Radiocarbon dating sample problems in analytic geometry

Radiometric Dating and the Geological Time Scale

Unstable nuclei decay. However, some nuclides decay faster than others. For example, radium and polonium, discovered by the Curies, decay faster than. In this section we will explore the use of carbon dating to determine the age of fossil remains. Problem 1- Calculate the amount ofC remaining in a sample. Problems Such a phenomenon is called radioactive decay. . For example , the half life of Polonium is less than 1 microseconds, but the half life of.

All paleontologists recognized unmistakable trends in morphology through time in the succession of fossil organisms. This observation led to attempts to explain the fossil succession by various mechanisms. Perhaps the best known example is Darwin's theory of evolution by natural selection. Note that chronologically, fossil succession was well and independently established long before Darwin's evolutionary theory was proposed in Fossil succession and the geologic time scale are constrained by the observed order of the stratigraphy -- basically geometry -- not by evolutionary theory.

Calibrating the Relative Time Scale For almost the next years, geologists operated using relative dating methods, both using the basic principles of geology and fossil succession biostratigraphy. Various attempts were made as far back as the s to scientifically estimate the age of the Earth, and, later, to use this to calibrate the relative time scale to numeric values refer to "Changing views of the history of the Earth" by Richard Harter and Chris Stassen.

Most of the early attempts were based on rates of deposition, erosion, and other geological processes, which yielded uncertain time estimates, but which clearly indicated Earth history was at least million or more years old. A challenge to this interpretation came in the form of Lord Kelvin's William Thomson's calculations of the heat flow from the Earth, and the implication this had for the age -- rather than hundreds of millions of years, the Earth could be as young as tens of million of years old.

This evaluation was subsequently invalidated by the discovery of radioactivity in the last years of the 19th century, which was an unaccounted for source of heat in Kelvin's original calculations.

With it factored in, the Earth could be vastly older. Estimates of the age of the Earth again returned to the prior methods. The discovery of radioactivity also had another side effect, although it was several more decades before its additional significance to geology became apparent and the techniques became refined.

Because of the chemistry of rocks, it was possible to calculate how much radioactive decay had occurred since an appropriate mineral had formed, and how much time had therefore expired, by looking at the ratio between the original radioactive isotope and its product, if the decay rate was known.

Many geological complications and measurement difficulties existed, but initial attempts at the method clearly demonstrated that the Earth was very old. In fact, the numbers that became available were significantly older than even some geologists were expecting -- rather than hundreds of millions of years, which was the minimum age expected, the Earth's history was clearly at least billions of years long. Radiometric dating provides numerical values for the age of an appropriate rock, usually expressed in millions of years.

Therefore, by dating a series of rocks in a vertical succession of strata previously recognized with basic geologic principles see Stratigraphic principles and relative timeit can provide a numerical calibration for what would otherwise be only an ordering of events -- i.

The integration of relative dating and radiometric dating has resulted in a series of increasingly precise "absolute" i. Given the background above, the information used for a geologic time scale can be related like this: How relative dating of events and radiometric numeric dates are combined to produce a calibrated geological time scale. In this example, the data demonstrates that "fossil B time" was somewhere between and million years ago, and that "fossil A time" is older than million years ago.

Note that because of the position of the dated beds, there is room for improvement in the time constraints on these fossil-bearing intervals e.

A continuous vertical stratigraphic section will provide the order of occurrence of events column 1 of Figure 2. These are summarized in terms of a "relative time scale" column 2 of Figure 2. Geologists can refer to intervals of time as being "pre-first appearance of species A" or "during the existence of species A", or "after volcanic eruption 1" at least six subdivisions are possible in the example in Figure 2.

For this type of "relative dating" to work it must be known that the succession of events is unique or at least that duplicate events are recognized -- e. Unique events can be biological e. Ideally, geologists are looking for events that are unmistakably unique, in a consistent order, and of global extent in order to construct a geological time scale with global significance.

Some of these events do exist. For example, the boundary between the Cretaceous and Tertiary periods is recognized on the basis of the extinction of a large number of organisms globally including ammonites, dinosaurs, and othersthe first appearance of new types of organisms, the presence of geochemical anomalies notably iridiumand unusual types of minerals related to meteorite impact processes impact spherules and shocked quartz.

These types of distinctive events provide confirmation that the Earth's stratigraphy is genuinely successional on a global scale. Even without that knowledge, it is still possible to construct local geologic time scales. Although the idea that unique physical and biotic events are synchronous might sound like an "assumption", it is not.

It can, and has been, tested in innumerable ways since the 19th century, in some cases by physically tracing distinct units laterally for hundreds or thousands of kilometres and looking very carefully to see if the order of events changes. Geologists do sometimes find events that are "diachronous" i. Because any newly-studied locality will have independent fossil, superpositional, or radiometric data that have not yet been incorporated into the global geological time scale, all data types serve as both an independent test of each other on a local scaleand of the global geological time scale itself.

The test is more than just a "right" or "wrong" assessment, because there is a certain level of uncertainty in all age determinations. For example, an inconsistency may indicate that a particular geological boundary occurred 76 million years ago, rather than 75 million years ago, which might be cause for revising the age estimate, but does not make the original estimate flagrantly "wrong".

It depends upon the exact situation, and how much data are present to test hypotheses e. Whatever the situation, the current global geological time scale makes predictions about relationships between relative and absolute age-dating at a local scale, and the input of new data means the global geologic time scale is continually refined and is known with increasing precision. This trend can be seen by looking at the history of proposed geologic time scales described in the first chapter of [Harland et al,p.

The unfortunate part of the natural process of refinement of time scales is the appearance of circularity if people do not look at the source of the data carefully enough.

Radiometric Dating and the Geological Time Scale

Most commonly, this is characterised by oversimplified statements like: When a geologist collects a rock sample for radiometric age dating, or collects a fossil, there are independent constraints on the relative and numerical age of the resulting data. Stratigraphic position is an obvious one, but there are many others. There is no way for a geologist to choose what numerical value a radiometric date will yield, or what position a fossil will be found at in a stratigraphic section.

Every piece of data collected like this is an independent check of what has been previously studied. The data are determined by the rocks, not by preconceived notions about what will be found. Every time a rock is picked up it is a test of the predictions made by the current understanding of the geological time scale. The time scale is refined to reflect the relatively few and progressively smaller inconsistencies that are found. This is not circularity, it is the normal scientific process of refining one's understanding with new data.

It happens in all sciences. If an inconsistent data point is found, geologists ask the question: However, this statistical likelihood is not assumed, it is tested, usually by using other methods e.

BioMath: Carbon Dating

Geologists search for an explanation of the inconsistency, and will not arbitrarily decide that, "because it conflicts, the data must be wrong. The continued revision of the time scale as a result of new data demonstrates that geologists are willing to question it and change it. The geological time scale is far from dogma. If the new data have a large inconsistency by "large" I mean orders of magnitudeit is far more likely to be a problem with the new data, but geologists are not satisfied until a specific geological explanation is found and tested.

An inconsistency often means something geologically interesting is happening, and there is always a tiny possibility that it could be the tip of a revolution in understanding about geological history. Admittedly, this latter possibility is VERY unlikely. There is almost zero chance that the broad understanding of geological history e. The amount of data supporting that interpretation is immense, is derived from many fields and methods not only radiometric datingand a discovery would have to be found that invalidated practically all previous data in order for the interpretation to change greatly.

So far, I know of no valid theory that explains how this could occur, let alone evidence in support of such a theory, although there have been highly fallacious attempts e.

When Radiometric Dating "Just Works" or not A poor example There are many situations where radiometric dating is not possible, or where a dating attempt will be fraught with difficulty. This is the inevitable nature of rocks that have experienced millions of years of history: The real question is what happens when conditions are ideal, versus when they are marginal, because ideal samples should give the most reliable dates.

If there are good reasons to expect problems with a sample, it is hardly surprising if there are! It contains a mixture of minerals from a volcanic eruption and detrital mineral grains eroded from other, older rocks. If the age of this unit were not so crucial to important associated hominid fossils, it probably would not have been dated at all because of the potential problems. After some initial and prolonged troubles over many years, the bed was eventually dated successfully by careful sample preparation that eliminated the detrital minerals.

Lubenow's work is fairly unique in characterising the normal scientific process of refining a difficult date as an arbitrary and inappropriate "game", and documenting the history of the process in some detail, as if such problems were typical. Another example is "John Woodmorappe's" paper on radiometric datingwhich adopts a "compilation" approach, and gives only superficial treatment to the individual dates. Among other problems documented in an FAQ by Steven Schimmrichmany of Woodmorappe's examples neglect the geological complexities that are expected to cause problems for some radiometrically-dated samples.

A good example By contrast, the example presented here is a geologically simple situation -- it consists of several primary i. It demonstrates how consistent radiometric data can be when the rocks are more suitable for dating. In old rocks, there will be less potassium present than was required to form the mineral, because some of it has been transmuted to argon. The decrease in the amount of potassium required to form the original mineral has consistently confirmed the age as determined by the amount of argon formed.

See Carbon 14 Dating in this web site. The nuclide rubidium decays, with a half life of Strontium is a stable element; it does not undergo further radioactive decay.

Do not confuse with the highly radioactive isotope, strontium Strontium occurs naturally as a mixture of several nuclides, including the stable isotope strontium If three different strontium-containing minerals form at the same time in the same magma, each strontium containing mineral will have the same ratios of the different strontium nuclides, since all strontium nuclides behave the same chemically.

Note that this does not mean that the ratios are the same everywhere on earth. It merely means that the ratios are the same in the particular magma from which the test sample was later taken. As strontium forms, its ratio to strontium will increase.

Strontium is a stable element that does not undergo radioactive change. In addition, it is not formed as the result of a radioactive decay process. The amount of strontium in a given mineral sample will not change. Therefore the relative amounts of rubidium and strontium can be determined by expressing their ratios to strontium These curves are illustrated in Fig It turns out to be a straight line with a slope of The corresponding half lives for each plotted point are marked on the line and identified.

It can be readily seen from the plots that when this procedure is followed with different amounts of Rb87 in different minerals, if the plotted half life points are connected, a straight line going through the origin is produced. These lines are called "isochrons".

Radioactive Dating

The steeper the slope of the isochron, the more half lives it represents. When the fraction of rubidium is plotted against the fraction of strontium for a number of different minerals from the same magma an isochron is obtained.

If the points lie on a straight line, this indicates that the data is consistent and probably accurate. An example of this can be found in Strahler, Fig If the strontium isotope was not present in the mineral at the time it was formed from the molten magma, then the geometry of the plotted isochron lines requires that they all intersect the origin, as shown in figure However, if strontium 87 was present in the mineral when it was first formed from molten magma, that amount will be shown by an intercept of the isochron lines on the y-axis, as shown in Fig Thus it is possible to correct for strontium initially present.

The age of the sample can be obtained by choosing the origin at the y intercept. Note that the amounts of rubidium 87 and strontium 87 are given as ratios to an inert isotope, strontium However, in calculating the ratio of Rb87 to Sr87, we can use a simple analytical geometry solution to the plotted data. Again referring to Fig. These molecules are subsequently incorporated into the cells and tissues that make up living things.

Therefore, organisms from a single-celled bacteria to the largest of the dinosaurs leave behind carbon-based remains. Carbon dating is based upon the decay of 14C, a radioactive isotope of carbon with a relatively long half-life years.

While 12C is the most abundant carbon isotope, there is a close to constant ratio of 12C to 14C in the environment, and hence in the molecules, cells, and tissues of living organisms. This constant ratio is maintained until the death of an organism, when 14C stops being replenished. At this point, the overall amount of 14C in the organism begins to decay exponentially. Therefore, by knowing the amount of 14C in fossil remains, you can determine how long ago an organism died by examining the departure of the observed 12C to 14C ratio from the expected ratio for a living organism.

Decay of radioactive isotopes Radioactive isotopes, such as 14C, decay exponentially.