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Half Life

Using the half-life of radioactive elements for dating

This section has been adapted from ‘Geology 101: Introduction to Physical Geology’, Wentachee Valley College, http://commons.wvc.edu/rdawes/G101OCL/Basics/geotime.html

In geology, an absolute age is a quantitative measurement of how old something is, or how long ago it occurred, usually expressed in terms of years.

Most absolute age determinations in geology rely on radiometric methods.

Earth is billions of years old. The most useful methods for measuring the ages of geologic materials make use of radioactive parent isotopes and their stable daughter products, as preserved in rocks, minerals, or other geologic materials.

An isotope is a particular type of atom of a chemical element, which differs from other isotopes of that element in the number of neutrons it has in its nucleus.

By definition, all atoms of a given element have the same number of protons.
However, they do not all have the same number of neutrons.
The different numbers of neutrons possible in the atoms of a given element correspond to the different possible isotopes of that element.

For example, all carbon atoms have 6 protons.
Carbon-12 is the isotope of carbon that has 6 neutrons.
Carbon-13 is the isotope of carbon that has 7 neutrons.
Carbon-14 has 8 neutrons in its nucleus, along with its 6 protons, which is not a stable combination.

That is why carbon-14 is a radioactive isotope-it contains a combination of protons and neutrons in its nucleus that is not stable enough to hold together indefinitely. Eventually, it will undergo a spontaneous nuclear reaction and turn into a stable daughter product – a different isotope, which is not radioactive.

Each type of radioactive isotope has a half-life, a length of time that it will take for half of the atoms in a sample of that isotope to decay into the stable daughter product.

Physicists have measured the half-lives of most radioactive isotopes to a high level of precision.

The properties of radioactive isotopes and the way they turn into their stable daughter products are not affected by variations in temperature, pressure, or chemistry. Therefore the half-lives and other properties of isotopes are unaffected by the changing conditions that a rock is subjected to as it moves through the rock cycle. If a granite crystallizes with minerals containing radioactive isotopes, it is as though the rock crystallizes with a built-in batch of stopwatches that begin ticking away as soon as the granite has cooled….

Parent Isotopes, Daughter Isotopes, and Half-Lives

 

The dots in the cartoon below represent atoms of a parent isotope, decaying to its stable daughter product, through two half-lives.

At time zero in the diagram, which could represent the crystallization of minerals in a rock, there are 32 red dots.

After one half-life has passed, there are 16 red dots and 16 green dots.

After two half-lives have passed, there are 8 red dots and 24 green dots.

schematic half-lives diagram with three boxes, from left to right:<br /><br /><br /> 0 half-lives, contains 32 red dots; 1 half-life, contains 16 red dots and 16 green dots; 2 half-lives, contains 8 red dots and 24 green dots

For Uranium-238 the half life is 4.5 billion years
{ http://en.wikiversity.org/wiki/Age_of_the_Earth }

The following graph illustrates radioactive decay of a fixed amount of an isotope.

You can see how the proportions of the isotopes from the cartoon above are graphed as percentages at half-lives 0, 1, and 2 below.

The following table lists a selection of isotope pairs that are used in making radiometric age determination.

Carbon-14 has a relatively short half-life, which makes it useful only for young, carbon-rich geologic materials, less than about 70,000 years old.

Igneous rocks and high-grade metamorphic rocks are the most likely to be entirely formed of minerals that crystallized when the rocks formed.

As most fossils are found in clastic sedimentary rocks, which are made of weathered and eroded minerals and bits of rock of various ages, it is unlikely to be able to make an radiometric age determination of a rock in which a fossil is found.

The age of a rock containing fossils can usually be narrowed down by measuring the ages of metamorphic or igneous rocks in stratigraphic relation to it, such as a lava flow on top of a layer of sedimentary rock.

Parent Daughter Half Life (years) Dating Range (years) Minerals/materials
238U
Uranium-238
206Pb
Lead-206
4.5 billion 10 million –
4.6 billion
Minerals include zircon, uraninite. Igneous or metamorphic rocks.
40K
Potassium-40
40Ar
Argon-40
1.3 billion 0.05 million –
4.6 billion
Minerals include muscovite, biotite, K-feldspar. Volcanic rocks.
87Rb
Rubidium-87
87Sr
Strontium-87
47 billion 10 million –
4.6 billion
Minerals include muscovite, biotite, K-feldspar. Igneous or metamorphic rocks.
14C
Carbon-14
14N
Nitrogen-14
5,730 years 100 – 70,000 years Not used for dating rocks, except carbonates from earth’s surface such as recent coral reefs.

Used for young organic materials, or surface-water samples:
Wood, charcoal, peat, bone, tissue, carbonate minerals from surficial environments, water containing dissolved carbon.

______________________________

Online lab: Learn about different types of radiometric dating, such as carbon dating.
radioactive-dating-game-screenshot
Understand how decay and half life work to enable radiometric dating. Play a game that tests your ability to match the percentage of the dating element that remains to the age of the object.
http://phet.colorado.edu/en/simulation/radioactive-dating-game

__________________________________________________

the following section is from http://blunt-science.tumblr.com/post/109954909373/a-representation-of-the-age-span-carbon-dating-is

What is Carbon dating?

Here is a representation of the age span that carbon dating is able to accurately predict.

carbon dating part 1

Carbon dating works by understanding the properties of two isotopes of carbon: C12 and C14.

C12 does not decay and remains constant in a sample, whereas C14 decays at an even, constant rate.

By measuring the ratio of C12 to C14, we can understand how long a sample has been around for.

The half life of C 14 is around 5,730 years.

As seen by the second graph, this means that if a sample has half of the C14 it should usually have, it has been around for 5,730 years. A quarter of the amount, double that time, one eight of the original amount, more still.

Carbon dating is only as accurate as the consistency of it’s decay rate, which is unchanging and extremely uniform.

It is almost exclusively used for organic material as all life on earth is carbon based.

There is a misconception that carbon dating is used to date the age of the earth. As seen by the graph this isn’t possible as {almost} all carbon 14 decays at a certain point – and can only be used accurately up to about 60,000 years. For longer time scales, other elements are used that is based off the same principles.

The graphs are taken from a video by The Scientific American that explains carbon dating in a very straight-forward 2 minutes. Watch the full video here How Does Radiocarbon Dating Work? – Instant Egghead #28: Scientific American

  • text from http://blunt-science.tumblr.com/post/109954909373/a-representation-of-the-age-span-carbon-dating-is

30.8: Half-Life and Rate of Decay
30.9: Calculations Involving Decay Rates and Half-Life
30.10: Decay Series
30.11: Radioactive Dating
30.12: Stability and Tunneling
30.13: Detection of Particles

Learning Standards

SAT Subject Test: Physics

Quantum phenomena, such as photons and photoelectric effect
Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra
Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS1-8. Develop a model to illustrate the energy released or absorbed during the processes of fission, fusion, and radioactive decay.

Massachusetts Science and Technology/Engineering Curriculum Framework 2006

Chemistry

2. Atomic Structure and Nuclear Chemistry
Central Concepts: Atomic models are used to explain atoms and help us understand the interaction of elements and compounds observed on a macroscopic scale. Nuclear chemistry deals with radioactivity, nuclear processes, and nuclear properties. Nuclear reactions produce tremendous amounts of energy and lead to the formation of elements.

2.1 Recognize discoveries from Dalton (atomic theory), Thomson (the electron), Rutherford (the nucleus), and Bohr (planetary model of atom), and understand how each discovery leads to modern theory.
2.2 Describe Rutherford’s “gold foil” experiment that led to the discovery of the nuclear atom. Identify the major components (protons, neutrons, and electrons) of the nuclear atom and explain how they interact.
2.3 Interpret and apply the laws of conservation of mass, constant composition (definite proportions), and multiple proportions.
2.4 Write the electron configurations for the first twenty elements of the periodic table.
2.5 Identify the three main types of radioactive decay (alpha, beta, and gamma) and compare their properties (composition, mass, charge, and penetrating power).
2.6 Describe the process of radioactive decay by using nuclear equations, and explain the concept of half-life for an isotope (for example, C-14 is a powerful tool in determining the age of objects).
2.7 Compare and contrast nuclear fission and nuclear fusion.

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

Electromagnetic radiation can be modeled as a wave of changing electric and magnetic fields or as particles called photons. The wave model is useful for explaining many features of electromagnetic radiation, and the particle model explains other features. Quantum theory relates the two models…. Knowledge of quantum physics enabled the development of semiconductors, computer chips, and lasers, all of which are now essential components of modern imaging, communications, and information technologies.

 

 

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