Dating calculation

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. Thus we could tell whether the rock was derived from the mantle or crust be determining its initial Sr isotopic ratio as we discussed previously 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.

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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 curve 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 sphene. Discordant dates will not fall on the Concordia curve. Sometimes, however, numerous discordant dates 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 the , and 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 tells when the elements were formed that make up the Earth, but does not really give us the age of the Earth.

It does, 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 best 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. Some 40 Ar could be absorbed onto the sample surface.

This can be corrected for. 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. 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. 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.

Number of years, months, weeks, and days between two dates

Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0. Some examples of isotope systems used to date geologic materials. To see how we actually use this information to date rocks, consider the following: To account for this, we first note that there is an isotope of Sr, 86 Sr, that is: 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 87 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 Concordia curve can be calculated by defining the following: From this point, many attempts were made to align the Republican calendar with the solar year including the addition of an extra month to certain years to supplant the lack of days in a particular year. In 46 BC, the calendar was further reformed by Julius Caesar, introducing an algorithm that removed the dependence of calendars from the observation of the new moon.

In order to accomplish this, Caesar inserted an additional 10 days to the Republican calendar, making the total number of days in a year He also added the intercalation of a leap day every fourth year, all in an attempt to further synchronize the Roman calendar with the solar year. Despite all efforts, the Julian calendar still required further reform, since the calendar drifted with respect to the equinoxes and solstices by approximately 11 minutes per year.

By , this resulted in a difference of 10 days from what was expected. An adjustment was also made to the algorithm of the Julian calendar that changed which century years would be considered leap years. Under the Gregorian calendar, century years not divisible by would not be leap years. These changes reduced the error from 1 day in years, to 1 day in 3, years with respect to the current value of the mean solar year. The adoption of the Gregorian calendar occurred slowly over a period of centuries, and despite many proposals to further reform the calendar, the Gregorian Calendar still prevails as the most commonly used dating system worldwide.