1. science
2. geology

GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Today
Law of Radioactivity
Integration of this differential equation
•  Lecture:
–  Geochronology Using Radioactive Decay
–  Reading: Lowrie 4.1.3 - 4.1.4
–  Recommended: concordia module (only)
from: http://ansatte.uit.no/webgeology/
webgeology_files/english/upb.swf
•  Group Presentations: choice of group and
topic due before end of Lab
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
dP/dt = - λ P
gives:
P = P0 e-λt
where P0 is number of atoms present at time t = 0.
Decay of number of parent nuclides is therefore exponential.
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
Half-Life
Decay
Half-life (t1/2): defined as time required for half of
radionuclides to decay:
P = P0 e-λt =>
•  Imagine batch of 36
parent atoms (grey).
•  These spontaneously
decay to daughter atoms
(in green).
•  Decay rate given as 1/6
per unit of time.
P0/2 = P0 e-λt1/2
=> 1/2 = e-λt1/2
=> ln(1/2) = -λ t1/2
=> ln(1) - ln(2) = -ln(2) = -λ t1/2
=> t1/2 = 0.693/λ
5/14/15
Cal Poly Pomona
5/14/15
Cal Poly Pomona
1
GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Decay curve of parent atom and growth curve of its stable daughter in linear coordinates. Growth of Daughter
As radioactive parent elements decay, each disintegrates into a
daughter nuclide. Mass lost in this process is converted into
energy: radiation.
Growth curve of daughter D = P0(1 - e-λt )
D = P0 - P
where D is number of stable, radiogenic daughter atoms. Then:
Decay curve of parent D = P0 - P0 e-λt = P0(1 - e-λt ) = P (eλt - 1)
P = P0 e-λt
indicates growth of number of daughter atoms as function of
time.
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
Half-Life?
Example Question
A parent isotope’s half-life is 100 million years.
25% of the original parent isotope is still present in the
sample.
What is the age of the sample?
5/14/15
Cal Poly Pomona
5/14/15
Cal Poly Pomona
2
GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Estimating the Age of a Rock
Half Lives
D = P (eλt - 1)
=> t = 1/λ ln (1 + D/P)
Indicates time elapsed (t) as function of number of daughter (D)
and parent (P) atoms present, which can be measured by a
mass spectrometer.
Rocks usually contain trace amounts of several
radioactive elements, each with a different half-life.
If a rock is thought to be about 500 million years old, which parent/
daughter pair listed would likely give the most accurate age of the rock?
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
Assumptions Made
•  All measured daughter atoms are a product of
parent
•  System is closed (no exchange with surrounding
material
⇒ Different dating methods should produce similar
(concordant) ages
⇒ If not (discordant ages), assumptions should be
reviewed
Rubidium-Strontium
87Rb
decays to 87Sr, so D = P (eλt – 1) is:
[87Sr]now = [87Rb]now(eλt-1)
However, strontium also occurs naturally independent of
rubidium, so some may have been present originally:
[87Sr]now = [87Sr]0 + [87Rb]now(eλt-1)
We will use that strontium-86 is not product of radioactive decay:
[86Sr]now = [86Sr]0
5/14/15
Cal Poly Pomona
5/14/15
Cal Poly Pomona
3
GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Rubidium-Strontium
Rubidium-Strontium Isochron
Normalizing the equation gives:
[87Sr/86Sr]
y
now
[87Sr/86Sr]0
=
=
b
+
+
x
a
In magmatic rock [87Sr/86Sr]0
is same for all samples
precipitated from melt
because the isotopes are
chemically identical
However, [87Rb/86Sr] varies
from one sample to another
5/14/15
[87Sr/86Sr]now = [87Sr/86Sr]0 + [87Rb/86Sr]now(eλt-1)
y
=
b
+
x
a
[87Rb/86Sr]now(eλt-1)
So,
when you plot two
current ratios with
respect to each other
for various samples
from one rock, slope
of this line
(isochron) is eλt-1
and thus you can
determine t.
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
[87Sr/86Sr]now = [87Sr/86Sr]0 + [87Rb/86Sr]now(eλt-1)
y
=
b
+
x
a
Determining Age of Rock
[87Sr/86Sr]now = [87Sr/86Sr]0 + [87Rb/86Sr]now(eλt-1)
y
=
b
+
x
a
5/14/15
Cal Poly Pomona
5/14/15
Cal Poly Pomona
4
GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Moon Rock
Dating
Uranium-Lead
Two isotopes of U decay to Pb with different half lives.
Chemical processes will not change ratio of two U isotopes to
each other and will not change ratio of two Pb daughter
isotopes to each other.
[206Pb]now = [238U]now(eλ238t - 1)
[207Pb]now = [235U]now (eλ235t - 1)
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
5/14/15
GSC307
Introduction to Global Geophysics
Uranium-Lead
[206Pb]now = [238U]now(eλ238t - 1)
[207Pb]now = [235U]now (eλ235t - 1)
And their ratio:
[207Pb/206Pb]now = [235U/ 238U]now (eλ235t - 1)/ (eλ238t - 1)
Present day uranium ratio (235U to 238U) is 1/137.88,
independent of age and history of sample => Pb ratio is a
function only of time => t can be estimated from lead ratio of
a single sample (often zircon is used)
5/14/15
Cal Poly Pomona
Cal Poly Pomona
Zircon: Nature’s Best Clock
•  Zircon is a mineral that is:
–  very hard: resistant to
mechanical weathering
–  resistant to chemical
weathering and metamorphism
=> likely to remain closed system
•  concentrates U and excludes
Pb
5/14/15
Cal Poly Pomona
5
GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Concordia
Diagram
•  Concordia diagram: plot of 206Pb/238U vs. 207Pb/235U, both of
these ratios are proportional with time.
=> plot of 238U–206Pb age against 235U–207Pb age
•  ‘concordia’ curve show points where 238U–206Pb age equals
235U–207Pb age: ages are concordant
5/14/15
Cal Poly Pomona
•  Let’s take a 4.0 Ga old zircon as an example. When it first
formed, or “closed”, where would it have plotted?
•  Why does the concordia bend?
5/14/15
GSC307
Introduction to Global Geophysics
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
Concordia
Diagram
•  Rocks experiencing no Pb or U mobility move along the
concordia as they age. Any rock or mineral not on concordia
yields discordant dates.
5/14/15
Concordia
Diagram
Cal Poly Pomona
Open System
Behavior:
Pb Loss
•  Zircon must lose 207Pb and 206Pb in exactly the
proportions they exist in zircon because they are
chemically identical: a zircon will not lose 206Pb in
preference to 207Pb or visa versa.
•  Specific example of a 4.0 Ga zircon that experienced
some Pb loss during metamorphic event at 3.0 Ga.
5/14/15
Cal Poly Pomona
6
GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Where Would These Zircons Plot
at Present?
Pb
Loss
•  If loss was complete: where would zircon have plotted?
•  And if it would have lost half its Pb?
•  All zircons with Pb loss plot on a “cord”: how defined?
5/14/15
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
5/14/15
GSC307
Introduction to Global Geophysics
Discordia
So, different samples of zircon that experience different amounts of
Pb loss during same metamorphic event would plot along straight
line between crystallization age and metamorphic age: discordia.
How many samples are needed to determine these two ages from a discordia?
5/14/15
Cal Poly Pomona
Cal Poly Pomona
U Gain or Loss
•  How would Uranium gain affect the position of
zircons on the concordia diagram?
•  And Uranium loss?
5/14/15
Cal Poly Pomona
7