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Radiometric Dating Methods
You may recall from the Chemistry Review there are three kinds of radioactive decay, alpha, beta and gamma decay. For example an atom of U238 (atomic# = 92) emits an alpha particle and becomes an atom of Th234 ( atomic# = 90). The radioactive decay proceeds according to the equation:
N_t = N_o e ^{- γ t}
N_o = number atoms initially present ( at time to)
N_t = number of atom left after time t .
γ = decay constant

The half life of a radioactive nuclide is defined as the time it takes half of the sample to decay.

N_{t[half life]} = 1/2 N_o
1/2N_o = N_o e ^{- γ t_{[half life]}}
e ^{+ γ t_{[half life]}} = 2
γ t_{[half life]} = ln2     or     t_{[half life]} = 0.693/γ

N_t = N_o e ^{- γ t}     or     N_t = N_o e ^{- (0.693 / t_{[half life]}) t}
Radiometric dating uses the decay rates of radio-active nuclides to determine the age rocks or formations. Obviously,it is important to know how much of the radioactive nuclide was present at the time of rock formation or sediment deposition.

C-14 Dating
Carbon occurs in two stable nuclides: C-12 (98.89%) and C-13 (1.1 %) and a very samll amount of beta emitting with a half-life of 5730 years. C-14 is continuously formed in the upper atmosphere from N-14 via electron capture, C-14 appears in all terrestrial living organisms in the same proportions it occurs in the atmosphere. When an organism dies, it stops taking up C14. The C14 already in the organism contineous to decay. The amount of C-14 is a measure for how old the sample is. Corrective factors have to be taken into account when using C14 dating, since the C-14 content of the atmosphere was not constant over the entire period of time for which C-14 dating is used.

Potassium-Argon Dating
Potassium has three nuclides, K-39, K-40, and K-41. Only K-40 is radioactive (half life= 1.26 billion years), it breaks down to Ca-40 (beta emission) or it can form Ar-40 through electron capture. Potassium can easily be incorporated into minerals. At the time a mineral is formed the concentration of Ar-40 is zero since it escapes as a gas. Any argon formed after the mineralization will be trapped in the crystallin matrix and can be used for dating ( K-40/Ar-40 ratios are measured), Problems arise if argon has escaped from the mineral or argon from another source has found its way into the mineral.

Rubidium-Strontium Dating.
Rb-87 decays to Sr-87 with a half-life of 47 billion years. Strontium occurs naturally as a mixture of several nuclides. Dating is more complex than in the above case, but is also based on measuring isotopic ratios of Rb-87:Sr-87.

  Geological History of Earth

Cenozoic Era (65 mya to today): Holocene   Pleistocene   Miocene   Oligocene   Eocene   Paleocene
   Mesozoic Era (245 to 65 mya): Cretaceous   Jurassic   Triassic
   Paleozoic Era (544 to 245 mya): Permian   Carboniferous   Devonian   Silurian   Ordovician   Cambrian
   Precambrian Era (4,500 to 544 mya): Vendian   Archaean

• The first traces of life (fossilized algea) appear nearly 3.5 billion years ago (early Archaean).
  
• Cambrian : major groups of animal appear
• mass extinction in Ordovician, Devonian, Permian
• devonian: early tetrapods
• triassic: dinosaurs
• boundry cretaceous/tertiary mass extinction ( Meteoroid impact, Yukatan )

• early Earth had a reducing atmosphere (anaerobic metabolic pathways
• iron stones of the precambrian document onset of oxygen production
• formation of oxygen : primitive photosystems (use H₂S as electron donor) evolve into more sophisticated photosystems, capable of using water as electron donor
• presence of oxygen changes fundamentally the biosphere
• oxygen is chemically reactive, aerobic metabolism supports rapid growth, larger cell size. Diffussional properties of oxygen limit the development of multicellular organisms.
• Fate of organic matter. Geocycle, Biocycle. For every carbon burried , one oxygen remains in the atmosphere.

• Historical aspects

• Plate Motions: Divergent boundaries , Mid Atlantic Ridge , Iceland , East African rift valley

• Convergence The oceanic Nazca Plate collides and slides under the South American Plate along the Peru / Chile coast, creating an oceanic trench. The South American Plate is being lifted up, creating the Andes. Because of these tectonic activities earthquakes are common. The Marianas Trench ( at it's deepest, 11,000 m) marks where the fast-moving Pacific Plate converges against the slower moving Philippine Plate. Indian plate / Eurasian plate

• Hot spots: Hawaii     hot spot
  Kauai, the northwesternmost Hawaiian island, is about 5.5 million years old and is deeply eroded. Hawaii's big island Hawaii is very young (less than 0.7 m.y.) and has ongoing volcanic activity. The pacific Plate move west-northwest and carries the Island of Hawaii beyond the hotspot . A new island is presently formed by Loihi Seamount, an active submarine volcano

• Plate tectonics through time
  Cambrian
  Devonian
  Permian to present day

Climate
Ice ages occured throughout of the history of Earth. During the Pleistocene Epoch (2 mya to 10000 ya) glaciers advanced and receeded four times across the northern hemisphere. At its maximum, the ice mass covered about three times its current extent (reached heights of 4,000 m) causing ocean levels to drop about 130 m below current levels.
The primary cause of the seasons is the 23.5 degree of the Earth's rotation axis. The cause for ice ages is related to: plate movement, atmospheric composition e.g. CO2, eccentricity of Earth's orbit, Earth axis wobble. The amount of tilt in the Earth's rotation (wobble) affects the amount of sunlight reaching the Earth. The greater the tilt, the stronger the difference in seasons (i.e., more tilt equals sharper differences between summer and winter temperatures). Major glacial events in the Quaternary have coincided with the phases of axial tilt and earth orbit eccentricity.
The last ice age peaked at 18000 ya and we live presently in an interglacial period. Climate changes can be very rapid (little ice age 1450 - 1850)
The global climate plays a critical role in in the survival of species. The distribution of species is sensitive climate changes. Rapid climatic changes can be caused by vulcanism through the release of immense quantities of vulcanic ash, CO2 and SO2. Supervulcanos and meteroitic impact may be responsible for mass extinctions

Fig. 20.4 Earth Temperature History

Sea Level Variations
At present, most fresh water is concentrated in the polar ice caps. Sea level are controlled by glaciation
Fig. 20.3 Earth Sea Level History

History of Life

• The fossil record gives information about lineages (most are now extinct) and reflects the changing biological life
• most species (99%) that have existed on Earth are now extinct
• The fossil record is incomplete and biased
• fossilization is a rare event, it occurs only under certain conditions in certain sedimentary environments. If organisms don't live in such they will not be part of the fossil record
• organisms with skeletons are best preserved, soft organisms are usually not preserved
• the fossil record shows major extinction events (e.g. end of permian). Extinction may be caused by climatic changes, plate motions, volcanism ( Toba ), meteoroid impact. Largest extinction event at the end of permian, Mass extinction at the end of cretaceous caused by meteoroid impact.

• evolutionary radiations (major diversifications) are driven environmental changes (accumulation of O2), appearance of new species (e.g. multicellular organisms), evolutionary changes driven by the predator / prey relationship.

• Major groups of animals appear during the cambrian period. Prior to this period the fossil record shows evidence for bacterial and algal organisms.
  Ancient fossil cyanobacteria (850 million years old) from Bitter Springs (Central Australia) On the left is a colonial chroococcalean form, and on the right is the filamentous Palaeolyngbya.

  Stromatolites ( layered mounds produced by the growth of microbial mats) continue to form today (Shark Bay, western Australia) as layers of calcium carbonate, precipitated over the growing mat of bacterial filaments in response to a depletion of carbon dioxide.
  

• the beginning of Cambrian Period is marked by the appearance of major groups of animals. ( "Cambrian Explosion"). Eventhough these animals are of great variety and appear for the first time in the fossil record, the oldest animal fossils are found in the earlier Vendian strata. Ediacaran fauna Dickinsonia: polyp like or anneloid worm fossil. Rocks of Cambrian age are located in the Great Basin of the western United States, Scandinavia, Siberia and China, among other places. The map shows the location of the present day Burgess shale (western North America) during the Cambrian Period.

  trilobites next to dinosaurs most famous groups of extinct organisms. They went extinct about 245 million years ago. ( drawing )
  Horseshoe crabs evolved in the shallow seas of the Paleozoic Era (540-248 mya), Brachiopods look like clams however they are not closely related to the molluscs. There are about 300 living species of brachiopods. Brachiopods diversifies and became very abundant during the Paleozoic era. However, their numbers were reduced in the mass extinction of the Permian-Triassic period ( 250 million years ago) .

• The first major radiations of the plants is recorded in the fossil record of the devonian. Devonian fossil tree. Another important event in the Devonian is the appearance of tetrapods (an anthracosaur called Seymouria) Coelacanth which also dates back to the Devonian period ( 400 mya) was long thought to be the missing link ( the ancester) to the tetrapod (dentrogram)

• During the Jurassic period transitionary species such as Archaeopteryx appear. It is the ancester to birds
  
• The ancestors of dinosaurs ( archosaurs ) appear during the Permian ) 250 million years ago) and their descendants (such as the dinosaurs) dominated the terrestrial environment from the end of permian throughout the majority of the Mesozoic Era. Dinosaurs became extinct at the end of the Cretaceous.