1. AA&A spring 2002 1

2. 2 Today’s issues Review of method –How it works –Systematic problems Counting precision and statistical error Limitations of method –Practical counting times –Background Mass spectrometry –How to beat 10 -12 –Background

3. AA&A spring 2002 3 Ideal case Measure R t = C14/C12 for sample: –C12 from weight of pure carbon compound –C14 from radioactive counting experiment –Suppose R t = 0.15 x 10 -12 What is calendar date of death of sample?

4. AA&A spring 2002 4 Ideal case C12 C14 C12 always C14 always = R 0 x C12 C14 now = 0.15 x R 0 x C12 T 1/2 t now Make plots versus time: –C12 remains always the same –C14 in atmosphere remains always the same –Plot C14 decay in sample that goes through 0.15 point “now” –Can read off C14 in sample any earlier time

5. AA&A spring 2002 5 Ideal case C12 C14 C12 always C14 always = R 0 x C12 C14 now = 0.15 x R 0 x C12 T 1/2 t now What was time of death? –When C14 = perpetual atmosphere value! (at X) –Time of death, t years before “now” X t death t

6. AA&A spring 2002 6 Ideal case C12 C14 C12 always C14 always = R 0 x C12 C14 now = 0.15 x R 0 x C12 T 1/2 t now What is conventional radiocarbon age? –Conventional age is (t* years BP) (if 5568 years was taken as T 1/2 ) X t death t* 1950

7. AA&A spring 2002 7 Real case—C14 variation in time C12 C14 C12 always C14 always? = R 0 x C12 C14 now = 0.15 x R 0 x C12 T 1/2 t now t 1 is time of death in conventional analysis t 2 is real time of death t1t1 t2t2 X

8. AA&A spring 2002 8 Real case–anomalous local C14 C12 C14 C12 always C14 always = R 0 x C12 C14 now = 0.15 x R 0 x C12 T 1/2 t now t 1 is time of death in conventional analysis t 2 is real time of death X t1t1 t2t2 Locality deficit

9. AA&A spring 2002 9 Real case–bread crumbs in sample C12 C14 C12 always C14 always = R 0 x C12 T 1/2 t now t 1 is time of death in conventional analysis t 2 is real time of death X t1t1 t2t2 bread sample C14 now

10. AA&A spring 2002 10 Counting C14 activity C14 Electron path photomultiplier Photons (light) Sample cell photomultiplier

11. AA&A spring 2002 11 The problem Repeated experiments, get answers for 10 minute counts C14 activity: 1620, 1574, 1611, 1595, … What do I do?

12. AA&A spring 2002 12 The problem Repeated experiments, get answers for 10 minute counts C14 activity: 1620, 1574, 1611, 1595, … What do I do? –Surely take the average But if do whole thing again, will the average be the same?

13. AA&A spring 2002 13 A serious problem Repeated experiments, get answers for 10 minute counts C14 activity: 1620, 1574, 1611, 1595, … What do I do? –Surely take the average But if do whole thing again, will the average be the same? Of course not! But how far off might it be?

14. AA&A spring 2002 14 The best we can do Probability that “real” number is N Suppose we count 1600 Plot probability, count “should have been” N? (better curve, page 163 in T & M) N 152016001680

15. AA&A spring 2002 15 The best we can do Probability that “real” number is N N = 1600  40 with probability 68% N = 1600  80 with probability 95% N = 1600  120 with probability 99.7% N 152016001680 standard deviation  =  sigma = 

16. AA&A spring 2002 16 Error limits on results N real = N measured  N –With 68% confidence, right count is in  N range –If want 95% confidence, use  N NOTE: Fractional error =  N/N = 1/  N systematic versus random (statistical) error –Polls –C14 dating –1% error limit in counting does NOT imply accuracy to 1% “error” = uncertainty (NOT mistake) 1% error in counting, error in R 0 (from time or locality dependence), … ––> 83 year error in dating

17. AA&A spring 2002 17 How long to count? How to get –1% counting accuracy (at one sigma) or  80 years –On 10 gram sample –Of fresh material (NO decay of the C14) –1% ––> 1/  N = 0.01,  N = 100 or Need 10,000 counts at 150 counts/minute or one hour of counting (no problem) We’ll use this as reference case for comparison

18. AA&A spring 2002 18 Old samples What about 30,000 years? (1/2) 5 = 1/32 –Count rate now is 5 per minute Need to count for 32 hours –Expensive but possible Another problem—background –Shielding from cosmic rays –Anti-coincidence techniques

19. AA&A spring 2002 19 Quantulus LSC More information

20. AA&A spring 2002 20 Older samples What about 60,000 years? (Double the age) –(1/2) 10 = 1/1024 = 10 -3 Count rate now is 6 minutes per count Doubling the age has made problems 30 x worse!! –Need to count for 1,000 hours = 40 days Who can afford it? Background—1 count/minute (Quantulus) (ask for 90,000 years—count for ~3 years?) It’s a losing battle!!

21. AA&A spring 2002 21 Smaller samples You’re asked to date a small wood carving with possible age of 17,000 years –How many grams can you get? 10 mg if lucky –Size (10 -3 ) and age (1/8) –––> 10 4 hours = 400 days –Remember background issue A chip of paint, or a small slice of a single tree ring— maybe 1 mg? Don’t bother!

22. AA&A spring 2002 22 *****Try these***** I get good results from sample A, counting for 1 hour. Sample B is 1/10 the size of A. How long must I count to get the same precision? Sample C is 5730 years older than sample A, but the same size. How long must I count to get the same precision? Sample D is 11,460 years older than A. I want to count for only 1 hour. How much bigger must D be than A to give me that luxury? I wish to improve the precision of the counting experiment with sample A by a factor of 3. How long must I count? 10 hours, 2 hours, 4 times the size, 9 hours

23. AA&A spring 2002 23 Counting small samples no good!! Our 10 g sample had –5 x 10 23 C12 –5 x 10 11 C14 –In one hour we count only 10 4 of these!!! Can’t we use the other 5 x 10 11 somehow How to separate out some of the C14 from the C12 and count them another way?

24. AA&A spring 2002 24 Can Mass Spectrometer help? Ion source Detector Magnetic field Large mass Small mass detector current position (mass) Small mass Large mass 10 11

25. AA&A spring 2002 25 Not mine! Recall: C14/C12 < 10 -12 Inevitable is overwhelming contamination by: –(C12)H 2 and (C13)H molecular fragments –N14 Need much fancier machine

26. AA&A spring 2002 26 Accelerator Mass Spectrometer (Better picture, T & M page 197)

27. AA&A spring 2002 27 Advantages Discrimination against N14 (Murphy’s law fails) And (C12)H 2, (C13)H Cosmic ray background not issue (bread crumbs just as serious) C13/C12 ratio allows to calibrate out problems of isotope fractionation Smaller sample size

28. AA&A spring 2002 28 Quantulus specs

29. AA&A spring 2002 29 Beta-analytic sample specs

30. AA&A spring 2002 30 *****Commercial printout*****Commercial printout

31. AA&A spring 2002 31 NO MORE SLIDES

32. AA&A spring 2002 32 Counting precision