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Table of Isotopic Masses and Natural Abudances
Atomic weight element =Mi(abuni)+Mj(abunj) + …
in amu, where 1amu = 1/12 mass 12C
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Four types of radioactive decay1) alpha () decay - 4He nucleus (2p + 2n) ejected2) beta () decay - change of nucleus charge, conserves mass3) gamma () decay - photon emission, no change in A or Z4) spontaneous fission - for Z=92 and above, generates two smaller nuclei
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Spontaneous fission
Fission tracks from 238U fission in old zircon
- heavy nuclides split into two daughtersand neutrons
- U most common (fission-track dating)
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Decay chains
- three heavy elements feed large decay chains, where decay continues through radioactive daughters until a stable isotope is reached
238U --> radioactive daughters --> 206PbAlso 235U (t1/2) = 700 MaAnd 232Th (t1/2) =10 Ga
234Th24d
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Counting Statistics and Error Estimation
Radioactive decay process behaves according to binomial statistics.For large number of decays, binomial statistics approach a perfect Guassian.
Observed # disintegrations
Num
ber
of O
bser
vatio
ns
Ex: 100 students measure 14C disintegrations in 1g of modern coral (A = 13.56 dpm)with perfect geiger counters, for 10 minutes
135.6
Ex
pe
cte
d v
alu
e (
N)
N+
sqrt
(N)
N-s
qrt
(N)
N+
2sq
rt(N
)
N-2
sqrt
(N)
N+
3sq
rt(N
)
N-3
sqrt
(N) 1=68.3%
2=95%3=99%
147.2124.0
Since the students only counted 135.6 disintegrations, they will only achieve a 1 accuracyof ±sqrt(135.6)=±11.6 disintegrations …. Or in relative terms, 11.6d/135.6d = 8.5%
In other words, your 1 relative error (in %) will be equal to (1/(sqrt(total counts)))*100
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Introduction to Mass Spectrometry
Sample introduction
IonizationMinimize collisions, interferences
Separatemasses
Count ionsCollect results
Nier-type mass spec
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Decay systems of interest for geologists
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Various isotopic systems start ticking the clock at different temperatures. Above these temperatures, parent and/or daughter isotopes move freely in and out of the system
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K (radioactive parent) - Ar (daughter)
Example
K
Ar
At T’s above a certain # (say, Tc), all or some Ar atoms are lost from the system considered the “chronometer”.
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K (radioactive parent) - Ar (daughter)
Example
K
Ar
When T is < than Tc, all Ar atoms remain within the system considered the “chronometer”, e.g. a K-spar grain.
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Closure temperature
To a first approximation, there is one temperature below which diffusion is so slow that radiogenic parent or daughter atoms become static.
The corollary is that every age we measure with an isotopic system records the time elapsed since the temperature cooled below that value.
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Stability of nuclei as a function of proton (Z) vs. neutron (N) numbers
A (mass #)= Z+N
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Isotope stability
How many isotopes per element?
The “stability” line is a thick one with some isotopes that are energetically stable and others that tend to “decay” into a different nuclear state.
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The Chart of the NuclidesZ
(at
omic
num
ber)
N (neutron number)
Isotopes of phosphorus
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How many isotopes per element
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Not all of these isotopes are stable as they depart from the idealized stability line.
The isotopes that are not stable will tend to decay into more stable configurations.
Let’s look at the element Rb and its various isotopes.
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Essentially there are only two isotopes that don’t decay away within short time scales, 87Rb and 85Rb. All others are not present in nature. Of these, one is stable (85Rb), and one is radiogenic (87Rb)
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How do we quantify stable or not?
If isotopes decay away within laboratory time scales, that’s a no brainer - they are not stable.
Slower decaying species - need to know their:
A. Decay constant orB. Half life
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Measuring radioactive decay
Half life (t1/2) = the time required for half of the parent atoms to decay, alternatively use:
The decay constant () = ln2/t1/2
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What is geologically useful?Systems that have half lives comparable to or longer than the age of the planet. Fast decaying systems are evidently no good.
E.g. 87Rb’s half life is ten times the age of the earth.
Some super slow decaying systems have yet to be figured out. In the meantime, they count as “stable” isotopes.
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Decay equationLaw of decay- the rate of decay of an unstable parent is proportional to the number of atoms remaining at any time t.
The proportionality constant is lambda — decay constant — units reciprocal of time.
€
dn
dt= −λn-dn
dt= n
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Integrate from 0 to time “t”
€
dn
n= −λ dt
0
t
∫n0
n
∫n0 = atoms present at time 0, λ - decay constant
lnn
n0
= −λ t
n = n0e−λ t
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The # of radiogenic daughter atoms formed (D*) is equal to the # of
parent atoms consumed
€
D* = n0 − n
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General geochronological equation
€
D* = neλ t − n
D* = n(eλ t −1)
D = D0 + n(eλt −1)
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Decay curve of a radionuclide and growth curve of its stable daughter in linear coordinates.
Decay curve of parentteNN −= 0
( )teND λ−−= 10*
Growth curve of daughter
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Isochron Diagram
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0.5126
0.5130
0.5134
0.5138
0.5142
0.5146
0.0 0.2 0.4 0.6 0.8
147Sm/144Nd
143Nd/144Nd
QuickTime™ and a decompressor
are needed to see this picture.
Age = 315±35 Ma
Initial 143Nd/144Nd =0.51273±0.00011
MSWD = 0.0061
data-point error ellipses are 2
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K-Ar and 40Ar-39Ar Dating
Hornblende thin section
Many K-bearing minerals: biotite, muscovite, hornblende,K-feldspar, etc.
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Closed vs. Open System Behavior
The K-Ar age is only accurate if the sample has remained a CLOSED SYSTEM:i.e. there has been no gain or loss of K or Ar through time.
In reality, this is almost never the case, because Ar is a noble gas and is highly mobile.
You will get an inaccurate K-Ar age if:1. Your initial Ar was not zero (the mantle contains appreciable 40Ar that may not
have been completely degassed during rock formation).2. You lose Ar because of low-temperature alteration.3. Your sample is contaminated by atmospheric Ar (which is ~97% 40Ar).
We can address #3 by monitoring 36Ar (~20,000 more abundant in air than in the mantle)
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Step-wise heating and 40Ar-39Ar Dating
vs
Plot (40Ar*/39Ar) vs heating stepsOr
Plot Apparent Age vs. fraction 39Ar released
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Plot (40Ar*/39Ar) vs heating stepsOr
Plot Apparent Age vs. fraction 39Ar released
Step-wise heating and 40Ar-39Ar Dating
“plateau” gives most reliable crystallization age
low-temperature stepsreveal sample has lost 40Ar*
higher T steps give consistent 40Ar*/39Ar ratios
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. . . or measure many grains and use isochron method
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Laser applications in Ar-Ar dating
laser spot
Allows for step-wise heating of different zones within grains
Lee et al., 1991
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U-Pb
• U-Pb is a special system…Why?
• There are two independent isotopic clocks ticking at the same time (actually three but two with U as a parent and Pb as daughter.
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Multiple simultaneous decay sequences
• Decay route t1/2, Ga Decay const., yr-1
• 238U — 206Pb 4.47 1.55125 x 10 -10
• • 235U — 207Pb 0.704 9.8485 x 10 -10
• • 232Th — 208Pb 14.01 0.49475 x 10 -10
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Equations
€
206Pb204Pb
=206Pb204Pb 0
+238U
204Pb(eλ 238t −1)
207Pb204Pb
=207Pb204Pb 0
+235U
204Pb(eλ 235t −1)
but we know :238U235U
= μ = constan t = 137.88
Δ207Pb204Pb
Δ206Pb204Pb
=(eλ 235t −1)
137.88(eλ 238t −1)
Do not need parent/daughter ratios
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When initial Pb is insignificant and lots of U
available…. • Such as in zircon crystals
• Things get even simpler/better:
€
206Pb204Pb
= 00 +238U
204Pb(eλ 238t −1)
207Pb204Pb
= 0 +235U
204Pb(eλ 235t −1)
Two independent systems that should yield the same age
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Concordia diagrams
• Only U-Pb provides that kind of luxury of cross-checking ages
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Zircon — ZrSiO4
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