# Dating with accelerators

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## 66-110: The Structure of Matter

### Notes

• First part of a first year university combined physics and chemistry course
• The figures are unavailable as they were paper cut and pasted to the printed report, before I had a scanner

### Project

Dating with accelerators uses the basic principles of radioactive dating and combines them with advanced isotope measurements to obtain very precise results from small samples. The principle measurement device is a modified mass spectrometer called an accelerator mass spectrometer (A.M.S.) This essay will cover the topics of radioactive dating, accelerator mass spectrometry, and how both of these work together to date materials.

Radiocarbon dating is based on the idea that plants(atmospheric–through photosynthesis) and animals(eat plants) absorb and release carbon continuously throughout their lives, but once they die they no longer absorb carbon. Since 14 C (a radioactive isotope of carbon) is constantly decaying, if it is not replenished, there will be a smaller and smaller amount of it. (In the atmosphere we can measure the current ratio of 12 C | 13 C | 14 C, and approximate the amount of carbon that were present in the atmosphere by using our knowledge of radioactive decay. This is supported by comparing dating using the counting of tree rings and radiocarbon dating in 5-6000 years ago range.) The contemporary ratio of natural carbon is approximately 12 C 98.84% | 13 C 1.1% | 14 C .01%. Combining these facts it can be seen that the amount of 14 C that is left in a plant or animal can be compared to the amount of 13 C, to determine how much the 14 C has decayed, and thus by using the formula for radioactive decay (using t1/2 = 5730 years), determine how old the specimen is. This process of dating depends on two factors, namely, that the atmospheric ratios of carbon isotopes be known and that the measurements of the ratios of carbon isotopes in the specimen be precise.

Other radioactive dating methods depend on the same types of thing: a known initial ratio (which can be supported by other evidence) and precise measurement of the remaining ratio (and a large enough sample that the random nature of radioactive decay does(/did) not distort the results too much). A good example is the dating of volcanic rocks by measuring the amount of a radioactive isotope of krypton that remains compared to a none radioactive isotope which remains.

Initially Geiger counters were used for the measurement of the radioactive isotopes which required that large samples be taken from the specimen. In addition these large samples could easily be/have been contaminated by new carbon being deposited on the specimen, after it died. Overall the “window” of accuracy using this method was 10-20,000 years ago. Improved accuracy was gained by using a chemical process which separates out collagen in the bone of an animal (and then carbon out of collagen). Using collagen has the advantage that new carbon is very unlikely to have been added to it after the animal died. Another improvement was the use of mass spectrometry to measure the isotopes of carbon present in the collagen. These increased the window to about 40,000 years ago. More recently, an advanced form of mass spectrometry called accelerator mass spectrometry has been used with very good success to get even more precise measurements (the window being 60,000 years +) from samples with masses measured in milligrams.

A basic mass spectrometer consists of an ion source, a velocity selector (makes sure all velocities are equal), a mass separator, and a detector(see Figure 2). The sample is excited so that a stream of ions is emitted from it. These ions must pass through crossed electric and magnetic fields which are set up so that only ions with v = E / B (a uniform velocity is desired so that the ions of equal mass will follow the same path in the next section). The mass separator is a magnetic field perpendicular to the path of the ions which causes the ions to be deflected from their original path. Ions with heavier mass will follow a larger radius (see Figure 2) and will therefore land in a different position on the detector. It is therefore possible, by examining the detector, to determine the (relative) masses and frequencies of the particles which were emitted.

Accelerators mass spectrometry takes the ‘velocity analyzer’ of the mass spectrometer (E/B), and combines it with electric and magnetic analyzers. Each of these analyzers can have rejection ratios of 105 or higher, and with a combination of these, a rejection ratio of up to 1015 can be obtained. Figure 1 shows a schematic drawing of the accelerator mass spectrometer at Isotrace Laboratory in Toronto. This AMS system does not in fact use the ideal arrangement for the analyzer, rather it was chosen because of the requirements for testing during setup, nonetheless it performs quite well. It uses a cesium gun to cause the sample to produce a current of negative ions which is then pulled, and focused into a beam. The ions are then passed through an electric analyzer, then a magnetic analyzer (essentially a mass spectrometer set up) to eliminate the background of ions that are of greater, or smaller mass than the isotopes that are being investigated(for dating usually 12 C, 13 C, and 14 C). Faraday cups 1 and 2 are used to measure this background count. The negative ions enter the accelerator system, in this case a tandem accelerator.

In the accelerator, ions are accelerated so the they acquire additional energy. The ions then go through a canal containing an electron stripping gas such as argon or krypton, and are then accelerated again. As a result the ions have a charge (q + 1)eV from the acceleration. Since no molecular ions with a charge q=+3 have been observed to emerge from a tandem accelerator, only atomic ions are present after the accelerator. There are however additional atomic ions present, as a result of the breakup of molecules in the accelerator. For this reason another electric analyzer is used after acceleration. Finally a magnetic analyzer is used which allows the 12 C current to be measured in Faraday cup F4, and the 13 C in Faraday cup F5. The remaining ion stream is passed through an additional analyzer, and the 14 C counting rate is measured in ionization detector ID. This measurement system requires the aid of a computer.

The result of all this work is that the AMS system gives very accurate measurements of isotope ratios in a given sample, which allows dating of fossils and other artifacts to be made with greater accuracy (especially older ones) than ever before.

### Bibliography

Kilius, et al., “AMS of heavy ions with small accelerators”, Nucl. Instr. and Meth. B52(1990) 357-365

Litherland, A.E., “Fundamentals of accelerator mass spectrometry”, Phil. Trans. R. Soc. Lond. A232 (1987), 5-21

Litherland, A.E., “A recombinator for radiocarbon accelerator mass spectrometry”, Nucl. Instr. and Meth. B52(1990) 375-377

Purser, K.H. et al., “A precision 14C accelerator mass spectrometer”, Nucl. Instr. and Meth. B52(1990) 263-268

Puser, H. Kenneth and Litherland, Albert E., “The elimination of charge-changing backgrounds in an AMS radiocarbon system”, Nucl. Instr. and Meth. B52(1990) 424-427

Suter, M., “Accelerator mass spectrometry: state of the art in 1990”, Nucl. Instr. and Meth. B52(1990) 211-223

Credit for cover image: Hah; BioMed Central Ltd., CC BY 2.0, via Wikimedia Commons