AA&A spring 2002
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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
AA&A spring 2002
2
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?
AA&A spring 2002
3
Ideal case
C12
C12 always
C14 always
= R0 x C12
C14
T1/2
• Make plots versus time:
–
–
–
–
tnow
C14 now
= 0.15 x
R0 x C12
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
AA&A spring 2002
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Ideal case
C12
C14
C12 always
C14 always
= R0 x C12
X
T1/2
t
tdeath
tnow
C14 now
= 0.15 x
R0 x C12
• What was time of death?
– When C14 = perpetual atmosphere value! (at X)
– Time of death, t years before “now”
AA&A spring 2002
5
Ideal case
C12
C14
C12 always
C14 always
= R0 x C12
X
T1/2
t*
tdeath
1950
tnow
C14 now
= 0.15 x
R0 x C12
• What is conventional radiocarbon age?
– Conventional age is (t* years BP)
(if 5568 years was taken as T1/2)
AA&A spring 2002
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Real case—C14 variation in time
C12
C14
X
t1 t2
C12 always
C14 always?
= R0 x C12
T1/2
tnow
C14 now
= 0.15 x
R0 x C12
• t1 is time of death in conventional analysis
• t2 is real time of death
AA&A spring 2002
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Real case–anomalous local C14
C12
C14
X
Locality
deficit
t1 t2
C12 always
C14 always
= R0 x C12
T1/2
tnow
C14 now
= 0.15 x
R0 x C12
• t1 is time of death in conventional analysis
• t2 is real time of death
AA&A spring 2002
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Real case–bread crumbs in sample
C12
C14
C12 always
C14 always
= R0 x C12
X
T1/2
t2
t1
bread
C14 now
tnow
sample
• t1 is time of death in conventional analysis
• t2 is real time of death
AA&A spring 2002
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Counting C14 activity
C14
Electron
path
Photons
(light)
photomultiplier
AA&A spring 2002
photomultiplier
Sample
cell
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The problem
• Repeated experiments, get answers for 10
minute counts C14 activity:
1620, 1574, 1611, 1595, …
• What do I do?
AA&A spring 2002
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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?
AA&A spring 2002
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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?
AA&A spring 2002
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The best we can do
Probability
that “real”
number is N
1520
1600
1680
N
• Suppose we count 1600
• Plot probability, count “should have been” N?
• (better curve, page 163 in T & M)
AA&A spring 2002
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The best we can do
Probability
that “real”
number is N
1520
standard
deviation
 = sigma
= 
1600
1680
N
• N = 1600  40 with probability 68%
• N = 1600  80 with probability 95%
• N = 1600  120 with probability 99.7%
AA&A spring 2002
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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
AA&A spring 2002
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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
AA&A spring 2002
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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
AA&A spring 2002
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Quantulus LSC
More
information
AA&A spring 2002
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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!!
AA&A spring 2002
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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!
AA&A spring 2002
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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
AA&A spring 2002
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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?
AA&A spring 2002
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Can Mass Spectrometer help?
Detector
Small
mass
Large
mass
Ion source
Magnetic
field
detector
current
Small
mass
10
AA&A spring 2002
Large
mass
11
position (mass)
24
Not mine!
• Recall: C14/C12 < 10-12
• Inevitable is overwhelming contamination by:
– (C12)H2 and (C13)H molecular fragments
– N14
• Need much fancier machine
AA&A spring 2002
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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
AA&A spring 2002
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Quantulus specs
AA&A spring 2002
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Beta-analytic sample specs
AA&A spring 2002
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*****Commercial printout*****
AA&A spring 2002
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NO MORE SLIDES
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