Radiometric dating
Radiometric dating (often called radioactive dating) is a technique used to date materials, usually based on a comparison between the observed abundance of a naturally occurring radioactive isotope and its decay products, using known decay rates. It is the principal source of information about the absolute age of rocks and other geological features, including the age of the Earth itself, and can be used to date a wide range of natural and man-made materials. Among the best-known techniques are radiocarbon dating, potassium-argon dating and uranium-lead dating. By allowing the establishment of geological timescales, it provides a significant source of information about the ages of fossils and the deduced rates of evolutionary change. Radiometric dating is also used to date archaeological materials, including ancient artifacts.
Different methods of radiometric dating vary in the timescale over which they are accurate and the materials to which they can be applied.

# Fundamentals of radiometric dating
All ordinary matter is made up of combinations of chemical elements, each with its own atomic number, indicating the number of protons in the atomic nucleus.  Additionally, elements may exist in different isotopes, with each isotope of an element differing in the number of neutrons in the nucleus.  A particular isotope of a particular element is called a nuclide. Some nuclides are inherently unstable.  That is, at some point in time, an atom of such a nuclide will spontaneously transform into a different nuclide.  This transformation may be accomplished in a number of different ways, including radioactive decay, either by emission of particles (usually electrons (beta decay), positrons or alpha particles) or by spontaneous fission, and electron capture.
While the moment in time at which a particular nucleus decays is unpredictable, a collection of atoms of a radioactive nuclide decays exponentially at a rate described by a parameter known as the half-life, usually given in units of years when discussing dating techniques.  After one half-life has elapsed, one half of the atoms of the nuclide in question will have decayed into a "daughter" nuclide or decay product.  In many cases, the daughter nuclide itself is radioactive, resulting in a decay chain, eventually ending with the formation of a stable (nonradioactive) daughter nuclide; each step in such a chain is characterized by a distinct half-life.  In these cases, usually the half-life of interest in radiometric dating is the longest one in the chain, which is the rate-limiting factor in the ultimate transformation of the radioactive nuclide into its stable daughter. Isotopic systems that have been exploited for radiometric dating have half-lives ranging only about 10 years (e.g., tritium) to over 100 billion years (e.g., Samarium-147).
In general, the half-life of a nuclide depends solely on its nuclear properties; it is not affected by external factors such as temperature, pressure, chemical environment, or presence of a magnetic or electric field. (For some nuclides which decay by the process of electron capture, such as Beryllium-7, Strontium-85, and Zirconium-89, the decay rate may be slightly affected by local electron density, therefore these isotopes may not be as suitable for radiometric dating.) But in general, the half-life of any nuclide is essentially a constant. Therefore, in any material containing a radioactive nuclide, the proportion of the original nuclide to its decay product(s) changes in a predictable way as the original nuclide decays over time.  This predictability allows the relative abundances of related nuclides to be used as a clock that measures the time from the incorporation of the original nuclide(s) into a material to the present.
The processes that form specific materials are often conveniently selective as to what elements they incorporate during their formation. In the simplest case, the material will incorporate a parent nuclide and reject the daughter nuclide. In this case, the only atoms of the daughter nuclide present in a sample must have been deposited by radioactive decay since the sample formed. When a material incorporates both the parent and daughter nuclides at the time of formation, a correction must be made for the initial proportion of the radioactive substance and its daughter; generally this is done by construction of an isochron, e.g. in Rubidium-strontium dating.
Accurate radiometric dating generally requires that neither the parent nuclide nor the daughter product can enter or leave the material after its formation, that the parent has a long enough half-life that it will still be present in significant amounts at the time of measurement (except as described below under "Dating with shortlived extinct radionuclides"), the half-life of the parent is accurately known, and enough of the daughter product is produced to be accurately measured and distinguished from the initial amount of the daughter present in the material.  The procedures used to isolate and analyze the parent and daughter nuclides must be precise and accurate.

### Blocking temperature
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 blocking temperature or closure 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.

### The age equation
Considering that radioactive parent elements decay to stable daughter elements , the mathematical expression that relates radioactive decay to geologic time, called the age equation, is :
The decay constant (or rate of decay) is the fraction of a number of atoms of a radioactive nuclide that disintegrates in a unit of time. The decay constant is inversely proportional to the radioactive half-life of the parent isotope, which can be obtained from tables such as the one on  this page.

## Limitation of techniques
Although radiometric dating is accurate in principle, the precision is very dependent on the care with which the procedure is performed. The possible confounding effects of initial contamination of parent and daughter isotopes have to be considered, as do the effects of any loss or gain of such isotopes since the sample was created.
Precision is enhanced if measurements are taken on different samples from the same rock body but at different locations. Alternatively, if several different minerals can be dated from the same sample and are assumed to be formed by the same event and were in equilibrium with the reservoir when they formed, they should form an isochron. Finally, correlation between different isotopic dating methods may be required to confirm the age of a sample.
The precision of a dating method depends in part on the half-life of the radioactive isotope involved.  For instance, carbon-14 has a half-life of about 6000 years.  After an organism has been dead for 60,000 years, so little carbon-14 is left in it that accurate dating becomes impossible.  On the other hand, the concentration of carbon-14 falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades.  The isotope used in uranium-thorium dating has a longer half-life, but other factors make it more accurate than radiocarbon dating.

# Modern dating techniques
Radiometric dating can be performed on samples as small as a billionth of a gram using a mass spectrometer. The mass spectrometer was invented in the 1940s and began to be used in radiometric dating in the 1950s. The mass spectrometer 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. 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.
The uranium-lead radiometric dating scheme is one of the oldest available, as well as one of the most highly respected. It has been refined to the point that the error in dates of rocks about three billion years old is no more than two million years.
Uranium-lead dating is often performed on the mineral "zircon" (ZrSiO4), though it can be used on other materials. Zircon incorporates uranium atoms into its crystalline structure as substitutes for zirconium, but strongly rejects lead. It has a very high blocking 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. In situ micro-beam analysis can be achieved via laser ICP-MS or SIMS techniques  .
One of its great advantages is that any sample provides two clocks, one based on uranium-235's decay to lead-207 with a half-life of about 700 million years, and one based on uranium-238's decay to lead-206 with a half-life of about 4.5 billion years, providing a built-in crosscheck that allows accurate determination of the age of the sample even if some of the lead has been lost.
Two other radiometric techniques are used for long-term dating. Potassium-argon dating involves electron capture or positron  decay of potassium-40 to argon-40. Potassium-40 has a half-life of 1.3 billion years, and so this method is applicable to the oldest rocks. Radioactive potassium-40 is common in micas, feldspars, and hornblendes, though the blocking temperature is fairly low in these materials, about 125C (mica) to 450C (hornblende).
Rubidium-strontium dating is based on the beta decay of rubidium-87 to strontium-87, 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. Blocking 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.

# Short-range dating techniques
There are a number of dating techniques that have short ranges and are so used for historical or archaeological studies. One of the best-known is the carbon-14 (C14) radiometric technique.
Carbon-14 is a radioactive isotope of carbon, with a half-life of 5,730 years (very short compared with the above). In other radiometric dating methods, the heavy parent isotopes were synthesized in the explosions of massive stars that scattered materials through the Galaxy, to be formed into planets and other stars. The parent isotopes have been decaying since that time, and so any parent isotope with a short half-life should be extinct by now.
Carbon-14 is an exception. It is continuously created through collisions of neutrons generated by cosmic rays with nitrogen in the upper atmosphere. The carbon-14 ends up as a trace component in atmospheric carbon dioxide (CO2).
An organism acquires carbon from carbon dioxide 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 intake new carbon-14 and the existing isotope decays with a characteristic half-life (5730 years). The proportion of carbon-14 left when the remains of the organism are examined provides an indication of the time lapsed since its death. The carbon-14 dating limit lies around 58,000 to 62,000 years .
The rate of creation of carbon-14 appears to be roughly constant, as cross-checks of carbon-14 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-14 and give inaccurate dates. 
The releases of carbon dioxide into the biosphere as a consequence of industrialization have also depressed the proportion of carbon-14 by a few percent; conversely, the amount of carbon-14 was increased by above-ground nuclear bomb tests that were conducted into the early 1960s.  Also, an increase in the solar wind or the earth's magnetic field above the current value would depress the amount of carbon-14 created in the atmosphere. These effects are corrected for by the calibration of the radiocarbon dating scale. See the article on radiocarbon dating.
Another relatively short-range dating technique is based on the decay of uranium-238 into thorium-230, a substance with a half-life of about 80,000 years. It is accompanied by a sister process, in which uranium-235 decays into protactinium-231, which has a half-life of 34,300 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.
Natural sources of radiation in the environment knock loose electrons in, say, a piece of pottery, and these electrons accumulate in defects in the material's crystal lattice structure.  Heating the object will release the captured electrons, producing a luminescence. When the sample is heated, at a certain temperature it will glow from the emission of electrons released from the defects, and this glow can be used to estimate the age of the sample to a threshold of approximately 15 percent of its true age. The date of a rock is reset when volcanic activity remelts it. The date of a piece of pottery is reset by the heat of the kiln. Typically temperatures greater than 400 degrees Celsius will reset the "clock".  This is termed thermoluminescence.
Finally, fission track dating 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-238 impurities.
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 235U, as opposed to the spontaneous fission of 238U. 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. Because the fission tracks are healed by temperatures over about 200C the technique has limitations as well as benefits. The technique has potential applications for detailing the thermal history of a deposit.
Large amounts of otherwise rare 36Cl were produced by irradiation of seawater during atmospheric detonations of nuclear weapons between 1952 and 1958. The residence time of 36Cl in the atmosphere is about 1 week. Thus, as an event marker of 1950s water in soil and ground water, 36Cl is also useful for dating waters less than 50 years before the present. 36Cl has seen use in other areas of the geological sciences, including dating ice and sediments.

# Dating with shortlived extinct radionuclides
At the beginning of the solar system there were several relatively shortlived radionuclides like 26Al, 60Fe, 53Mn, and 129I present within the solar nebula. These radionuclidespossibly produced by the explosion of a supernovaare extinct today but their decay products can be detected in very old material such as meteorites. Measuring the decay products of extinct radionuclides with a mass spectrometer and using isochronplots it is possible to determine relative ages between different events in the early history of the solar system. Dating methods based on extinct radionuclides can also be calibrated with the U-Pb method to give absolute ages.

# Types of radiometric dating
- argon-argon (Ar-Ar)
- fission track dating
- helium (He-He)
- iodine-xenon (I-Xe)
- lanthanum-barium (La-Ba)
- lead-lead (Pb-Pb)
- lutetium-hafnium (Lu-Hf)
- neon-neon (Ne-Ne)
- optically stimulated luminescence dating
- potassium-argon (K-Ar)
- radiocarbon dating
- rhenium-osmium (Re-Os)
- rubidium-strontium (Rb-Sr)
- samarium-neodymium (Sm-Nd)
- uranium-lead (U-Pb)
- uranium-lead-helium (U-Pb-He)
- uranium-thorium (U-Th)
- uranium-uranium (U-U)