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Radiometric Dating: Understanding Carbon-14 and Other Decay Systems, Study notes of Physics

University of London (Lond)Physics

An overview of radiometric dating, focusing on the use of carbon-14 and other decay systems for determining the age of organic and mineral samples. The concepts of parent, daughter, nonradiogenic elements, half-life, and radiocarbon dating. It also discusses the challenges of measuring isotopic ratios and the importance of closed systems for accurate results.

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2010/2011

Uploaded on 09/10/2011

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PX266 Geophysics (2010/11)
Lecture 4 Handout – Radiometric Dating
Dr. Gavin Bell
A summary of some radiometrically useful decay systems. The variables N,D,Rand T½are
used in the lecture notes. The 14C to 14N half-life (by beta decay) is only about 5700
years: too short for geology but good for archaeology.
Parent (N) Daughter (D) Nonradiogenic (R)T½(Ma)
Carbon-14 Nitrogen-14 Carbon-12 0.00573
Samarium-147 Neodymium-143 Neodymium-144 106000
Potassium-40 Argon-40 Argon-36 11850
Rubidium-87 Strontium-87 Strontium-86 48800
Uranium-235 Lead-207 Lead-204 704
Uranium-238 Lead-206 Lead-204 4468
Thorium-232 Lead-208 Lead-204 14010
Radiocarbon dating – short exercise during the lecture
A sample of a leather strap from this helmet is obtained, trying to prevent any
contamination of it by atmospheric carbon, fingers, plastic tools/bags, etc. It is
analysed in an accelerator mass spectrometer where the 14C / 12C ratio is found to be
8.7×10-13 ± 3%.
Is the helmet Viking, mediaeval or modern?
pf2

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PX266 Geophysics (2010/11)

Lecture 4 Handout – Radiometric Dating

Dr. Gavin Bell A summary of some radiometrically useful decay systems. The variables N , D , R and T ½ are used in the lecture notes. The 14 C to 14 N half-life (by beta decay) is only about 5700 years: too short for geology but good for archaeology. Parent ( N ) Daughter ( D ) Nonradiogenic ( R ) T ½ (Ma) Carbon-14 Nitrogen-14 Carbon-12 0. Samarium-147 Neodymium-143 Neodymium-144 106000 Potassium-40 Argon-40 Argon-36 11850 Rubidium-87 Strontium-87 Strontium-86 48800 Uranium-235 Lead-207 Lead-204 704 Uranium-238 Lead-206 Lead-204 4468 Thorium-232 Lead-208 Lead-204 14010 Radiocarbon dating – short exercise during the lecture A sample of a leather strap from this helmet is obtained, trying to prevent any contamination of it by atmospheric carbon, fingers, plastic tools/bags, etc. It is analysed in an accelerator mass spectrometer where the 14 C / 12 C ratio is found to be 8.7×10-13^ ± 3%. Is the helmet Viking, mediaeval or modern?

Radiocarbon dating – background Cosmic rays generate 14 C in the upper atmosphere by transforming 14 N, and this leads to an equilibrium ratio of 14 C / 13 C / 12 C in the biosphere (via the familiar carbon cycle). Living organisms share this equilibrium ratio. The equilibrium 14 C / 12 C ratio is very small, around 1.0×

  • . When an organism dies it no longer takes up C and so does not maintain the equilibrium ratio and the radioactive C isotopes begin to decay without replenishment. Therefore, the ‘ t = 0’ condition for radiocarbon dating is the death of the organism which is the origin of the organic material in question. As the sample ages its 14C radioactivity decreases and this provides a basic direct measure of the age. More sophisticated accelerator techniques are available for accurately measuring the ratio of 14C to other isotopes for old or small samples. Actually, the basic radiocarbon date must be corrected since the equilibrium ratio in the atmosphere changes slightly over time. Corrections going back to around 5000 BC are available by calibration again dendrochronology (tree ring dating). The ratio is presently changing rather rapidly because of fossil fuel burning, which liberates large amounts of non-radioactive 12C, thereby reducing the 14C / 12C ratio. Radiometric dating – general considerations  Different isotopes of the same element behave nearly identically under chemical and physical influences.  The samples we will consider are typically mineral samples extracted from a rock, minimising contamination etc.  Different minerals will, in general, have different elemental ratios (i.e. the chemical formulae are different). Alternatively, different samples of a single mineral may have different elemental abundances, e.g. if the mineral is a solid solution like a (Mg,Fe) silicate.  If a sample system is “closed” then there have been no physical or chemical influences on the sample which affect the isotopic ratios. The mineral has been isolated from outside influence throughout its geological history. A closed system is essential otherwise isotopic ratios will change due to processes other than nuclear decay.  If a sample is contaminated or not closed the isotopic ratios can be meaningless.  Measuring isotopic ratios can be difficult since some occur in very low abundance. We generally use a mass spectrometer, which can measure the atomic masses of the constituents of a sample with high accuracy and high sensitivity (low abundance isotopes can still be measured). Still, signal-to noise ratio can be a problem leading to uncertainty in the measured ratio.  We do not know, a priori, the “initial” abundance of different isotopes of the same element.  We do not know, a priori, what “ t = 0” means in our decay equation. These problems can be overcome by using a whole-rock isochron****. Further Study Check you are happy with the concepts outlined above.