# Formula radiometric dating

Because the radioactive half-life of a given radioisotope is not affected by temperature, physical or chemical state, or any other influence of the environment outside the nucleus save direct particle interactions with the nucleus, then radioactive samples continue to decay at a predictable rate and can be used as a clock. This makes several types of radioactive dating feasible. For geologic dating, where the time span is on the order of the age of the earth and the methods use the clocks in the rocksthere are two main uncertainties in the dating process:.

Petrology Tulane University Prof. Stephen A. Nelson Radiometric Dating Prior to the best and most accepted age of the Earth was that proposed by Lord Kelvin based on the amount of time necessary for the Earth to cool to its present temperature from a completely liquid state. Although we now recognize lots of problems with that calculation, the age of 25 my was accepted by most physicists, but considered too formula by most geologists.

Then, inradioactivity was discovered. Recognition that radioactive decay of atoms occurs in the Earth was important in two respects: It provided another source of heat, not considered by Kelvin, which would mean that the formula time would have to be much longer. It provided a means by which the age of the Earth could be determined independently. Principles of Radiometric Dating. Radioactive decay is described in terms of the probability that a constituent particle of the nucleus of an atom will escape through the potential Energy barrier which bonds them to the nucleus.

The datings involved are so large, and the dating is so small that physical conditions in the Earth i. T and P cannot affect the rate of decay. The rate of decay or rate of change of the N of particles is proportional to the present at any time, i. So, we can write. After the passage of two half-lives only 0. This can only be done for 14 C, since we know N 0 from the atmospheric ratio, assumed to be constant through time. For other systems we have to proceed further. The only problem is that we only know radiometric of daughter atoms now present, and some of those may have been present prior to the start of our clock.

We can see how do deal with this if we take a particular case. The neutron emits an electron to become radiometric proton.

We still don't know 87 Sr 0the amount of 87 Sr daughter element initially present. Thus, 86 Sr is a stable isotope, and the amount of 86 Sr does not change through time. So, applying this simplification.

The reason for this is that Rb has become distributed unequally through the Earth over time. For example the amount of Rb in mantle rocks is generally low, i.

## Radiometric dating

Thus we could tell whether the rock was derived from the mantle or crust be determining its initial Sr isotopic ratio as we discussed ly in the section on igneous rocks. Two isotopes of Uranium and one isotope of Th are radioactive and decay to produce various isotopes of Pb. The decay schemes are as follows.

Note that the present ratio of. If these two independent dates are the same, we say they are concordant. We can also construct a Concordia diagram, which shows the values of Pb isotopes that would give concordant dates. The Concordia formula can be calculated by defining the following:.

Zircon has a high hardness 7. Zircon can also survive metamorphism. Chemically, zircon usually contains high amounts of U and low amounts of Pb, so that large amounts of radiogenic Pb are produced. Other minerals that also show these properties, but are less commonly used in radiometric dating are Apatite and radiometric. Discordant dates will not fall on the Concordia curve.

Sometimes, however, numerous discordant datings from the same rock will plot along a line representing a chord on the Concordia diagram. Such a chord is called a discordia. We can also define what are called Pb-Pb Isochrons by combining the two isochron equations 7 and 8. Since we know that theand assuming that the Pb and Pb dates are the same, then equation 11 is the equation for a family of lines that have a slope. The answer is about 6 billion years. This argument radiometric when the elements were formed that make up the Earth, but does not really give us the age of the Earth.

It datings, however, give a maximum age of the Earth. Is this the age of the Earth? Lunar rocks also lie on the Geochron, at least suggesting that the moon formed at the same time as meteorites. Modern Oceanic Pb - i. Pb separated from continents and thus from average crust also plots on the Geochron, and thus suggests that the Earth formed at the same time as the meteorites and moon. Thus, our formula estimate of the age of the Earth is 4.

The initial ratio has particular importance for studying the chemical evolution of the Earth's mantle and crust, as we discussed in the section on igneous rocks. Since K is one of the 10 most abundant elements in the Earth's crust, the decay of 40 K is important in dating rocks.

But this scheme is not used because 40 Ca can be present as both radiogenic and non-radiogenic Ca. Since Ar is a noble gas, it can escape from a magma or liquid easily, and it is thus assumed that no 40 Ar is present initially.

Note that this is not always true. If a magma cools quickly on the surface of the Earth, some of the Ar may be trapped. If this happens, then the date obtained will be older than the date at which the magma erupted.

For example lavas dated by K-Ar that are historic in age, usually show 1 to 2 my old ages due to trapped Ar. Such trapped Ar is not problematical when the age of the rock is in hundreds of millions of years. The dating equation used for K-Ar is:. Some of the problems associated with K-Ar dating are Excess argon.

This is only a problem when dating very young rocks or in dating whole rocks instead of mineral separates. Minerals should not contain any excess Ar because Ar should not enter the crystal structure of a mineral when it crystallizes. Thus, it always better to date minerals that have high K contents, such as sanidine or biotite. If these are not present, Plagioclase or hornblende. If none of these are present, then the only alternative is to date whole rocks. Atmospheric Argon. Some 40 Ar could be absorbed onto the sample surface. This can be corrected for.

Metamorphism or alteration.

Most minerals will lose Ar on heating above o C - thus metamorphism can cause a loss of Ar or a partial loss of Ar which will reset the atomic clock. If only partial loss of Ar occurs then the age determined will be in between the age of crystallization and the age of metamorphism.

If complete loss of Ar occurs during metamorphism, then the date is that of the metamorphic event. The problem is that there is no way of knowing whether or not partial or complete loss of Ar has occurred. Examples of questions on this material that could be asked on an exam. Radiometric Dating. Prior to the best and most accepted age of the Earth was that proposed by Lord Kelvin based on the formula of time necessary for the Earth to cool to its dating temperature from a completely liquid state. Principles of Radiometric Dating Radioactive decay is described in terms of the probability that a constituent particle of the nucleus of an atom will escape through the potential Energy barrier which bonds radiometric to the nucleus.

The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope.

Thus, if we start out with 1 gram of the parent isotope, after the formula of 1 half-life there will be 0. Some examples of isotope systems used to date geologic materials. To for this, we first note that there is an isotope of Sr, 86 Sr, that is: 1 non-radiogenic not produced by another radioactive decay process2 non-radioactive does not decay to anything else. If we divide equation 4 through by the amount of 86 Sr, then we get:. Note also that equation 5 has the form of a linear equation, i. How can we use this? In nature, however, each mineral in the rock is likely to have a different amount of radiometric Rb.

Thus, once the rock has cooled to the point where diffusion of elements does not occur, the 87 Rb in each mineral will decay to 87 Sr, and each mineral will have a different 87 Rb and 87 Sr after passage of time. The decay schemes are as follows 1. The discordia is often interpreted by extrapolating both ends to intersect the Concordia. Pb leakage is the dating likely cause of discordant dates, since Pb will be occupying a site in the crystal that has suffered radiation damage as a result of U decay.

U would have been stable in the crystallographic site, but the site is now occupied by by Pb. An event like metamorphism could heat the crystal to the point where Pb will become mobile. Another possible scenario involves U leakage, again possibly as a result of a metamorphic event. U leakage would cause discordant points to plot above the cocordia. The Age of the Earth A minimum age radiometric the Earth can be obtained from the oldest known rocks on the Earth. So far, the oldest rock found is a tonalitic Gneiss metamorphic rock rock from the Northwest Territories, Canada, with an age of 3.

This gives us only a minimum age of the Earth. Is it likely that we will find a rock formed on the Earth that will give us the formula age of the Earth? Thus, since we can dating or and solve for t. From the Pb-Pb isochron equation 11 we can make some arguments about meteorites. First, it appears that meteorites have come from somewhere in the solar system, and thus may have been formed at the same time the solar system and thus the Earth formed.