For other systems we have to proceed further. The only problem is that we only know the number 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 a proton.

## 5.7: Calculating Half-Life

We still don't know 87 Sr 0 , the 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. 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.

## Radiometric Dating

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.

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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.

### How do we determine the age of a rock?

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.

co.organiccrap.com/92092.php 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. Login here for access. Log in or sign up to add this lesson to a Custom Course. Login or Sign up. Gillaspy has taught health science at University of Phoenix and Ashford University and has a degree from Palmer College of Chiropractic.

The aging process in human beings is easy to see. As we age, our hair turns gray, our skin wrinkles and our gait slows. However, rocks and other objects in nature do not give off such obvious clues about how long they have been around. So, we rely on radiometric dating to calculate their ages. Radiometric dating, or radioactive dating as it is sometimes called, is a method used to date rocks and other objects based on the known decay rate of radioactive isotopes.

Different methods of radiometric dating can be used to estimate the age of a variety of natural and even man-made materials. The methods work because radioactive elements are unstable, and they are always trying to move to a more stable state. So, they do this by giving off radiation. This process by which an unstable atomic nucleus loses energy by releasing radiation is called radioactive decay. The thing that makes this decay process so valuable for determining the age of an object is that each radioactive isotope decays at its own fixed rate, which is expressed in terms of its half-life.

So, if you know the radioactive isotope found in a substance and the isotope's half-life, you can calculate the age of the substance. So, what exactly is this thing called a half-life? Well, a simple explanation is that it is the time required for a quantity to fall to half of its starting value.

So, you might say that the 'full-life' of a radioactive isotope ends when it has given off all of its radiation and reaches a point of being non-radioactive. When the isotope is halfway to that point, it has reached its half-life. There are different methods of radiometric dating that will vary due to the type of material that is being dated.

For example, uranium-lead dating can be used to find the age of a uranium-containing mineral. It works because we know the fixed radioactive decay rates of uranium, which decays to lead, and for uranium, which decays to lead So, we start out with two isotopes of uranium that are unstable and radioactive. They release radiation until they eventually become stable isotopes of lead. These two uranium isotopes decay at different rates.

In other words, they have different half-lives. The half-life of the uranium to lead is 4. The uranium to lead decay series is marked by a half-life of million years.

These differing rates of decay help make uranium-lead dating one of the most reliable methods of radiometric dating because they provide two different decay clocks. This provides a built-in cross-check to more accurately determine the age of the sample. Uranium is not the only isotope that can be used to date rocks; we do see additional methods of radiometric dating based on the decay of different isotopes.

For example, with potassium-argon dating , we can tell the age of materials that contain potassium because we know that potassium decays into argon with a half-life of 1. With rubidium-strontium dating , we see that rubidium decays into strontium with a half-life of 50 billion years.

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By anyone's standards, 50 billion years is a long time. In fact, this form of dating has been used to date the age of rocks brought back to Earth from the moon. So, we see there are a number of different methods for dating rocks and other non-living things, but what if our sample is organic in nature? For example, how do we know that the Iceman, whose frozen body was chipped out of glacial ice in , is 5, years old? Well, we know this because samples of his bones and hair and even his grass boots and leather belongings were subjected to radiocarbon dating.

Radiocarbon dating , also known as carbon dating or simply carbon dating, is a method used to determine the age of organic material by measuring the radioactivity of its carbon content.