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- 5.7: Calculating Half-Life.
- Radiometric Dating: Methods, Uses & the Significance of Half-Life.
- Radiocarbon dating.
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Radioactive Dating Game inquiry. The precision of a dating method depends in part on the half-life of the radioactive isotope involved. For instance, carbon has a half-life of 5, years. After an organism has been dead for 60, years, so little carbon is left that accurate dating cannot be established. On the other hand, the concentration of carbon falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades.
If a material that selectively rejects the daughter nuclide is heated, any daughter nuclides that have been accumulated over time will be lost through diffusion , setting the isotopic "clock" to zero. The temperature at which this happens is known as the closure temperature or blocking temperature and is specific to a particular material and isotopic system. These temperatures are experimentally determined in the lab by artificially resetting sample minerals using a high-temperature furnace. As the mineral cools, the crystal structure begins to form and diffusion of isotopes is less easy.
At a certain temperature, the crystal structure has formed sufficiently to prevent diffusion of isotopes. This temperature is what is known as closure temperature and represents the temperature below which the mineral is a closed system to isotopes. Thus an igneous or metamorphic rock or melt, which is slowly cooling, does not begin to exhibit measurable radioactive decay until it cools below the closure temperature.
The age that can be calculated by radiometric dating is thus the time at which the rock or mineral cooled to closure temperature. This field is known as thermochronology or thermochronometry. The mathematical expression that relates radioactive decay to geologic time is  . The equation is most conveniently expressed in terms of the measured quantity N t rather than the constant initial value N o.
Principles of Radiometric Dating
The above equation makes use of information on the composition of parent and daughter isotopes at the time the material being tested cooled below its closure temperature. This is well-established for most isotopic systems. Plotting an isochron is used to solve the age equation graphically and calculate the age of the sample and the original composition. Radiometric dating has been carried out since when it was invented by Ernest Rutherford as a method by which one might determine the age of the Earth.
In the century since then the techniques have been greatly improved and expanded. The mass spectrometer was invented in the s and began to be used in radiometric dating in the s. It operates by generating a beam of ionized atoms from the sample under test. The ions then travel through a magnetic field, which diverts them into different sampling sensors, known as " Faraday cups ", depending on their mass and level of ionization.
Radioactive Dating Game
On impact in the cups, the ions set up a very weak current that can be measured to determine the rate of impacts and the relative concentrations of different atoms in the beams. Uranium—lead radiometric dating involves using uranium or uranium to date a substance's absolute age.
This scheme has been refined to the point that the error margin in dates of rocks can be as low as less than two million years in two-and-a-half billion years. Uranium—lead dating is often performed on the mineral zircon ZrSiO 4 , though it can be used on other materials, such as baddeleyite , as well as monazite see: Zircon has a very high closure temperature, is resistant to mechanical weathering and is very chemically inert. Zircon also forms multiple crystal layers during metamorphic events, which each may record an isotopic age of the event.
One of its great advantages is that any sample provides two clocks, one based on uranium's decay to lead with a half-life of about million years, and one based on uranium's decay to lead with a half-life of about 4. This can be seen in the concordia diagram, where the samples plot along an errorchron straight line which intersects the concordia curve at the age of the sample. This involves the alpha decay of Sm to Nd with a half-life of 1. Accuracy levels of within twenty million years in ages of two-and-a-half billion years are achievable.
This involves electron capture or positron decay of potassium to argon Potassium has a half-life of 1. This is based on the beta decay of rubidium to strontium , with a half-life of 50 billion years. This scheme is used to date old igneous and metamorphic rocks , and has also been used to date lunar samples. Closure temperatures are so high that they are not a concern.
Rubidium-strontium dating is not as precise as the uranium-lead method, with errors of 30 to 50 million years for a 3-billion-year-old sample. A relatively short-range dating technique is based on the decay of uranium into thorium, a substance with a half-life of about 80, years. It is accompanied by a sister process, in which uranium decays into protactinium, which has a half-life of 32, years.
While uranium is water-soluble, thorium and protactinium are not, and so they are selectively precipitated into ocean-floor sediments , from which their ratios are measured. The scheme has a range of several hundred thousand years.
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A related method is ionium—thorium dating , which measures the ratio of ionium thorium to thorium in ocean sediment. Radiocarbon dating is also simply called Carbon dating. Carbon is a radioactive isotope of carbon, with a half-life of 5, years,   which is very short compared with the above isotopes and decays into nitrogen. Carbon, though, is continuously created through collisions of neutrons generated by cosmic rays with nitrogen in the upper atmosphere and thus remains at a near-constant level on Earth. The carbon ends up as a trace component in atmospheric carbon dioxide CO 2.
A carbon-based life form acquires carbon during its lifetime. Plants acquire it through photosynthesis , and animals acquire it from consumption of plants and other animals. When an organism dies, it ceases to take in new carbon, and the existing isotope decays with a characteristic half-life years. The proportion of carbon left when the remains of the organism are examined provides an indication of the time elapsed since its death.
This makes carbon an ideal dating method to date the age of bones or the remains of an organism.
The carbon dating limit lies around 58, to 62, years. The rate of creation of carbon appears to be roughly constant, as cross-checks of carbon dating with other dating methods show it gives consistent results. However, local eruptions of volcanoes or other events that give off large amounts of carbon dioxide can reduce local concentrations of carbon and give inaccurate dates. The releases of carbon dioxide into the biosphere as a consequence of industrialization have also depressed the proportion of carbon by a few percent; conversely, the amount of carbon was increased by above-ground nuclear bomb tests that were conducted into the early s.
Also, an increase in the solar wind or the Earth's magnetic field above the current value would depress the amount of carbon created in the atmosphere. This involves inspection of a polished slice of a material to determine the density of "track" markings left in it by the spontaneous fission of uranium impurities.
Carbon 14 Dating - Math Central
The uranium content of the sample has to be known, but that can be determined by placing a plastic film over the polished slice of the material, and bombarding it with slow neutrons. This causes induced fission of U, as opposed to the spontaneous fission of U. The fission tracks produced by this process are recorded in the plastic film. The uranium content of the material can then be calculated from the number of tracks and the neutron flux. This scheme has application over a wide range of geologic dates.
For dates up to a few million years micas , tektites glass fragments from volcanic eruptions , and meteorites are best used. Older materials can be dated using zircon , apatite , titanite , epidote and garnet which have a variable amount of uranium content. The technique has potential applications for detailing the thermal history of a deposit.
The residence time of 36 Cl in the atmosphere is about 1 week. Thus, as an event marker of s water in soil and ground water, 36 Cl is also useful for dating waters less than 50 years before the present. Luminescence dating methods are not radiometric dating methods in that they do not rely on abundances of isotopes to calculate age. Instead, they are a consequence of background radiation on certain minerals.
Over time, ionizing radiation is absorbed by mineral grains in sediments and archaeological materials such as quartz and potassium feldspar. The radiation causes charge to remain within the grains in structurally unstable "electron traps". Exposure to sunlight or heat releases these charges, effectively "bleaching" the sample and resetting the clock to zero. The trapped charge accumulates over time at a rate determined by the amount of background radiation at the location where the sample was buried.
Stimulating these mineral grains using either light optically stimulated luminescence or infrared stimulated luminescence dating or heat thermoluminescence dating causes a luminescence signal to be emitted as the stored unstable electron energy is released, the intensity of which varies depending on the amount of radiation absorbed during burial and specific properties of the mineral.
These methods can be used to date the age of a sediment layer, as layers deposited on top would prevent the grains from being "bleached" and reset by sunlight.