# What do geologists use radioactive dating formulas

### Radiometric Dating

The discovery of the natural radioactive decay of uranium in by Henry for using radioactivity as a tool for measuring geologic time directly; Atoms of the same element with differing atomic weights are called isotopes. Equation. Dating rocks by these radioactive timekeepers is simple in theory, but. Radiometric Dating: Methods, Uses & the Significance of Half-Life Radioactive Decay: Definition, Formula & Types Radioactive dating enables geologists to record the history of the earth and its events, Carbon, uranium, and potassium are just a few examples of elements used in radioactive dating. The Geologic Time Scale (courtesy of the Geological Society of America) In order to use this equation for decay over a given time period, we will need the.

Isotopes of an element are atoms that all have the same atomic number or number of protons in the nucleus but have different atomic masses hence different numbers of neutrons in the nucleus.

## Radiometric dating

For example, all atoms of oxygen have 8 protons in the nucleus and hence have an atomic number of 8. However, oxygen atoms can have between 8 and 10 neutrons in the nucleus and therefore the isotopes of oxygen have atomic masses of 16, 17, and 18 a. Samarium Sm has 7 naturally occurring isotopes 3 are radioactive. Remind them that geologists only use certain radioactive isotopes to date rocks.

The atoms that are involved in radioactive decay are called isotopes. In reality, every atom is an isotope of one element or another. However, we generally refer to isotopes of a particular element e.

The number associated with an isotope is its atomic mass i. The element itself is defined by the atomic number i. Only certain isotopes are radioactive and not all radioactive isotopes are appropriate for geological applications -- we have to choose wisely. Those that decay are called radioactive or parent isotopes; those that are generated by decay are called radiogenic or daughter isotopes.

The unit that we use to measure time is called half-life and it has to do with the time it takes for half of the radioactive isotopes to decay see below. Mathematically, the half-life can be represented by an exponential function, a concept with which entry-level students may not have much experience and therefore may have little intuition about it.

I find that entry-level students in my courses get stuck on the term "half-life".

## How do geologists use carbon dating to find the age of rocks?

Even if they have been given the definition, they interpret the term to mean one-half the life of the system. Instead, it is really the lifetime of half of the isotopes present in the system at any given time. Marie and Pierre Curie.

Details Problem solving in the geosciences was forever changed with the discovery of radioactivity. Radioactive elements can be used to understand numerical age of geological materials on time scales as long as and even longer than the age of the Earth. In order to determine the age of a geologic material, we must understand the concept of half-life.

Half-life is a term that describes time. The time required for one-half of the radioactive parent isotopes in a sample to decay to radiogenic daughter isotopes. The units of half-life are always time seconds, minutes, years, etc.

If we know the half-life of an isotope and we can measure it with special equipmentwe can use the number of radiogenic isotopes that have been generated in a rock since its formation to determine the age of formation. Radiometric dating is the method of obtaining a rock's age by measuring the relative abundance of radioactive and radiogenic isotopes.

### Radioactive Decay

Plotting the results of these demonstrations results in a curve of an exponential decay function. Showing this plot and asking them questions about the shape and changes in number of isotopes through time may help students to develop some intuition about half-life.

Although most introductory students may not be prepared for the equation for exponential decay, discussion of half-life and radioactive decay prepares entry-level students for the introduction of more mathematical discussion of exponential growth and decay in upper level classes.

So many systems, how do we choose? Most students don't really know how isotopes are used to determine age. In particular, they have a hard time understanding that different systems are appropriate for different types of radiometric dating and why. There are several important points that can be emphasized to help avoid confusion when talking about the various systems: Geologists have a plethora of choices for calculating the age of a rock using big and complicated systems.

Check out this table of isotope systems and half-lives Excel 18kB Jun24 04 ; all of these are used to date rocks or sediment! With all these systems, how do we choose? Geologists use a number of criteria to decide which of the systems to use: 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. The above equation makes use of information on the composition of parent and daughter isotopes at the time the material being tested cooled below its closure temperature.

This is well-established for most isotopic systems. Plotting an isochron is used to solve the age equation graphically and calculate the age of the sample and the original composition. Modern dating methods[ edit ] Radiometric dating has been carried out since when it was invented by Ernest Rutherford as a method by which one might determine the age of the Earth. In the century since then the techniques have been greatly improved and expanded.

The mass spectrometer was invented in the s and began to be used in radiometric dating in the s. It 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. Uranium—lead dating method[ edit ] Main article: Uranium—lead dating A concordia diagram as used in uranium—lead datingwith data from the Pfunze BeltZimbabwe. This scheme has been refined to the point that the error margin in dates of rocks can be as low as less than two million years in two-and-a-half billion years.

Zircon has a very high closure 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.

This can be seen in the concordia diagram, where the samples plot along an errorchron straight line which intersects the concordia curve at the age of the sample. Samarium—neodymium dating method[ edit ] Main article: Samarium—neodymium dating This involves the alpha decay of Sm to Nd with a half-life of 1.

Accuracy levels of within twenty million years in ages of two-and-a-half billion years are achievable. Potassium—argon dating This involves electron capture or positron decay of potassium to argon Potassium has a half-life of 1. Rubidium—strontium dating method[ edit ] Main article: Rubidium—strontium dating This is based on the beta decay of rubidium to strontiumwith a half-life of 50 billion years.

This scheme is used to date old igneous and metamorphic rocksand has also been used to date lunar samples. Closure 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. Uranium—thorium dating method[ edit ] Main article: Uranium—thorium dating A relatively short-range dating technique is based on the decay of uranium into thorium, a substance with a half-life of about 80, years.

It is accompanied by a sister process, in which uranium decays into protactinium, which has a half-life of 32, years. While uranium is water-soluble, thorium and protactinium are not, and so they are selectively precipitated into ocean-floor sedimentsfrom which their ratios are measured.

The scheme has a range of several hundred thousand years. A related method is ionium—thorium datingwhich measures the ratio of ionium thorium to thorium in ocean sediment. Radiocarbon dating method[ edit ] Main article: Carbon is a radioactive isotope of carbon, with a half-life of 5, years, [25] [26] which is very short compared with the above isotopes and decays into nitrogen. Carbon, though, is continuously created through collisions of neutrons generated by cosmic rays with nitrogen in the upper atmosphere and thus remains at a near-constant level on Earth.

The carbon ends up as a trace component in atmospheric carbon dioxide CO2. A carbon-based life form acquires carbon during its lifetime. Plants acquire it through photosynthesisand animals acquire it from consumption of plants and other animals. When an organism dies, it ceases to take in new carbon, and the existing isotope decays with a characteristic half-life years.

The proportion of carbon left when the remains of the organism are examined provides an indication of the time elapsed since its death. This makes carbon an ideal dating method to date the age of bones or the remains of an organism.