# Stratigraphy and radiometric dating calculator

### Radiometric dating - Wikipedia

way radiometric dating and stratigraphic principles are used to establish Because of the chemistry of rocks, it was possible to calculate how. 1 08 - Mathematical calculation of radiometric dating involves the use of a simple techniques that had a revolutionary effect on archaeology and geology. Later. AFTER ONE HALF LIFE, HALF OF THE SAMPLE REMAINS RADIOACTIVE AND Finding the age of an object using radiometric dating is a four step process.

However, by pattern matching, five layers within the series at A can be correlated with five layers at the top of B. Similarly, by pattern matching, five layers in the series at B can be correlated with five layers at the top of C.

Since the ages of the layers at A are known by counting down from the top, layers at B that correlate with them can also be assigned ages.

Then, the ages of the rest of the layers at B may be determined by counting down. In similar fashion, layers at C that correlate with layers at B may be assigned ages, and the rest of the layers at C may be assigned by counting down.

Using this method, ages of varves that formed tens of thousands of years ago may be determined. For example, varves close to forty thousand years old have been dated in Japan. Pattern matching is also used to date trees by examining growth rings dendrochronology. Ages up to 14, years have been determined in this fashion. He drills a hole and extracts a drill core that shows a series of layers of sediment one of which contains pottery fragment 'X'. The archeologist then contacts his colleague who is working in a nearby area location 'B' where there is a modern floodplain to which a layer of sediment is added every year.

He asks his colleague to extract and send him a drill core from location 'B', making sure to include and label the most recent layer, deposited in She does so, and also includes another drill core from a third location 'C', where she has recently worked.

She tells him that location 'C', like location 'A', is also a dried out, abandoned floodplain. The first archeologist wants to know in what year the layer containing pottery fragment 'X' was deposited. My answer to Question 1: The layer containing 'X' was deposited in: Indeed, dating of lake sediments using varves was undertaken as early as Their disadvantage is that they are restricted to sites where annual deposition has occurred and the absolute age of at least one layer can be determined with confidence by some other means for example, by counting or by pattern matching with places where annual deposition continues through to today.

Places satisfying these requirements are relatively few. Another disadvantage is that over geologic time, preservation of such layers is limited.

Absolute age determination by varve counting is only suitable for materials less than several tens of thousands of years old. These limitations are overcome in radiometric dating. Radioactive elements, such as certain isotopes of uranium, thorium, rubidium, potassium, carbon and others, have the property that over set periods of time, known as their 'half lives' which are different for each radioactive elementhalf of their atoms decay to form atoms of different elements.

For example, over the course of million years, half the atoms of the 'parent' element uranium U decay to form atoms of the 'daughter' element lead Pb Over the next million years, half of the remaining U atoms change to Pb, and so on. By comparing the ratios of U to Pb that are found in the material today, the time when the process started may be ascertained see table below.

Examples of radioactive parent-daughter pairs and their half lives include: U - Pb 4. An error of that magnitude may be quite acceptable for such old rocks.

The number of years ago that the sample formed is: It is important to choose a radioactive parent-daughter pair whose half life is appropriate for the age of the material being dated.

On the one hand, the half life should be short enough so that a measurable amount of the daughter element has formed. On the other hand, if the half life is too short, the amount of parent element left may not be measurable. Thus, K-Ar dating would not be appropriate for a material that is 50, years old, as hardly any daughter element would have formed.

Similarly, C dating is not be appropriate for materials older than about 70, years as the amount of the parent element left becomes too small to be measured accurately. Radiometric dating depends on certain assumptions. The most fundamental assumption is that the half life of a parent-daughter pair does not change through time.

Experimentally and theoretically, that assumption seems justified. Also, successful cross-checking of ages using different dating techniques on the same sample supports the constancy of half lives. For example, C dates may be checked against ages determined through varve counting. A second assumption is that the system is closed. That is, no parent or daughter material has been added to or lost from the material being dated.

Such addition or subtraction may occur if the material mineral or rock has been weathered or metamorphosed. Therefore, material to be dated must be carefully examined to determine whether such processes may have taken place. Because the dating method depends upon comparing the ratio of parent to daughter element, the assumption must be made that the amount of daughter element initially present be zero or else be determinable.

Igneous rocks and highly metamorphosed rocks are the best candidates for radiometric dating because for them, for reasons that won't be discussed here, it can relatively easily be determined whether the initial amount of daughter element present was zero or, if it wasn't zero, what was the initial amount. The 'age' of an igneous rock refers to the time when the magma or lava from which it formed cooled below a certain temperature. A useful material for dating that time is the mineral zircon, a minor but common constituent of igneous rocks.

As magma or lava solidifies, the elements zirconium Zrsilicon Si and oxygen O link together to form zircon crystals. If uranium U atoms are in the vicinity, they may be incorporated into the zircon in place of Zr atoms. This substitution is possible because the size and charge of the U is similar to that of Zr.

That is, the U can 'fit' in the sites normally occupied by Zr. Any lead Pb in the vicinity cannot be incorporated in the zircon because it can't 'fit' in any of the sites. Assuming the zircon has not been affected by weathering or metamorphism, any Pb subsequently found in the zircon must have come from decay of the U; it was not there to start with. It is true that not all minerals that crystallize from a magma or lava form simultaneously, but except for extremely young igneous rocks, the time required for solidification is very short compared compared to the age of the rock.

Accurate radiometric dating of metamorphic rocks is more difficult. That is, at some point in time, an atom of such a nuclide will undergo radioactive decay and spontaneously transform into a different nuclide. This transformation may be accomplished in a number of different ways, including alpha decay emission of alpha particles and beta decay electron emission, positron emission, or electron capture.

Another possibility is spontaneous fission into two or more nuclides.

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-lifeusually 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 chaineventually 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 from only about 10 years e. It is not affected by external factors such as temperaturepressurechemical environment, or presence of a magnetic or electric field. For all other nuclides, the proportion of the original nuclide to its decay products 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 to measure the time from the incorporation of the original nuclides into a material to the present. Accuracy of radiometric dating[ edit ] Thermal ionization mass spectrometer used in radiometric dating. The basic equation of radiometric dating requires that neither the parent nuclide nor the daughter product can enter or leave the material after its formation.

The possible confounding effects of 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. It is therefore essential to have as much information as possible about the material being dated and to check for possible signs of alteration.

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.

This can reduce the problem of contamination. In uranium—lead datingthe concordia diagram is used which also decreases the problem of nuclide loss. Finally, correlation between different isotopic dating methods may be required to confirm the age of a sample. For example, the age of the Amitsoq gneisses from western Greenland was determined to be 3. The procedures used to isolate and analyze the parent and daughter nuclides must be precise and accurate.

## Radiometric dating

This normally involves isotope-ratio mass spectrometry. 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.

Closure 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 diffusionsetting 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 age is calculated from the slope of the isochron line and the original composition from the intercept of the isochron with the y-axis. The equation is most conveniently expressed in terms of the measured quantity N t rather than the constant initial value No. Atomic number, atomic mass, and isotopes Video transcript What I want to do in this video is kind of introduce you to the idea of, one, how carbon comes about, and how it gets into all living things.

And then either later in this video or in future videos we'll talk about how it's actually used to date things, how we use it actually figure out that that bone is 12, years old, or that person died 18, years ago, whatever it might be. So let me draw the Earth. So let me just draw the surface of the Earth like that. It's just a little section of the surface of the Earth.

And then we have the atmosphere of the Earth. I'll draw that in yellow. So then you have the Earth's atmosphere right over here. Let me write that down, atmosphere. And I'll write nitrogen. Its symbol is just N. And it has seven protons, and it also has seven neutrons. So it has an atomic mass of roughly Then this is the most typical isotope of nitrogen.

### Radiometric Dating

And we talk about the word isotope in the chemistry playlist. An isotope, the protons define what element it is. But this number up here can change depending on the number of neutrons you have. So the different versions of a given element, those are each called isotopes.

## Carbon 14 dating 1

I just view in my head as versions of an element. So anyway, we have our atmosphere, and then coming from our sun, we have what's commonly called cosmic rays, but they're actually not rays.

You can view them as just single protons, which is the same thing as a hydrogen nucleus. They can also be alpha particles, which is the same thing as a helium nucleus. And there's even a few electrons. And they're going to come in, and they're going to bump into things in our atmosphere, and they're actually going to form neutrons. So they're actually going to form neutrons. And we'll show a neutron with a lowercase n, and a 1 for its mass number.

And we don't write anything, because it has no protons down here. Like we had for nitrogen, we had seven protons. So it's not really an element. It is a subatomic particle. But you have these neutrons form.

And every now and then-- and let's just be clear-- this isn't like a typical reaction. But every now and then one of those neutrons will bump into one of the nitrogen's in just the right way so that it bumps off one of the protons in the nitrogen and essentially replaces that proton with itself.

So let me make it clear.

So it bumps off one of the protons.