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ABSOLUTE DATING

 

 

Some Early Attempts to Date the Earth

 

Chronological Analysis of the Scriptures- Literal interpretation of the scriptures led some people to conclude that the Earth was created approximately 6,000 years old.  In fact, Archbishop Usher of Ireland calculated that the Earth was created at 9 AM on October 26, 4004 BC!  The presence of marine fossils in rock layers, sometimes high in the mountains, seemed to provide “evidence” of a Great Deluge.

 

It was believed that prior to the Great Flood, Earth’s surface was flat and its climate was mild.  Mountains, erosion, and variations in climate were considered to be punishment for the sins committed by humanity.

 

Uniformitarianism- The ideas of James Hutton, Charles Lyell, and Charles Darwin required significantly longer amounts of time (millions of years) for uniformity of geological processes and for organic evolution.

 

Buffon's Iron Sphere Experiments- On the basis of iron sphere cooling experiments, Frenchman Georges de Buffon estimated that the Earth would have needed 75,000 years to cool to its present temperature.

 

 

 

In 1749, Frenchman G.L. de Buffon calculated a cooling time for the Earth of 75,000 years based upon experiments with heated steel spheres.

 

The quantitative approach is admirable, but Buffon's assumptions are flawed.  First, the Earth is not made of steel.   Silicate minerals have lower heat conductivity than steels and are better insulators leading to slower cooling rates.  Second, the calculations did not incorporate the heating effects of radioactive decay.

 

We now know that Buffon's estimate is very low, but his work was important because it challenged the young Earth concept.

 

Strata Thickness- In the late 1800’s, a British geologist estimated that 75 million years has lapsed since the beginning of the Cambrian.  This estimate was based upon the maximum known thickness of strata (from Cambrian to present) divided by the average rate of sedimentation in modern environments.

 

Sea-water composition- In 1899, Irish scientist J. Joly used the salinity of ocean water to determine the age of the earth.  He calculated the modern rate of salt delivery to the oceans, and suggested that the present salinity of ocean water would take at least 100 million years to develop.

 

Several of these attempts are flawed in that it is “sketchy” to extrapolate the modern rates of geologic processes far back into Earth's past because geologic rates can vary over time.

 

 

 

Lord Kelvin’s Attempt to Date the Earth

 

In the 1860's, English physicist Lord Kelvin disagreed with Charles Lyell’s proposition that the earth behaves in a uniform, unchanging manner.  Lyell's extreme form of uniformitarianism would have required a perfect balance between heat production and heat loss.  Kelvin argued that this was physically impossible (the concept is akin to a perpetual motion machine).

 

Kelvin knew that the Earth gets hotter with increasing depth (the geothermal gradient), and took this observation as evidence that the Earth is cooling off.  He believed the Earth started off as a molten mass and subsequently transformed to a hot solid mass during cooling.

 

On the basis of cooling rate calculations, Kelvin estimated the Earth's age at 20-30 million years.

 

Kelvin’s age of the earth was displeasing to many geologists, who believed the earth was much older.

 

Today we know that Kelvin's method was flawed in two aspects:

 

1) In 1899 American geologist T.C. Chamberlain challenged Kelvin’s assumption that the earth started as a molten body.  Instead, Chamberlain proposed a model of “cold accretion” for the Earth.  That is, the earth accreted from small, cold chunks of material and then heated up at a later time.

 

2) Kelvin did not recognize the important role of radioactive decay as an internal heat source.

 

 

 

Introduction to Radioactivity

 

In 1896, French physicist Henri Becquerel discovered radioactivity: the spontaneous emission of particles and energy from unstable nuclei of elements.

 

Isotope:  A version of an atom that differs from other atoms of the same element only in the number of neutrons.  Different isotopes of an element have similar chemical properties (undergo similar chemical reactions) but have different physical properties (such as evaporation rates).

 

NOTATION FOR EXPRESSING ISOTOPES

NOTATION 1

NOTATION 2

ATOMIC #

ATOMIC MASS

# PROTONS

# ELECTRONS

# NEUTRONS

Carbon-12

12

   C

6

6

12

6

6

6

 

Carbon-14

 

14

   C

6

6

14

6

6

8

 

Stable Isotope:  An isotope that persists forever because it has a “stable” ratio of protons to neutrons.  For example, carbon-12 is a stable isotope.

 

Radioactive (or unstable) Isotope:  An isotope that decays into another element because it has an “unstable” ratio of protons to neutrons.  For example, carbon-14 is a radioactive isotope.

 

During radioactive decay, the radioactive parent isotope changes to a stable daughter isotope giving off heat in the process.  There are 3 types of radioactive emissions:

Wikipedia Image.

 

Alpha ray: Equivalent to two protons and two neutrons (essentially a helium nucleus, 42He).

Beta ray: A free electron is released when a neutron converts to a proton.

Gamma ray: Consists of a photon (a packet of energy).

 

Some radioactive parent isotopes decay directly to a daughter isotope.  However, some radioactive atoms decay to the daughter atom through a series of intermediate steps (called a decay series).  The 238U decay series is a good example.

 

Radioactive decay is a spontaneous and statistical process.  It is impossible to predict when a particular radioactive parent atom will decay to a daughter atom.

 

However, we can predict what fraction of the parent atoms will decay over a certain amount of time because each radioactive isotope has a constant rate of decay (unaffected by temperature, pressure, or chemical state).

 

The half-life is the amount of time required for one half of the parent to decay to daughter.

 

Initially, there are many radioactive parent atoms so there are more radioactive emissions.  As decay proceeds and there are fewer parent atoms and fewer emissions.  By the 1st half life, 50% of the parent atoms will have decayed to daughter.  By the 2nd half life, another 50% of the remaining parent will have decayed (leaving 25% parent and 75% daughter).

 

 

 

Radioactive Dating of Minerals

 

Absolute age dating is based upon the decay of radioactive (unstable) isotopes.

 

At the blocking temperature, the radioactive parent isotope starts decaying to the stable daughter isotope.

File:Wooden hourglass 3.jpg

Wikipedia Image.

 

Since the decay rate is constant over time, the parent:daughter ratio can be used to calculate the age of the mineral or rock.

 

Dating basically depends upon 3 measurements:

 

1) the amount of unstable parent isotope in the mineral

2) the amount of stable daughter isotope in the mineral

3) the decay constant (l) of the particular radioactive parent isotope.

 

The parent:daughter ratio is the key to age-dating.  In young rocks, the ratio will be _____.  In old rocks, the ratio will be _____.

 

The radiometric age of a rock is given by the equation:

 

t = ln(D/P + 1) · 1/l

 

where D is the number of daughter atoms, P is the number of parent atoms remaining, and l is the decay constant.

 

The relationship between half-life and decay constant is:

 

t1/2 = .693/l.

 

Therefore the radiometric age equation can be rewritten as:

 

 t = ln(D/P +1) · t1/2 / 0.693

 

A final equation can be written in terms of N0, the total amount of parent initially present in the mineral.  Since N0 = P + D, we can write:

P = N0 e-lt

 

Isotope Systems Commonly Used for Age-Dating

Parent

Daughter

Half-Life

87Rb

87Sr

48.8 billion years

238U

206Pb

4.5 billion years

40K

40Ar

1.25 billion years

235U

207Pb

713,000,000 years

14C

14N

5,730 years

 

Example: A mineral is analyzed and found to contain 440,000 atoms of 235U and 760,000 atoms of 207Pb.  Determine the age of the mineral.

 

 

 

Which Isotopic System Should We Use?

 

It depends!  To obtain accurate dates, there must be enough measurable quantities of both parent and daughter atoms in the mineral.

 

For example, isotopes with very long half lives are no good for dating rocks younger than about 100 million years.  This is because, in just 100,000,000 years of time, not enough parent will have decayed for daughter concentrations to be reliably measured.

 

In summary, we use isotope systems with long half-lives to date old rocks, and isotopes with short half-lives to date young rocks.

 

The Potassium-Argon system is susceptible to resetting by metamorphism.  The reheating cause leakage of gaseous 40Ar from rocks, essentially resetting the isotopic clock.  Therefore, the K-Ar system is useful for dating the age of metamorphism.

 

To obtain accurate dates, any pre-existing (background) amount of daughter isotope must be subtracted out.  Otherwise, the rocks age will appear “older” than it really is. 

 

When isotopic ages obtained from different chemical systems are in agreement, they are considered “concordant”.

 

If they do not agree, isotopic ages are considered to be discordant, and a reasonable explanation is needed.  Metamorphism is a likely reason that two isotopic systems may provide discordant ages.

 

 

 

What kind of rocks can be dated?

 

Igneous rocks- Isotopic age dating of igneous rocks can yield the age of crystallization of magmas and lavas.

 

Metamorphic rocks- Since isotopic systems are often “reset” by increases in temperature, isotopic dating of metamorphic rocks allows us to measure the timing of metamorphic events.

 

Sedimentary rocks- Sedimentary rocks are generally not datable using isotopic methods because the grains in sedimentary rocks may come from many different rocks of different ages.  Isotopic age dating would not give the age of the sediment deposition or lithification, but rather the age of the source rocks. 

 

Geologists look at cross cutting relationships first to constrain an age, and then use isotopic ages to get the absolute age.

 

Absolute age dating is very time consuming and expensive so you want to choose your rocks carefully!

 

 

 

What Else Has Radiometric Dating Told Us?

 

It has established the 4.6 billion year age of the Earth, moon, meteorites, and the Solar System.

 

It allows us to assign numerical ages to the geologic time column, and provides a “double-check” on the relative ages determined by fossil correlation.

 

It allows correlation of Precambrian rocks, most of which do not contain any fossils.

 

It provides a way to measure rates of geologic processes, such as cooling rates and erosion rates.

 

 

 

Accuracy of Isotopic Dates

 

The accuracy of isotopic dating is affected by:

 

1) The limits of our abilities to determine decay constants (usually this introduces only a small degree of uncertainty).

2) Uncertainties of the instrumentation (mass spectrometer).

3) The “degree of weathering” of the sample.  Fresher is always better!

 

Overall, a good uncertainty range is ± 0.2 to 2.0%.

 

On ages of 100,000,000 years, this may reflect in an uncertainty of ± 5 million years.

 

 

 

Carbon-14: A Special Type of Age Dating

 

Carbon-14 is produced in the upper atmosphere when high energy cosmic rays interact with oxygen and nitrogen nuclei causing nuclear reactions:

 

147N  + neutron →  146C  + proton

 

The atmospheric 14C is incorporated into carbon dioxide molecules (CO2).  Organisms acquire 14C from the air and water (along with 13C and 12C), and they acquire the environmental ratios of these isotopes.  However, when organisms die, they stop acquiring any carbon and the 14C starts to decay back to 14N via beta decay.  The 14C:14N ratio decreases over time, and this ratio can be used to calculate a material's age.

 

All organic matter (bones, shells, wood, charcoal, cloth, and limestone) contains 14C and can be dated with this technique.

 

Carbon-14 has a relatively short half life of 5,730 years.  It is good for dating young rocks and artifacts.  Beyond 60,000 - 80,000 years, there is too little Carbon-14 left in the sample and this technique cannot be used.

 

 

 

A Final Type of Age Dating: The Fission-Track Method

 

Fission-track dating is a more recent application of the decay of radioisotopes, but this technique does not use the ratio of parent to daughter isotope to obtain an age.

 

Most 238U undergoes alpha decay.  However, a very small proportion of 238U nuclei undergo fission and the nucleus splits to form two smaller but very energetic nuclei that move away from each other.  When this happens in a mineral, the two departing nuclei leave behind a trail of destruction in the crystal lattice.  The trail is called a fission track.

 

The density of fission tracks in a mineral increase with age and can be used to calculate the mineral's age.

 

Fission track dating is ideal for samples from “recent” times back to 100,000,000 years.  Beyond 100,000,000 years, the density of the tracks becomes so great (saturated) that they cannot be counted reliably.

 

Fission tracks can “anneal” or heal with reheating, and so this method is affected by metamorphism.

 

 

 

Important Dates to Remember

 

The oldest dated rocks on Earth (Canada, China, Wyoming) are dated at 3.96 billion years.  Continental crust had at least partially formed by this time!

 

The oldest known mineral grains are detrital (not in situ) zircon grains in Australia that were dated at 4.3-4.4 billion years.

 

The moon rocks have been dated at 3.5 - 4.2 billion years.

 

Meteorites are dated at 4.3 - 4.6 billion years.