Misleading results can occur if the index fossils are incorrectly dated. Stratigraphy and biostratigraphy can in general provide only relative dating A was before B , which is often sufficient for studying evolution. This is difficult for some time periods, however, because of the barriers involved in matching rocks of the same age across continents. Family-tree relationships can help to narrow down the date when lineages first appeared.
It is also possible to estimate how long ago two living branches of a family tree diverged by assuming that DNA mutations accumulate at a constant rate. For example, they are not sufficiently precise and reliable for estimating when the groups that feature in the Cambrian explosion first evolved, and estimates produced by different approaches to this method may vary as well.
Together with stratigraphic principles, radiometric dating methods are used in geochronology to establish the geological time scale. The principle of radiocarbon dating is simple: the rates at which various radioactive elements decay are known, and the ratio of the radioactive element to its decay products shows how long the radioactive element has existed in the rock. This rate is represented by the half-life, which is the time it takes for half of a sample to decay.
The half-life of carbon is 5, years, so carbon dating is only relevant for dating fossils less than 60, years old. Radioactive elements are common only in rocks with a volcanic origin, so the only fossil-bearing rocks that can be dated radiometrically are volcanic ash layers. Carbon dating uses the decay of carbon to estimate the age of organic materials, such as wood and leather.
Learning Objectives Summarize the available methods for dating fossils. Key Points Determining the ages of fossils is an important step in mapping out how life evolved across geologic time. The study of stratigraphy enables scientists to determine the age of a fossil if they know the age of layers of rock that surround it.
Biostratigraphy enables scientists to match rocks with particular fossils to other rocks with those fossils to determine age. Scientists use carbon dating when determining the age of fossils that are less than 60, years old, and that are composed of organic materials such as wood or leather. Key Terms half-life : The time required for half of the nuclei in a sample of a specific isotope to undergo radioactive decay.
Determining Fossil Ages Paleontology seeks to map out how life evolved across geologic time. Give Feedback External Websites. Let us know if you have suggestions to improve this article requires login. External Websites.
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Thus, measuring the ratio of D to L in a sample enables one to estimate how long ago the specimen died. This dating method is considered to be accurate for ages up to several hundred thousand years. It is calibrated by C14 dating, and the ages given by the two methods are in close agreement after such calibration.
A chart of the ratio of D to L for samples of various radiocarbon ages shows that even for samples dated to 30, or 40, years, the ratio of D to L is significantly less than one. This is additional evidence that these bones are not millions of years old.
At any rate, it would be interesting to determine the D to L ratio for the proteins found in dinosaur bones. Another interesting fact about amino acid dating is that the transformation of L to D forms seems to occur more and more slowly the older the sample is: This means that the rate of racemization was thousands of times up to 2, times different in the past than it is today. Many fossils have been dated both by racemization and by C14 dating.
The conventional time scale assumes that racemization occurs slower and slower as we go back in time. If we assume that racemization occurs at a constant rate, which is a reasonable assumption, then we get a time scale that is more compressed even than the C14 time scale.
This would imply that any date within 50, years by C14 dating is really at most 18, years, and even any date within a million years by conventional dating is really at most 18, years. This would imply that the dinosaur bones are also at most 18, years old! One response of evolutionary scientists to the relatively young C14 dates is to say that they are due to contamination of the bones by modern carbon, having a higher proportion of C But other times they accept C14 ages in the range of 20, to 40, years as valid.
Also, as mentioned earlier, extraordinary methods were used to eliminate all possible contamination when measuring the C14 in these supposedly ancient bones. In addition, the preservation of soft tissue together with bone has implications for the possible contamination of the dinosaur bones. Based on current tests, it appears that many and perhaps all fossils with organic matter have young carbon 14 dates, and also that a significant number of dinosaur fossils have soft tissue.
Thus many dinosaur bones with soft tissue should be typically found in similar environments as dinosaur bones with young C14 dates. However, it turns out that an environment that can preserve both bones and soft tissue has to be dry. If such dinosaur bones with soft tissue had been wet for a significant length of time, bacteria would have consumed the remaining proteins and there would be no soft tissue left.
This is how nutrients are made available to plants. But Mary Schweitzer has shown that the proteins are still there in the dinosaur bones. Thus these bones must have been dry since their burial. If this is so, then how could they be contaminated? Contamination would have to come through water flowing through the bones. Soft tissue and even bones do not survive long in damp conditions, except under highly unusual conditions such as in peat bogs 12 where soft tissue can survive in highly acidic anaerobic conditions and low temperatures.
However, under such acidic conditions, bone is rapidly dissolved. Because the soft tissues and bones are still intact, they must have been kept very dry since their burial. A considerable amount is known 13 , 14 about the preservation of bones in soil and the need for a basic environment for bones to survive.
Perhaps a highly basic environment would inhibit bacterial growth and permit soft tissue to be preserved. But a basic environment breaks down organic matter and soft tissue: Common corrosives are either strong acids, strong bases, or concentrated solutions of certain weak acids or weak bases. A corrosive substance is one that will destroy and damage other substances with which it comes into contact. It may attack a great variety of materials, including metals and various organic compounds, but people are mostly concerned with its effects on living tissue: it causes chemical burns on contact.
Concentrated or strong bases are caustic on organic matter and react violently with acidic substances. The definition of caustic is: capable of burning, corroding, or destroying living tissue. A strongly alkaline environment would destroy tissue because it is caustic. So if there is some wet environment permitting both bone and soft tissue to be preserved for millions of years, it must be highly unusual. It seems that it could not be highly acidic, highly basic, or neutral.
So such an environment could not explain how fossil remains from all through the fossil record could contain significant amounts of C14, dating to about 40, years or less because most of them would not be in such an unusual environment, if it could even exist. But if the environment were dry, then the bones could not be contaminated. Now, could air bring contamination to these bones? Air would bring moisture, which again would enable the growth of bacteria.
Dry air would contain carbon dioxide, but this is a highly stable molecule and would not transfer carbon to the bone without an input of energy from somewhere. In any event, such contamination would be on the surface and would be omitted by thorough cleaning methods. Now, how much contamination would there have to be if the dinosaur bones were really of infinite C14 age as the scientists claim? Suppose X parts of carbon were original and Y parts were contamination.
This means that nearly one percent of the carbon would have to be contamination. Thus nearly 10 percent of the carbon would have to be contamination! Similarly, to get a measured age of 40, years if the contaminating material had a C14 age of 20, years would mean that nearly 10 percent of the total carbon would have to be contamination!
Surely this would be noticed. This is a large amount and should be detectable by some means. This figure is for contamination from recent organic matter. If the contamination is by older carbon, then the amount would even have to be larger. And in any case, in a dry environment, contamination would be impossible. Recent bones have about one part in 10 12 of C14 in their carbon.
This is not considered as contamination. Then why should one part in 10 12 C14 not be considered contamination but one part in 10 14 is? This cutoff is purely arbitrary. Could contamination of the bones come from bacteria? And, of course, in a dry environment there would be essentially no bacteria. Dry environments preserve organic matter well. Even if dinosaur bones were percent C14 originally in their carbon content, a ridiculous assumption, after a million years there would be very few C14 atoms left, and this much C14 in the beginning might give off too much radiation for the animal to survive.
Also, this would require a lot of radiation entering the earth to generate so much C14, and this radiation alone would drive many species extinct. To get from percent C14 to 10 parts C14 per unit of C12 takes a factor of about This is an absolute upper bound on the ages of these fossils regardless of atmospheric conditions, assuming no contamination. Some people attempt to explain away these young dates by saying that neutrons were generated in the earth and created the C14 in the dinosaur bones.
These neutrons could have been generated by the decay of uranium and thorium in the soil. However, referring to this possibility for C14 found in diamonds, Dr. Paul Giem writes: One can hypothesize that neutrons were once much more plentiful than they are now, and that is why there is so much carbon in our experimental samples.
But the number of neutrons required must be over a million times more than those found today, for at least 6, years Also, it was presented at the Singapore conference 18 , 19 that there were less than 20 parts per million of uranium and thorium in the dinosaur bones, which is not an exceptionally large amount. In addition, the Wikipedia article on C14 dating does not even mention uranium decay as a problem for C14 dating.
Thus the concentration of uranium and thorium in the dinosaur bones is near or in the normal range. If this amount could invalidate C14 dates, then it would be mentioned as a significant factor in C14 dating. Furthermore, historic C14 dates are relatively accurate.
Uranium does not seem to be affecting them. Another possible explanation for the young C14 dates is that some kind of radiation from space is causing them. If the problem is radiation from outer space, then why do some bones date to 20, years, others to 40, years?
Radiation from space would strike everywhere the same. And such radiation might even cause the remaining C14 to decay faster. If uranium is producing neutrons that make C14 from C12, then why are C14 dates of 20, years to 40, years ever accepted?
They are accepted for example for the mastodons. The following quotation is from The date was established by radiocarbon tests, and reinforced by a careful study of pollen found in clay samples recovered by the Maryland Geological Survey. By measuring the ratio of carbon 14 remaining in plant or animal material, scientists can determine approximately when it died—provided it falls within last 40, years.
If radiation from space and uranium were significant factors in C14 dating then they should be used to correct historic C14 dates as well, but they are not. Likewise radiation coming from millions of miles away in space has an uncanny ability to hit dinosaur bones only. It must be then that these bones are really young.
However, this conclusion is not likely to be accepted by the scientific community. There is tremendous inertia in science. Those who propose radical changes risk damage to their careers and ridicule. Evolution needs long ages, so the scientists have to defend long ages or else give up evolution, which they do not want to do or are afraid to do. It is based on the fact that radiocarbon 14 C is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen.
The resulting 14 C combines with atmospheric oxygen to form radioactive carbon dioxide , which is incorporated into plants by photosynthesis ; animals then acquire 14 C by eating the plants. When the animal or plant dies, it stops exchanging carbon with its environment, and thereafter the amount of 14 C it contains begins to decrease as the 14 C undergoes radioactive decay.
Measuring the amount of 14 C in a sample from a dead plant or animal, such as a piece of wood or a fragment of bone, provides information that can be used to calculate when the animal or plant died. The older a sample is, the less 14 C there is to be detected, and because the half-life of 14 C the period of time after which half of a given sample will have decayed is about 5, years, the oldest dates that can be reliably measured by this process date to approximately 50, years ago, although special preparation methods occasionally make accurate analysis of older samples possible.
Research has been ongoing since the s to determine what the proportion of 14 C in the atmosphere has been over the past fifty thousand years. The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age. Other corrections must be made to account for the proportion of 14 C in different types of organisms fractionation , and the varying levels of 14 C throughout the biosphere reservoir effects.
Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the s and s. Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its 14 C to decay below detectable levels, fossil fuels contain almost no 14 C. As a result, beginning in the late 19th century, there was a noticeable drop in the proportion of 14 C as the carbon dioxide generated from burning fossil fuels began to accumulate in the atmosphere.
Conversely, nuclear testing increased the amount of 14 C in the atmosphere, which reached a maximum in about of almost double the amount present in the atmosphere prior to nuclear testing. Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying 14 C atoms in a sample.
More recently, accelerator mass spectrometry has become the method of choice; it counts all the 14 C atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples as small as individual plant seeds , and gives results much more quickly. The development of radiocarbon dating has had a profound impact on archaeology. In addition to permitting more accurate dating within archaeological sites than previous methods, it allows comparison of dates of events across great distances.
Histories of archaeology often refer to its impact as the "radiocarbon revolution". Radiocarbon dating has allowed key transitions in prehistory to be dated, such as the end of the last ice age , and the beginning of the Neolithic and Bronze Age in different regions. In , Martin Kamen and Samuel Ruben of the Radiation Laboratory at Berkeley began experiments to determine if any of the elements common in organic matter had isotopes with half-lives long enough to be of value in biomedical research.
They synthesized 14 C using the laboratory's cyclotron accelerator and soon discovered that the atom's half-life was far longer than had been previously thought. Korff , then employed at the Franklin Institute in Philadelphia , that the interaction of thermal neutrons with 14 N in the upper atmosphere would create 14 C.
In , Libby moved to the University of Chicago , where he began his work on radiocarbon dating. He published a paper in in which he proposed that the carbon in living matter might include 14 C as well as non-radioactive carbon.
By contrast, methane created from petroleum showed no radiocarbon activity because of its age. The results were summarized in a paper in Science in , in which the authors commented that their results implied it would be possible to date materials containing carbon of organic origin. Libby and James Arnold proceeded to test the radiocarbon dating theory by analyzing samples with known ages.
For example, two samples taken from the tombs of two Egyptian kings, Zoser and Sneferu , independently dated to BC plus or minus 75 years, were dated by radiocarbon measurement to an average of BC plus or minus years. These results were published in Science in December In nature, carbon exists as two stable, nonradioactive isotopes : carbon 12 C , and carbon 13 C , and a radioactive isotope, carbon 14 C , also known as "radiocarbon".
The half-life of 14 C the time it takes for half of a given amount of 14 C to decay is about 5, years, so its concentration in the atmosphere might be expected to decrease over thousands of years, but 14 C is constantly being produced in the lower stratosphere and upper troposphere , primarily by galactic cosmic rays , and to a lesser degree by solar cosmic rays. Once produced, the 14 C quickly combines with the oxygen in the atmosphere to form first carbon monoxide CO ,  and ultimately carbon dioxide CO 2.
Carbon dioxide produced in this way diffuses in the atmosphere, is dissolved in the ocean, and is taken up by plants via photosynthesis. Animals eat the plants, and ultimately the radiocarbon is distributed throughout the biosphere. The ratio of 14 C to 12 C is approximately 1. The equation for the radioactive decay of 14 C is: .
During its life, a plant or animal is in equilibrium with its surroundings by exchanging carbon either with the atmosphere or through its diet. It will, therefore, have the same proportion of 14 C as the atmosphere, or in the case of marine animals or plants, with the ocean.
Once it dies, it ceases to acquire 14 C , but the 14 C within its biological material at that time will continue to decay, and so the ratio of 14 C to 12 C in its remains will gradually decrease. Because 14 C decays at a known rate, the proportion of radiocarbon can be used to determine how long it has been since a given sample stopped exchanging carbon — the older the sample, the less 14 C will be left.
The equation governing the decay of a radioactive isotope is: . Measurement of N , the number of 14 C atoms currently in the sample, allows the calculation of t , the age of the sample, using the equation above. The above calculations make several assumptions, such as that the level of 14 C in the atmosphere has remained constant over time. Calculating radiocarbon ages also requires the value of the half-life for 14 C. Radiocarbon ages are still calculated using this half-life, and are known as "Conventional Radiocarbon Age".
Since the calibration curve IntCal also reports past atmospheric 14 C concentration using this conventional age, any conventional ages calibrated against the IntCal curve will produce a correct calibrated age. When a date is quoted, the reader should be aware that if it is an uncalibrated date a term used for dates given in radiocarbon years it may differ substantially from the best estimate of the actual calendar date, both because it uses the wrong value for the half-life of 14 C , and because no correction calibration has been applied for the historical variation of 14 C in the atmosphere over time.
Carbon is distributed throughout the atmosphere, the biosphere, and the oceans; these are referred to collectively as the carbon exchange reservoir,  and each component is also referred to individually as a carbon exchange reservoir.
The different elements of the carbon exchange reservoir vary in how much carbon they store, and in how long it takes for the 14 C generated by cosmic rays to fully mix with them. This affects the ratio of 14 C to 12 C in the different reservoirs, and hence the radiocarbon ages of samples that originated in each reservoir.
There are several other possible sources of error that need to be considered. The errors are of four general types:. To verify the accuracy of the method, several artefacts that were datable by other techniques were tested; the results of the testing were in reasonable agreement with the true ages of the objects. Over time, however, discrepancies began to appear between the known chronology for the oldest Egyptian dynasties and the radiocarbon dates of Egyptian artefacts.
The question was resolved by the study of tree rings :    comparison of overlapping series of tree rings allowed the construction of a continuous sequence of tree-ring data that spanned 8, years. Coal and oil began to be burned in large quantities during the 19th century. Dating an object from the early 20th century hence gives an apparent date older than the true date. For the same reason, 14 C concentrations in the neighbourhood of large cities are lower than the atmospheric average.
This fossil fuel effect also known as the Suess effect, after Hans Suess, who first reported it in would only amount to a reduction of 0. A much larger effect comes from above-ground nuclear testing, which released large numbers of neutrons into the atmosphere, resulting in the creation of 14 C. From about until , when atmospheric nuclear testing was banned, it is estimated that several tonnes of 14 C were created.
The level has since dropped, as this bomb pulse or "bomb carbon" as it is sometimes called percolates into the rest of the reservoir. Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. In photosynthetic pathways 12 C is absorbed slightly more easily than 13 C , which in turn is more easily absorbed than 14 C.
This effect is known as isotopic fractionation. At higher temperatures, CO 2 has poor solubility in water, which means there is less CO 2 available for the photosynthetic reactions. The enrichment of bone 13 C also implies that excreted material is depleted in 13 C relative to the diet. The carbon exchange between atmospheric CO 2 and carbonate at the ocean surface is also subject to fractionation, with 14 C in the atmosphere more likely than 12 C to dissolve in the ocean. This increase in 14 C concentration almost exactly cancels out the decrease caused by the upwelling of water containing old, and hence 14 C depleted, carbon from the deep ocean, so that direct measurements of 14 C radiation are similar to measurements for the rest of the biosphere.
Correcting for isotopic fractionation, as is done for all radiocarbon dates to allow comparison between results from different parts of the biosphere, gives an apparent age of about years for ocean surface water. The marine effect : The CO 2 in the atmosphere transfers to the ocean by dissolving in the surface water as carbonate and bicarbonate ions; at the same time the carbonate ions in the water are returning to the air as CO 2.
The deepest parts of the ocean mix very slowly with the surface waters, and the mixing is uneven. The main mechanism that brings deep water to the surface is upwelling, which is more common in regions closer to the equator. Upwelling is also influenced by factors such as the topography of the local ocean bottom and coastlines, the climate, and wind patterns. Overall, the mixing of deep and surface waters takes far longer than the mixing of atmospheric CO 2 with the surface waters, and as a result water from some deep ocean areas has an apparent radiocarbon age of several thousand years.
Upwelling mixes this "old" water with the surface water, giving the surface water an apparent age of about several hundred years after correcting for fractionation. The northern and southern hemispheres have atmospheric circulation systems that are sufficiently independent of each other that there is a noticeable time lag in mixing between the two. Since the surface ocean is depleted in 14 C because of the marine effect, 14 C is removed from the southern atmosphere more quickly than in the north.
For example, rivers that pass over limestone , which is mostly composed of calcium carbonate , will acquire carbonate ions. Similarly, groundwater can contain carbon derived from the rocks through which it has passed. Volcanic eruptions eject large amounts of carbon into the air.
Dormant volcanoes can also emit aged carbon. Any addition of carbon to a sample of a different age will cause the measured date to be inaccurate. Contamination with modern carbon causes a sample to appear to be younger than it really is: the effect is greater for older samples. Samples for dating need to be converted into a form suitable for measuring the 14 C content; this can mean conversion to gaseous, liquid, or solid form, depending on the measurement technique to be used.
Before this can be done, the sample must be treated to remove any contamination and any unwanted constituents. Particularly for older samples, it may be useful to enrich the amount of 14 C in the sample before testing. This can be done with a thermal diffusion column. Once contamination has been removed, samples must be converted to a form suitable for the measuring technology to be used.
For accelerator mass spectrometry , solid graphite targets are the most common, although gaseous CO 2 can also be used. The quantity of material needed for testing depends on the sample type and the technology being used. There are two types of testing technology: detectors that record radioactivity, known as beta counters, and accelerator mass spectrometers. For beta counters, a sample weighing at least 10 grams 0. For decades after Libby performed the first radiocarbon dating experiments, the only way to measure the 14 C in a sample was to detect the radioactive decay of individual carbon atoms.
Libby's first detector was a Geiger counter of his own design. He converted the carbon in his sample to lamp black soot and coated the inner surface of a cylinder with it. This cylinder was inserted into the counter in such a way that the counting wire was inside the sample cylinder, in order that there should be no material between the sample and the wire. Libby's method was soon superseded by gas proportional counters , which were less affected by bomb carbon the additional 14 C created by nuclear weapons testing.
These counters record bursts of ionization caused by the beta particles emitted by the decaying 14 C atoms; the bursts are proportional to the energy of the particle, so other sources of ionization, such as background radiation, can be identified and ignored. The counters are surrounded by lead or steel shielding, to eliminate background radiation and to reduce the incidence of cosmic rays.
In addition, anticoincidence detectors are used; these record events outside the counter and any event recorded simultaneously both inside and outside the counter is regarded as an extraneous event and ignored. The other common technology used for measuring 14 C activity is liquid scintillation counting, which was invented in , but which had to wait until the early s, when efficient methods of benzene synthesis were developed, to become competitive with gas counting; after liquid counters became the more common technology choice for newly constructed dating laboratories.
The counters work by detecting flashes of light caused by the beta particles emitted by 14 C as they interact with a fluorescing agent added to the benzene. Like gas counters, liquid scintillation counters require shielding and anticoincidence counters. For both the gas proportional counter and liquid scintillation counter, what is measured is the number of beta particles detected in a given time period. Each measuring device is also used to measure the activity of a blank sample — a sample prepared from carbon old enough to have no activity.
This provides a value for the background radiation, which must be subtracted from the measured activity of the sample being dated to get the activity attributable solely to that sample's 14 C. In addition, a sample with a standard activity is measured, to provide a baseline for comparison. The ions are accelerated and passed through a stripper, which removes several electrons so that the ions emerge with a positive charge.
A particle detector then records the number of ions detected in the 14 C stream, but since the volume of 12 C and 13 C , needed for calibration is too great for individual ion detection, counts are determined by measuring the electric current created in a Faraday cup. Any 14 C signal from the machine background blank is likely to be caused either by beams of ions that have not followed the expected path inside the detector or by carbon hydrides such as 12 CH 2 or 13 CH.
A 14 C signal from the process blank measures the amount of contamination introduced during the preparation of the sample. These measurements are used in the subsequent calculation of the age of the sample. The calculations to be performed on the measurements taken depend on the technology used, since beta counters measure the sample's radioactivity whereas AMS determines the ratio of the three different carbon isotopes in the sample.
To determine the age of a sample whose activity has been measured by beta counting, the ratio of its activity to the activity of the standard must be found. To determine this, a blank sample of old, or dead, carbon is measured, and a sample of known activity is measured. The additional samples allow errors such as background radiation and systematic errors in the laboratory setup to be detected and corrected for. The results from AMS testing are in the form of ratios of 12 C , 13 C , and 14 C , which are used to calculate Fm, the "fraction modern".
Both beta counting and AMS results have to be corrected for fractionation. The calculation uses 8,, the mean-life derived from Libby's half-life of 5, years, not 8,, the mean-life derived from the more accurate modern value of 5, years.
Libby's value for the half-life is used to maintain consistency with early radiocarbon testing results; calibration curves include a correction for this, so the accuracy of final reported calendar ages is assured. The reliability of the results can be improved by lengthening the testing time.
Radiocarbon dating is generally limited to dating samples no more than 50, years old, as samples older than that have insufficient 14 C to be measurable. Older dates have been obtained by using special sample preparation techniques, large samples, and very long measurement times. These techniques can allow measurement of dates up to 60, and in some cases up to 75, years before the present.
This was demonstrated in by an experiment run by the British Museum radiocarbon laboratory, in which weekly measurements were taken on the same sample for six months. The measurements included one with a range from about to about years ago, and another with a range from about to about Errors in procedure can also lead to errors in the results. The calculations given above produce dates in radiocarbon years: i. To produce a curve that can be used to relate calendar years to radiocarbon years, a sequence of securely dated samples is needed which can be tested to determine their radiocarbon age.
The study of tree rings led to the first such sequence: individual pieces of wood show characteristic sequences of rings that vary in thickness because of environmental factors such as the amount of rainfall in a given year. These factors affect all trees in an area, so examining tree-ring sequences from old wood allows the identification of overlapping sequences. In this way, an uninterrupted sequence of tree rings can be extended far into the past. The first such published sequence, based on bristlecone pine tree rings, was created by Wesley Ferguson.
Suess said he drew the line showing the wiggles by "cosmic schwung ", by which he meant that the variations were caused by extraterrestrial forces. It was unclear for some time whether the wiggles were real or not, but they are now well-established. A calibration curve is used by taking the radiocarbon date reported by a laboratory and reading across from that date on the vertical axis of the graph. The point where this horizontal line intersects the curve will give the calendar age of the sample on the horizontal axis.
This is the reverse of the way the curve is constructed: a point on the graph is derived from a sample of known age, such as a tree ring; when it is tested, the resulting radiocarbon age gives a data point for the graph. Over the next thirty years many calibration curves were published using a variety of methods and statistical approaches.
The age of fossils can be determined using stratigraphy, biostratigraphy, and radiocarbon dating. Paleontology seeks to map out how life evolved across geologic time. A substantial hurdle is the difficulty of working out fossil ages. There are several different methods for estimating the ages of fossils, including:.
Paleontologists rely on stratigraphy to date fossils. Stratigraphy is the science of understanding the strata, or layers, that form the sedimentary record. Strata are differentiated from each other by their different colors or compositions and are exposed in cliffs, quarries, and river banks. These rocks normally form relatively horizontal, parallel layers, with younger layers forming on top. Because rock sequences are not continuous, but may be broken up by faults or periods of erosion, it is difficult to match up rock beds that are not directly adjacent.
Fossils of species that survived for a relatively short time can be used to match isolated rocks: this technique is called biostratigraphy. For instance, the extinct chordate Eoplacognathus pseudoplanus is thought to have existed during a short range in the Middle Ordovician period.
If rocks of unknown age have traces of E. Such index fossils must be distinctive, globally distributed, and occupy a short time range to be useful. Misleading results can occur if the index fossils are incorrectly dated. Stratigraphy and biostratigraphy can in general provide only relative dating A was before B , which is often sufficient for studying evolution.
This is difficult for some time periods, however, because of the barriers involved in matching rocks of the same age across continents. Family-tree relationships can help to narrow down the date when lineages first appeared. It is also possible to estimate how long ago two living branches of a family tree diverged by assuming that DNA mutations accumulate at a constant rate. For example, they are not sufficiently precise and reliable for estimating when the groups that feature in the Cambrian explosion first evolved, and estimates produced by different approaches to this method may vary as well.
Returning to our example of carbon, knowing that the half-life of 14 C is years, we can use this to find the constant, k. Thus, we can write:. Simplifying this expression by canceling the N 0 on both sides of the equation gives,.
Solving for the unknown, k , we take the natural logarithm of both sides,. Other radioactive isotopes are also used to date fossils. The half-life for 14 C is approximately years, therefore the 14 C isotope is only useful for dating fossils up to about 50, years old.
Fossils older than 50, years may have an undetectable amount of 14 C. For older fossils, an isotope with a longer half-life should be used. For example, the radioactive isotope potassium decays to argon with a half life of 1. Other isotopes commonly used for dating include uranium half-life of 4. Problem 1- Calculate the amount of 14 C remaining in a sample.
Problem 2- Calculate the age of a fossil. Problem 3- Calculate the initial amount of 14 C in a fossil. Problem 4 - Calculate the age of a fossil. Problem 5- Calculate the amount of 14 C remaining after a given time has passed. Next Application: Allometry.
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