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Signing up enhances your TCE experience with the ability to save items to your personal reading list, and access the interactive map. For those researchers working in the field of human history, the chronology of events remains a major element of reflection. Archaeologists have access to various techniques for dating archaeological sites or the objects found on those sites. There are two main categories of dating methods in archaeology : indirect or relative dating and absolute dating. Relative dating includes methods that rely on the analysis of comparative data or the context eg, geological, regional, cultural in which the object one wishes to date is found.

Ancient arrow points and other prehistoric stone tools were thought to have been produced by thunderbolts and other natural phenomena. Prehistoric stone arrow points and axes were believed to have fallen from the sky at the moment when thunder stuck. These implements were called thunder-stones, ceraunia, or pierre de foudre. It generally was believed that all living plant and animal species were survivors of the Great Flood and that with careful biblical research, especially on the book of Genesis, it was possible to calculate the age of the earth.

For example, inDr. John Lightfoot, the vice-chancellor of Cambridge University, calculated that the universe was created in BC, on October 23, at am, coincidental with the beginning of the Fall Term.

Later inArchbishop James Ussher refined this estimate and suggested that the earth was actually created on the evening preceding October 23, BC.

Dating Techniques

This is the kind of pedantic to us debate that took place, so that although historical sites were being studied, prehistoric archaeology was being interpreted in light of the Bible. But, in situ materials also required theory for relative sorting, and this was provided by the Danish atomist and geologist Bishop Nicholas Steno They are: the Principle of Superposition: In a sedimentary sequence, the older beds are on the bottom, and the younger beds are on the top; the Principle of Original Horizontality: Sediments tend to be deposited in flat, horizontal layers; and the Principle of Original Lateral Continuity: a flat layer will tend to extend for a considerable distance in all directions.

Through human ingenuity, the last years have been witness to great number of techniques for sorting time applicable to the scientific study of the past.

These various dating techniques fall into one or more of three categories: absolute, relative, and radio-metric. Absolute techniques of varve analyses and dendrochronology are only such when they can be clearly calibrated to a known year; in all other cases, they are relative dating techniques.

Some techniques for example, obsidian hydration, archaeomagnetism require a radiometric technique for calibration; all benefit from their use. Other relative dating techniques require dated historical information astronomical dating. Contrary to popular belief, radiometric dating techniques, whether they are based on the exponential decay of a radioactive element or the ionizing damage effects of radiation, are only relatively absolute as they can only give a statistical approximation of an absolute age.

Radiometric dating techniques that rely on radioactive decay include potassium-argon dating, radiocarbon dating Carbon 14and uranium-thorium dating. Radiometric dating techniques that rely on the buildup of damaging ionization from radioactive decay include thermo luminescence dating, optically stimulated luminescence, electron spin resonance ESRand fission track dating.

Basically, all dating techniques can be seen as clock types. The analyst must know some basic information about each clock: How does the clock tick? How is the clock set? How is the clock read? Regulla, eds. Scientific Dating Methods. Boston: Kluwer Academic Publishers, Lewis, C.

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Fission-Track Dating. Movies and television have presented a romantic vision of archaeology as adventure in far-away and exotic locations.

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A more realistic picture might show researchers digging in smelly mud for hours under the hot sun while battling relentless mosquitoes. This type of archaeological research produces hundreds of small plastic bags containing pottery shards, animal bones, bits of worked stone, and other fragments.

These findings must be classified, which requires more hours of tedious work in a stuffy tent. At its best, archaeology involves a studious examination of the past with the goal of learning important information about the culture and customs of ancient or not so ancient peoples.

Much archaeology in the early twenty-first century investigates the recent past, a sub-branch called "historical archaeology. Archaeology is the study of the material remains of past human cultures. It is distinguished from other forms of inquiry by its method of study, excavation. Most archaeologists call this "digging. That sort of unscientific digging destroys the archaeological information. Archaeological excavation requires the removal of material layer by layer to expose artifacts in place.

The removed material is carefully sifted to find small artifactstiny animal bones, and other remains. Archaeologists even examine the soil in various layers for microscopic material, such as pollen. Excavations, in combination with surveys, may yield maps of a ruin or collections of artifacts.

Time is important to archaeologists.

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There is rarely enough time to complete the work, but of even greater interest is the time that has passed since the artifact was created. An important part of archaeology is the examination of how cultures change over time. It is therefore essential that the archaeologist is able to establish the age of the artifacts or other material remains and arrange them in a chronological sequence.

The archaeologist must be able to distinguish between objects that were made at the same time and objects that were made at different times. When objects that were made at different times are excavated, the archaeologist must be able to arrange them in a sequence from the oldest to the most recent. Before scientific dating techniques such as dendrochronology and radiocarbon dating were introduced to archaeology, the discipline was dominated by extensive discussions of the chronological sequence of events.

Most of those questions have now been settled and archaeologists have moved on to other issues.

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Scientific dating techniques have had a huge impact on archaeology. Archaeologists use many different techniques to determine the age of an object.

Geologists often need to know the age of material that they find. They use absolute dating methods, sometimes called numerical dating, to give rocks an actual date, or date range, in number of years. This is different to relative dating, which only puts geological events in time order. Start studying Anthropology 1: Dating Techniques. Learn vocabulary, terms, and more with flashcards, games, and other study tools. absolute dating methods. Anthropology Dating Techniques. 12 .

Usually, several different techniques are applied to the same object. Relative dating arranges artifacts in a chronological sequence from oldest to most recent without reference to the actual date. For example, by studying the decorations used on pottery, the types of materials used in the pottery, and the types and shapes of pots, it is often possible to arrange them into a sequence without knowing the actual date.

In absolute datingthe age of an object is determined by some chemical or physical process without reference to a chronology. Relative Dating Methods. The most common and widely used relative dating technique is stratigraphy. The principle of superposition borrowed from geology states that higher layers must be deposited on top of lower layers. Thus, higher layers are more recent than lower layers.

This only applies to undisturbed deposits. Rodent burrows, root action, and human activity can mix layers in a process known as bioturbation. However, the archaeologist can detect bioturbation and allow for its effects. Discrete layers of occupation can often be determined.

For example, Hisarlik, which is a hill in Turkeyis thought by some archaeologists to be the site of the ancient city of Troy. However, Hisarlik was occupied by many different cultures at various times both before and after the time of Troy, and each culture built on top of the ruins of the previous culture, often after violent conquest.

Consequently, the layers in this famous archaeological site represent many different cultures. An early excavator of Hisarlik, Heinrich Schleimann, inadvertently dug through the Troy layer into an earlier occupation and mistakenly assigned the gold artifacts he found there to Troy.

Other sites have been continuously occupied by the same culture for a long time and the different layers represent gradual changes. In both cases, stratigraphy will apply. A chronology based on stratigraphy often can be correlated to layers in other nearby sites. For example, a particular type or pattern of pottery may occur in only one layer in an excavation. If the same pottery type is found in another excavation nearby, it is safe to assume that the layers are the same age.

Archaeologists rarely make these determinations on the basis of a single example. Usually, a set of related artifacts is used to determine the age of a layer. Seriation simply means ordering. This technique was developed by the inventor of modern archaeology, Sir William Matthew Flinders Petrie.

Seriation is based on the assumption that cultural characteristics change over time. For example, consider how automobiles have changed in the last 50 years a relatively short time in archaeology. Automobile manufacturers frequently introduce new styles about every year, so archaeologists thousands of years from now will have no difficulty identifying the precise date of a layer if the layer contains automobile parts.

Cultural characteristics tend to show a particular pattern over time. The characteristic is introduced into the culture for example, using a certain type of projectile point for hunting or wearing low-riding jeansbecomes progressively more popular, then gradually wanes in popularity.

The method of seriation uses this distinctive pattern to arrange archaeological materials into a sequence. However, seriation only works when variations in a cultural characteristic are due to rapid and significant change over time. It also works best when a characteristic is widely shared among many different members of a group. Even then, it can only be applied to a small geographic area, because there is also geographic variation in cultural characteristics.

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For example, 50 years ago American automobiles changed every year while the Volkswagen Beetle hardly changed at all from year to year. Cross dating is also based on stratigraphy. It uses the principle that different archaeological sites will show a similar collection of artifacts in layers of the same age. Sir Flinders Petrie used this method to establish the time sequence of artifacts in Egyptian cemeteries by identifying which burials contained Greek pottery vessels.

These same Greek pottery styles could be associated with monuments in Greece whose construction dates were fairly well known. Since absolute dating techniques have become common, the use of cross dating has decreased significantly.

Dating techniques are procedures used by scientists to determine the age of rocks, fossils, or artifacts. Relative dating methods tell only if one sample is older or younger than another; absolute dating methods provide an approximate date in years. The latter have generally been available only since Many absolute dating techniques take. Contrary to popular belief, radiometric dating techniques, whether they are based on the exponential decay of a radioactive element or the ionizing damage effects of radiation, are only relatively absolute as they can only give a statistical approximation of an absolute age. Radiometric dating techniques that rely on radioactive decay include. Relative dating technique using comparison of fossils from different stratagraphic sequences to estimate which layers are older and which are younger; employed in the Early Pleistocene deposits at Olduvai and other African sites. Click again to see term ?? Tap again to see term ?? You just studied 10 terms!

Pollen grains also appear in archaeological layers. They are abundant and they survive very well in archaeological contexts.

Relative and Absolute Dating PP

As climates change over time, the plants that grow in a region change as well. People who examine pollen grains the study of which is known as pollen analysis can usually determine the genusand often the exact species producing a certain pollen type. Archaeologists can then use this information to determine the relative ages of some sites and layers within sites. However, climates do not change rapidly, so this type of analysis is best for archaeological sites dating back to the last ice age.

Absolute Dating Methods. Absolute dating methods produce an actual date, usually accurate to within a few years.

Relative dating

This date is established independent of stratigraphy and chronology. If a date for a certain layer in an excavation can be established using an absolute dating method, other artifacts in the same layer can safely be assigned the same age.

Dendrochronology, also known as tree-ring dating, is the earliest form of absolute dating. This method was first developed by the American astronomer Andrew Ellicott Douglas at the University of Arizona in the early s. Douglas was trying to develop a correlation between climate variations and sunspot activitybut archaeologists quickly recognized its usefulness as a dating tool. The technique was first applied in the American Southwest and later extended to other parts of the world.

Tree-ring dating is relatively simple. Trees add a new layer of cambium the layer right under the bark every year. The thickness of the layer depends on local weather and climate. In years with plenty of rain, the layer will be thick and healthy. Over the lifetime of the tree, these rings accumulate, and the rings form a record of regional variation in climate that may extend back hundreds of years. Since all of the trees in a region experience the same climate variations, they will have similar growth patterns and similar tree ring patterns.

One tree usually does not cover a period sufficiently long to be archaeologically useful. However, patterns of tree ring growth have been built up by "overlapping" ring sequences from different trees so that the tree ring record extends back several thousand years in many parts of the world.

The process starts with examination of the growth ring patterns of samples from living trees. Then older trees are added to the sequence by overlapping the inner rings of a younger sample with the outer rings of an older sample.

Older trees are recovered from old buildings, archaeological sites, peat bogs, and swamps. Eventually, a regional master chronology is constructed.

When dendrochronology can be used, it provides the most accurate dates of any technique. In the American Southwest, the accuracy and precision of dendrochronology has enabled the development of one of the most. Often events can be dated to within a decade.

This precision has allowed archaeologists working in the American Southwest to reconstruct patterns of village growth and subsequent abandonment with a fineness of detail unmatched in most of the world. Radiometric dating methods are more recent than dendrochronology. However, dendrochronology provides an important calibration technique for radiocarbon dating techniques.

All radiometric-dating techniques are based on the well-established principle from physics that large samples of radioactive isotopes decay at precisely known rates. The rate of decay of a radioactive isotope is usually given by its half-life. The decay of any individual nucleus is completely random. The half-life is a measure of the probability that a given atom will decay in a certain time.

The shorter the half-life, the more likely the atom will decay. This probability does not increase with time. If an atom has not decayed, the probability that it will decay in the future remains exactly the same. This means that no matter how many atoms are in a sample, approximately one-half will decay in one half-life. The remaining atoms have exactly the same decay probability, so in another half-life, one half of the remaining atoms will decay.

The amount of time required for one-half of a radioactive sample to decay can be precisely determined. The particular radioisotope used to determine the age of an object depends on the type of object and its age. Radiocarbon is the most common and best known of radiometric dating techniques, but it is also possibly the most misunderstood. It was developed at the University of Chicago in by a group of American scientists led by Willard F.

Radiocarbon dating has had an enormous impact on archaeology. In the last 50 years, radiocarbon dating has provided the basis for a worldwide cultural chronology.

Recognizing the importance of this technique, the Nobel Prize committee awarded the Prize in Chemistry to Libby in The physics behind radiocarbon dating is straightforward. Earth 's atmosphere is constantly bombarded with cosmic rays from outer space. Cosmic-ray neutrons collide with atoms of nitrogen in the upper atmosphere, converting them to atoms of radioactive carbon The carbon atom quickly combines with an oxygen molecule to form carbon dioxide.

This radioactive carbon dioxide spreads throughout Earth's atmosphere, where it is taken up by plants along with normal carbon As long as the plant is alive, the relative amount ratio of carbon to carbon remains constant at about one carbon atom for every one trillion carbon atoms. Some animals eat plants and other animals eat the plant-eaters. As long as they are alive, all living organisms have the same ratio of carbon to carbon as in the atmosphere because the radioactive carbon is continually replenished, either through photosynthesis or through the food animals eat.

However, when the plant or animal dies, the intake of carbon stops and the ratio of carbon to carbon immediately starts to decrease. The half-life of carbon is 5, years. After 5, years, about one-half of the carbon atoms will have decayed. After another 5, years, one-half of the remaining atoms will have decayed. So after 11, years, only one-fourth will remain. After 17, years, one-eighth of the original carbon will remain.

After 22, years, one-sixteenth will remain. Radiocarbon dating has become the standard technique for determining the age of organic remains those remains that contain carbon. There are many factors that must be taken into account when determining the age of an object.

The best objects are bits of charcoal that have been preserved in completely dry environments. The worst candidates are bits of wood that have been saturated with sea water, since sea water contains dissolved atmospheric carbon dioxide that may throw off the results.

Radiocarbon dating can be used for small bits of clothing or other fabric, bits of bone, baskets, or anything that contains organic material. There are well over labs worldwide that do radiocarbon dating. In the early twenty-first century, the dating of objects up to about 10 half-lives, or up to about 50, years old, is possible. However, objects less than years old cannot be reliably dated because of the widespread burning of fossil fuels, which began in the nineteenth century, and the production of carbon from atmospheric testing of nuclear weapons in the s and s.

Another problem with radiocarbon dating is that the production of carbon in the atmosphere has not been constant, due to variation in solar activity. For example, in the s, solar activity dropped a phenomenon called the "Maunder Minimum"so carbon production also decreased during this period. To achieve the highest level of accuracy, carbon dates must be calibrated by comparison to dates obtained from dendrochronology.

Calibration of Radiocarbon Dates. Samples of Bristlecone pine, a tree with a very long life span, have been dated using both dendrochronology and radiocarbon dating. The results do not agree, but the differences are consistent. That is, the radiocarbon dates were always wrong by the same number of years. Consequently, tree-ring chronologies have been used to calibrate radiocarbon dates to around 12, years ago.

When radiocarbon dating was first put into use, it was decided that dates would always be reported as B. That way, dates reported in magazine articles and books do not have to be adjusted as the years pass. So if a lab determines that an object has a radiocarbon age of 1, years inits age will be given as B.

Calibrated dates are given using the actual date, such as c. Potassium-Argon Dating. If an object is too old to be dated by radiocarbon dating, or if it contains no organic material, other methods must be used.

One of these is potassium-argon dating. All naturally occurring rocks contain potassium. Some of the potassium in rocks is the radioactive isotope potassium Potassium gradually decays to the stable isotope argon, which is a gas. When the rock is melted, as in a volcano, any argon gas trapped in the rock escapes. When the rock cools, the argon will begin to build up. So this method can be used to measure the age of any volcanic rock, fromyears up to around 5 billion years old.

This method is not widely used in archaeology, since most archaeological deposits are not associated with volcanic activity. However, Louis and Mary Leakey successfully used the method to determine the ages of fossils in Olduvai Gorge in Tanzania by examining rocks from lava flows above and below the fossils. They were able to establish an absolute chronology for humans and human ancestors extending back two million years.

Absolute dating techniques anthropology

At Laetolli, in Tanzania, volcanic ash containing early hominid footprints was dated by this method at 3. Other Methods. Uranium is present in most rocks. This isotope of uranium spontaneously undergoes fission. The fission fragments have a lot of energy, and they plow through the rock, leaving a track that can be made visible by treating the rock. So by counting fission tracks, the age of the rock can be determined. Like potassium-argon datingthis can only be used to determine the age of the rock, not the age of the artifact itself.

Thermoluminescence is a recently developed technique that uses the property of some crystals to "store" light. Sometimes an electron will be knocked out of its position in a crystal and will "stick" somewhere else in the crystal. These displaced electrons will accumulate over time. If the sample is heated, the electrons will fall back to their normal positions, emitting a small flash of light. By measuring the light emitted, the time that has passed since the artifact was heated can be determined.

This method should prove to be especially useful in determining the age of ceramics, rocks that have been used to build fire rings, and samples of chert and flint that have been deliberately heated to make them easier to flake into a projectile point.

Science continues to develop new methods to determine the age of objects. As our knowledge of past chronologies improves, archaeologists will be better able to understand how cultures change over time, and how different cultures interact with each other. As a result, this knowledge will enable us to achieve a progressively better understanding of our own culture.

Baillie, M. London U. Taylor, R. Radiocarbon Dating : An Archaeological Perspective. Orlando, FL: Academic Press, Long, and R. Wood, Michael. In Search of the Trojan War. New York : New American Library, Richmond, Elliot " Dating Techniques. Richmond, Elliot "Dating Techniques. Dating techniques are procedures used by scientists to determine the age of an object or a series of events. The two main types of dating methods are relative and absolute.

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Relative dating methods are used to determine only if one sample is older or younger than another. Absolute dating methods are used to determine an actual date in years for the age of an object. Before the advent of absolute dating methods in the twentieth century, nearly all dating was relative. The main relative dating method is stratigraphy pronounced stra-TI-gra-feewhich is the study of layers of rocks or the objects embedded within those layers.

This method is based on the assumption which nearly always holds true that deeper layers of rock were deposited earlier in Earth 's history, and thus are older than more shallow layers. The successive layers of rock represent successive intervals of time. Since certain species of animals existed on Earth at specific times in history, the fossils or remains of such animals embedded within those successive layers of rock also help scientists determine the age of the layers.

Similarly, pollen grains released by seed-bearing plants became fossilized in rock layers. If a certain kind of pollen is found in an archaeological site, scientists can check when the plant that produced that pollen lived to determine the relative age of the site. Absolute dating methods are carried out in a laboratory. The most widely used and accepted form of absolute dating is radioactive decay dating. Radioactive decay dating. Radioactive decay refers to the process in which a radioactive form of an element is converted into a nonradioactive product at a regular rate.

The nucleus of every radioactive element such as radium and uranium spontaneously disintegrates over time, transforming itself into the nucleus of an atom of a different element.

In the process of disintegration, the atom gives off radiation energy emitted in the form of waves. Hence the term radioactive decay. Each element decays at its own rate, unaffected by external physical conditions. By measuring the amount of original and transformed atoms in an object, scientists can determine the age of that object.

Cosmic rays: Invisible, high-energy particles that constantly bombard Earth from all directions in space.

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Dendrochronology: Also known as tree-ring dating, the science concerned with determining the age of trees by examining their growth rings. Half-life: Measurement of the time it takes for one-half of a radioactive substance to decay.

Radioactive decay: The predictable manner in which a population of atoms of a radioactive element spontaneously disintegrate over time. The age of the remains of plants, animals, and other organic material can be determined by measuring the amount of carbon contained in that material. Carbon, a radioactive form of the element carbon, is created in the atmosphere by cosmic rays invisible, high-energy particles that constantly bombard Earth from all directions in space. When carbon falls to Earth, it is absorbed by plants.

These plants are eaten by animals who, in turn, are eaten by even larger animals. Eventually, the entire ecosystem community of plants and animals of the planet, including humans, is filled with a concentration of carbon As long as an organism is alive, the supply of carbon is replenished. When the organism dies, the supply stops, and the carbon contained in the organism begins to spontaneously decay into nitrogen The time it takes for one-half of the carbon to decay a period called a half-life is 5, years.

By measuring the amount of carbon remaining, scientists can pinpoint the exact date of the organism's death. The range of conventional radiocarbon dating is 30, to 40, years. With sensitive instrumentation, this range can be extended to 70, years.

In addition to the radiocarbon dating technique, scientists have developed other dating methods based on the transformation of one element into another. These include the uranium-thorium method, the potassium-argon method, and the rubidium-strontium method. Thermoluminescence pronounced ther-moeloo-mi-NES-ence dating is very useful for determining the age of pottery.

The older the pottery, the brighter the light that will be emitted. Using thermoluminescence, pottery pieces as old asyears can be dated with precision.

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Tree-ring dating. Known as dendrochronology pronounced den-dro-crow-NOL-o-geetree-ring dating is based on the fact that trees produce one growth ring each year. Narrow rings grow in cold or dry years, and wide rings grow in warm or wet years. Thus, the growth pattern of a tree of a known age can be used as a standard to determine the age of similar trees. The ages of buildings and archaeological sites can also be determined by examining the ring patterns of the trees used in their construction.

Dendrochronology has a range of 1 to 10, years or more. Depositional rates of sediments have also been employed as a dating method, but only recently has absolute dating been made possible through the use of radioactive isotopes. Of the various methods the last is obviously the most precise, but fossilslithologiesand cross-cutting relationships do enable the geologist to give an approximate relative age in field studies.

Relative dating techniques date specimens in relation to one another; for example, stratigraphy is used to establish the succession of fossils. Absolute or chronometric techniques give an absolute estimate of the age and fall into two main groups.

The first depends on the existence of something that develops at a seasonally varying rate, as in dendrochronology and varve dating. The other uses some measurable change that occurs at a known rate, as in chemical datingradioactive or radiometric dating see carbon dating ; fission-track dating ; potassium-argon dating ; rubidium-strontium dating ; uranium-lead datingand thermoluminescence.

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A relative time scale, constructed in the last century, is based on correlations between palaeontological and stratigraphic data. The rate at which sediments accumulate can also be used for dating see varve. Absolute dating relies on the decay of radioactive isotopes of elements present in the material to be dated see decay constant ; decay curve ; decay series ; isotopic dating; radiocarbon dating ; and radiometric dating.

Dating Techniques gale. Dating Techniques Relative dating Stratigraphy Seriation Faunal dating Pollen dating palynology Absolute dating Amino acid racimization Cation-ratio dating Thermoluminescence dating Tree-ring dating Radioactive decay dating Potassium-argon dating Radiocarbon dating Uranium series dating Fission track dating Resources Dating techniques are procedures used by scientists to determine the age of rocks, fossils, or artifacts.

Relative dating Relative dating methods determine whether one sample is older or younger than another. Stratigraphy Stratigraphy is the study of layers of rocks or the objects embedded within those layers. Seriation Seriation is the ordering of objects according to their age. Faunal dating The term faunal dating refers to the use of animal bones to determine the age of sedimentary layers or objects such as cultural artifacts embedded within those layers.

Pollen dating palynology Each year seed-bearing plants release large numbers of pollen grains. Absolute dating Absolute dating is the term used to describe any dating technique that tells how old a specimen is in years. Amino acid racimization This dating technique was first conducted by Hare and Mitterer inand was popular in the s. Cation-ratio dating Cation-ratio dating is used to date rock surfaces such as stone artifacts and cliff and ground drawings.

Thermoluminescence dating Thermoluminescence dating is useful for determining the age of pottery. Tree-ring dating This absolute dating method is also known as dendrochronology. Radioactive decay dating As previously mentioned, radioactive decay refers to the process in which a radioactive form of an element is converted into a nonradioactive product at a regular rate.

Potassium-argon dating When volcanic rocks are heated to extremely high temperatures, they release any argon gas trapped in them.

Radiocarbon dating Radiocarbon is used to date charcoal, wood, and other biological materials. Fission track dating Some volcanic minerals and glasses, such as obsidian, contain uranium U. Kathryn M. Learn more about citation styles Citation styles Encyclopedia. Dating Methods gale. Dating methods Dating techniques are procedures used by scientists to determine the age of a specimen.

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Dating techniques Dating techniques are procedures used by scientists to determine the age of a specimen. Thermoluminescence dating Thermoluminescence dating is very useful for determining the age of pottery. Uranium series dating Uranium series dating techniques rely on the fact that radioactive uranium and thorium isotopes decay into a series of unstable, radioactive "daughter" isotopes; this process continues until a stable non-radioactive lead isotope is formed.

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