aa&a spring 2002 1. 2 today’s issues review of method –how it works –systematic problems...

AA&A spring 2002

1

AA&A spring 2002

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

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Ideal case

• Measure Rt = C14/C12 for sample:

– C12 from weight of pure carbon compound– C14 from radioactive counting experiment

– Suppose Rt = 0.15 x 10-12

• What is calendar date of death of sample?

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Ideal caseC12

C14

C12 always

C14 always= R0 x C12

C14 now= 0.15 xR0 x C12

T1/2

tnow• 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

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Ideal caseC12

C14

C12 always

C14 always= R0 x C12

C14 now= 0.15 xR0 x C12

T1/2

tnow

• What was time of death?– When C14 = perpetual atmosphere value! (at X)– Time of death, t years before “now”

X

tdeath

t

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Ideal caseC12

C14

C12 always

C14 always= R0 x C12

C14 now= 0.15 xR0 x C12

T1/2

tnow

• What is conventional radiocarbon age?– Conventional age is (t* years BP)

(if 5568 years was taken as T1/2)

X

tdeath

t*

1950

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Real case—C14 variation in timeC12

C14

C12 always

C14 always?= R0 x C12

C14 now= 0.15 xR0 x C12

T1/2

tnow

• t1 is time of death in conventional analysis• t2 is real time of death

t1 t2

X

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Real case–anomalous local C14C12

C14

C12 always

C14 always= R0 x C12

C14 now= 0.15 xR0 x C12

T1/2

tnow

• t1 is time of death in conventional analysis• t2 is real time of death

X

t1 t2

Localitydeficit

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Real case–bread crumbs in sampleC12

C14

C12 always

C14 always= R0 x C12

T1/2

tnow

• t1 is time of death in conventional analysis• t2 is real time of death

X

t1t2

bread

sample

C14 now

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Counting C14 activity

C14 Electron path

photomultiplier

Photons(light)

Samplecell

photomultiplier

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The problem

• Repeated experiments, get answers for 10 minute counts C14 activity:

1620, 1574, 1611, 1595, …

• What do I do?

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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?

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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?

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The best we can doProbabilitythat “real”number is N

• Suppose we count 1600

• Plot probability, count “should have been” N?

• (better curve, page 163 in T & M)

N1520 1600 1680

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The best we can doProbabilitythat “real”number is N

• N = 1600 40 with probability 68%• N = 1600 80 with probability 95%• N = 1600 120 with probability 99.7%

N1520 1600 1680

standard deviation

=sigma=

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Error limits on results

• Nreal = Nmeasured 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 R0 (from time or locality

dependence), … ––> 83 year error in dating

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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

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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

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Quantulus LSC

More information

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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!!

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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)– ––> 104 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!

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*****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

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Counting small samples no good!!

• Our 10 g sample had– 5 x 1023 C12– 5 x 1011 C14– In one hour we count only 104 of these!!!

• Can’t we use the other 5 x 1011 somehow

• How to separate out some of the C14 from the C12 and count them another way?

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Can Mass Spectrometer help?

Ion source

Detector

Magnetic field

Large mass

Small mass

detectorcurrent

position (mass)

Small mass

Large mass

10 11

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Not mine!

• Recall: C14/C12 < 10-12

• Inevitable is overwhelming contamination by:– (C12)H2 and (C13)H molecular fragments

– N14

• Need much fancier machine

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Accelerator Mass Spectrometer

(Better picture, T & M page 197)

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Advantages

• Discrimination against N14 (Murphy’s law fails)

• And (C12)H2, (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

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Quantulus specs

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Beta-analytic sample specs

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*****Commercial printout*****

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NO MORE SLIDES