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Lecture #02 Earth History
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The Fine Structure of The
Universe : The Elements
Elements are a basic building block of molecules,
and only 92 natural elements exist (109 total
elements have been identified).
The basic elements (H and He) were created during
the Big Bang, while the heavier elements are
created by stellar processes.
The particular abundance of elements is yet
another observation that can be used to test the
Big-Bang hypothesis (it also passes this test).
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Atoms & Atomic Numbers
The fundamental unit of an element is an atom, which can
be thought of as a nucleus of protons and neutrons,
surrounded by electrons.
The number of protons in the nucleus determines the type
(name) of the element.
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Isotopes
If you add neutrons to a nucleus, you still have the
same element, since the proton number is
unchanged.
To distinguish elements with different numbers of
neutrons, we call them isotopes.
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Radioactive Decay
It turns out that some elements will spontaneously
turn into other elements. This is called radioactivity
and was discovered in 1896 by Henri Becquerel.
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Radioactivity (Ex. 1)
238U
(an isotope of uranium) decays into
206Pb (a lead isotope) and 4He (a helium
isotope):
238U  206Pb + 84He
This happens spontaneously over time.
Note that mass is conserved.
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Radioactivity (Ex. 1, cont.)
The half-life of 238U is about 4.5 billion
years
If we initially have 128 g of pure 238U, after
4.5 billion years we will have 64 g of 206Pb
and 64 g of 238U
How much 238U will there be after 18 billion
years? How much 206Pb?
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Radioactivity (Ex. 2)
Can we invert this process? Can we
work backwards?
Yes. In other words, if we are given
1) The amount of
238U
2) The amount of
206Pb
3) The half-life of the reaction
Then, we can deduce the amount of time
it took to get to this point.
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Radioactivity (Ex. 2, cont.)
First we quantify the problem:
N=Noe-lt
where,
N = the present-day number (mass) of 238U
No = the original number (mass) of 238U
l = the decay constant
t = time
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Radioactivity (Ex. 2, cont.)
Step one is to determine l
After one half-life there is half as many
atoms of 238U as there were originally
In math, N=0.5N0 when t=4.5 billion years,
or:
0.5 = e-l4.5
Thus l is 0.154 (in units of inverse billion
years)
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Radioactivity (Ex. 2, cont.)
Thus,
N=Noe-0.154t
or,
N/No = e-0.154t
or,
ln(N/No) = -0.154 t
or,
t=ln(N/No)/-0.154
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Radioactivity (Ex. 2, cont.)
So, N is the number of 238U we observe in a rock
No is the original number of 238U. We assume
this to be the number of 238U plus the number of
206Pb (since the number of atoms is conserved
over time)
We plug these two observations into the
previous equation and get the age (t) of the
sample.
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Radioactivity (Ex. 2, cont.)
If we have a rock sample that has 8 atoms
of 238U and 120 atoms of 206Pb, how old is
it?
t = ln(8/(128))/-0.154
t = ln(0.0625)/-0.154
t = 18 billion years old
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Radioactivity (Ex. 3)
One of the most common radioactive
elements used for dating is 14C
It decays into nitrogen by releasing an
electron (referred to as a b particle):
14C
 14N + b
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Radioactivity (Ex. 3, cont.)
The half-life for 14C decay is only 30,000 years;
thus it is useful for dating young objects.
What is the decay constant, l, for this reaction?
N=Noe-lt
By definition of half-life, N=0.5No when t=30,000
years, thus
0.5=e-30,000l
or
l=2.3x10-5 (yr-1)
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Radioactivity (Ex. 3, cont.)
So, plugging back in to the original
equation we have:
14C
14C
-(2.3x10-5)t
=
e
today
original
Solving this equation for t (time) we get,
t = -43,280 x ln(14Ctoday/14Coriginal)
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Radioactivity (Ex. 3, cont.)
So, if we find a sample that has 90 14C
atoms and 10 14N atoms, how old is it?
t = -43,280 x ln(90/100)
t = -43,280 x (-0.1054)
t = 4,560 years
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Age of the Earth (simplified)
(1) Assume radioactive decay rates have
been constant throughout time (there is
actually good evidence for this).
(2) For example the half-life of Uranium 238
is about 4.5 billion years.
(3) Measure the ratio of Uranium 238 to its
daughter product Lead (206) in a piece
of rock (or even better a meteorite)
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Age of the Earth (simplified)
Use the observed ratio and the observed
half-life to work backwards and get the
time when there was only Uranium 238.
Assume this time represents the formation
of the rock.
– Why?
– Is this always true?
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Earth Formation
The definition of Earth formation is the
delivery of 99% of the mass
We need this definition because
technically the Earth is still growing
(accreting) by the influx of meteors and
cosmic dust.
It took the Earth a few tens of millions of
years to form.
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Earth Formation
The Earth formed in two basic steps:
– First was the condensation of a large
number of moon-sized bodies from the
dust of the solar nebula. This process
occurred relatively quickly, probably over
the time span of a few hundred thousand
years.
– Second was repeated collisions/impacts of
these moon-sized planetary embryos. This
process was much slower and took tens of
millions of years.
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Earth Formation
One of the these collisions between the
proto-Earth and a planetary embryo
caused a large chunk of the proto-Earth
to fly off from the main body.
This material stayed in orbit around the
Earth however, and accreted into the
moon.
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Earth Formation
One of the these collisions between the
proto-Earth and a planetary embryo
caused a large chunk of the proto-Earth
to fly off from the main body.
This material stayed in orbit around the
Earth however, and accreted into the
moon.
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Earth Formation
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Earth Formation
So:
– Did the Earth’s iron core accrete first from a
series of iron planetary embryos and then the
mantle accrete next from a series of silicate
planetary embryos?
Or:
– Did Earth accrete from planetary embryos
consisting of both iron and silicate and then
segregate into the present-day structure ?
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Earth Formation
The answer is the second case, which is
known as homogeneous accretion
The differentiation of the Earth into a
metallic core surrounded by a silicate
mantle probably occurred over a time
space of 10-30 millions years.
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Earth Formation
The core formed because the Earth was
extremely hot when it was accreting,
especially after big impacts from
planetary embryos.
The heat caused a large portion of the
Earth to become a magma ocean, out of
which the core material (metals) sank
because they were heavier than the
surrounding silicate lava.
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Earth Formation
This process of differentiation between
metals and silicates is common in
planetary bodies from the inner solar
system: Mercury, Venus, Earth, Mars
(probably), Moon (possibly).
We even have samples of meteorites
that show asteroids have differentiated
as well.
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Earth’s Composition
Ninety-eight percent of the continents are composed
of eight elements. Seven elements (iron, silicon,
magnesium, oxygen, sulfur, aluminum, and calcium)
account for 97% of the entire planet.
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Earth Dynamics
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Summary of Earth Formation
Earth has been formed by processes that we can
now observe in other parts of the Universe.
Our home is about 4.55 billions years old, and our
Sun is a typical star, with an expected lifetime of
about 10 billion years.
Our system condensed from a second- or thirdgeneration star, with some elements from at least one
supernova.
Earth is a dynamic planet with a hot, convecting
interior. That convection is the driving force for the
“tectonic” activity we see on the surface.
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