphere to give ratio R 0 = C14/C12 = 1.2 x 10 -12 in tissues of the organism

12. AA&A-Spring 200212 *****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?

13. AA&A-Spring 200213 t years after death NO CO 2 exchange with atmosphere C12 is stable C14 decays Ratio at time t is reduced to R t with R t = C14/C12 at time t = R 0 (1/2) t/T (T = T 1/2 ) = R 0 e -t/T (T = T m ) t = T 1/2 log 2 (R 0 /R t )= T m ln(R 0 /R t ) with T 1/2 = 5568 years or T m = 8033 years

14. AA&A-Spring 200214 **t = T 1/2 log 2 (R 0 /R t )= T m ln(R 0 /R t )** Do we know R0? See last few slides. Have we measured R t 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)

15. AA&A-Spring 200215 C14 age to calendar age Conversion graph

16. AA&A-Spring 200216 Calibrate for correct T 1/2

17. AA&A-Spring 200217 Calibration graph Calibration graph to convert from conventional radiocarbon age to calibrated calendar date.

18. AA&A-Spring 200218 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

19. AA&A-Spring 200219