Tracing Fast Food Beef to "Confined Animal Feeding Operations"
back to Average Atomic Weights
Cattle normally eat mostly grasses, but to maximize meat production most cattle in the US are fed corn in "Confined (or Concentrated) Animal Feeding Operations" (CAFOS).
The estimated 15,500 CAFOs confine about 30 million cattle and produce 300 million tons of manure anually, so they are a major source of pollution, and improper management has led the EPA to regulate them under the Clean Water Act 
Corn also puts high fertilizer demands on land, and is expensive to grow, compared to natural grasslands where cattle normally graze. Since corn is also valuable as human food and fuel, it is important to keep track of its production and use.
Although restaurants are not required to disclose sources of meat, a recent study found that most of the beef in fast food hamburgers comes from corn-fed cattle. The samples to the left of the chart below are lower in corn fed beef, those to the right are higher.
The technique used to identify corn fed beef depends on the "Stable Isotope Ratios" of two naturally occurring isotopes of carbon, 126C and 136C. Corn is a "C4" plant, photosynthetically producing a product with a four carbon atom chain. C4 plants have higher 136C/ 126C ratios than "C3" plants like grasses, so their presence can be detected by using a mass spectrometer to determine the "δ13C value". The delta value is reported on a "per mil" (‰, or parts per thousand) basis, because the range of isotopic compositions is small, and more negative values indicate lower 136C values.
The mean δ13C value for terrestrial C3 plants is −27‰ (range −35‰ to −21‰) and for C4 plants is −13‰ (range −14‰ to −10‰).
But is there a "normal" isotopic abundance ratio for an element?
The "Normal" Isotopic Ratio: Atomic Weights
All atoms of a given element do not necessarily have identical masses. But all elements combine in definite mass ratios, so they behave as if they had just one kind of atom. In order to solve this dilemma, we define the atomic weight as the weighted average mass of all naturally occurring (occasionally radioactive) isotopes of the element.
A weighted average is defined as
Atomic Weight =
Similar terms would be added for all the isotopes. Since the abundances change from place to place, IUPAC has established "normal" abundances which are most likely to be encountered in the laboratory. This important document that reports these values can be found at theIUPAC site. The abundances are also usually listed on the Table of the Nuclides which lists all isotopes for all elements. Surprisingly, a good number of elements have isotopic abundances that vary quite widely, so that atomic weights based on them have only 3 or 4 digit precision.
The atomic weight calculation is analogous to the method used to calculate grade point averages in most colleges:
Example: The Atomic Weight of Carbon
The IUPAC Report gives the following data for carbon:
98.93% 126C whose isotopic weight is 12.0000000.
1.07% 136C whose isotopic weight is 13.0033548.
Calculate the atomic weight of an average naturally occurring sample of carbon.
The exact isotopic mass of 126C may be surprising. It is assigned the value 12.0000000 as a standard for the atomic weight scale. Other masses are determined by mass spectrometers calibrated with this arbitrary standard.
δ13C Values for Beef
We saw above that carbon is normally 98.93% 126C and 1.07% 136C, but the range is about 98.85 - 99.02% 126C. The heavier isotope is enriched in C4 plants like corn, as measured by the δ13C values. The δ13C value assigned a value of 0 for a standard with a very high 136C/ 126C ratio, so values are more negative for sources with less 13C (like C3 grasses).
In a survey of fast food restaurant hamburgers, researchers found δ13C values less negative than −19.5‰, which implies a “final diet of corn silage”, while more negative values are associated with a grass (C3) diet. Their data suggest that ≈70% of beef servings had a corn-dominated (>50% C4) diet, with δ13C above −19‰; only 30% had a diet that could be >85% corn, with δ13C above −16‰. The data are summarized in the figure above.
Stable isotope analysis can be used generally to trace food origins. Mean δ13C values for conventional Irish (−24.5‰ ± 0.7‰) and other European (−21.6‰ ± 1.0‰) samples suggest a predominance of C3 dietary ingredients derived from temperate, C3 plants. By contrast, considerably less negative δ13C values for US (−12.3‰ ± 0.1‰) and Brazilian (−10.0‰ ± 0.6‰) beef reflect the almost exclusive use of C4 foodstuffs, likely maize or (sub)tropical C4 pasture grasses 
Defining the Mole
The SI definition of the mole also depends on the isotope 126C and can now be stated. One mole is defined as the amount of substance of a system which contains as many elementary entities as there are atoms in exactly 0.012 kg of 126C. The elementary entities may be atoms, molecules, ions, electrons, or other microscopic particles. This official definition of the mole makes possible a more accurate determination of the Avogadro constant than was reported earlier. The currently accepted value is NA = 6.02214179 × 1023 mol–1. This is accurate to 0.00000001 percent and contains five more significant figures than 6.022 × 1023 mol–1, the number used to define the mole previously. It is very seldom, however, that more than four significant digits are needed in the Avogadro constant. The value 6.022× 1023 mol–1 will certainly suffice for most calculations needed.
Naturally occurring lead is found to consist of four isotopes:
1.40% 20482Pb whose isotopic weight is 203.973.
24.10% 20682Pb whose isotopic weight is 205.974.
22.10% 20782Pb whose isotopic weight is 206.976.
52.40% 20882Pb whose isotopic weight is 207.977.
Calculate the atomic weight of an average naturally occurring sample of lead.
Atomic Weight =
- ↑ http://en.wikipedia.org/wiki/Concentrated_animal_feeding_operation
- ↑ http://en.wikipedia.org/wiki/Corn_fed_beef#Environmental_concerns
- ↑ http://www.epa.gov/npdes/regulations/cafo_fedrgstr_chapt1.pdf
- ↑ http://www.scientificamerican.com/article.cfm?id=that-burger-youre-eating-is-mostly-corn
- ↑ Bahar B, Monahan FJ, Moloney AP, O'Kiely P, Scrimgeour CM, Schmidt O;RAPID COMMUNICATIONS IN MASS SPECTROMETRY, 19,(14), 1937-1942 (2005); http://cel.isiknowledge.com/InboundService.do?product=CEL&action=retrieve&SrcApp=Highwire&UT=000230666700004&SID=1Comp2ABgkgLCMf5fh9&Init=Yes&SrcAuth=Highwire&mode=FullRecord&customersID=Highwire
- ↑ http://en.wikipedia.org/wiki/%CE%9413C#Reference_standard
- ↑ http://en.wikipedia.org/wiki/%CE%9413C
- ↑ J.F. Kelly, Stable isotopes of carbon and nitrogen in the study of avian and mammalian trophic ecology, Canadian Journal of Zoology 78 (2000), pp. 1–27.
- ↑ http://www.pnas.org/content/106/6/E9.full
- ↑ http://www.pnas.org/content/105/46/17855.full
- ↑ http://www.pnas.org/content/105/46/17855.abstract?ijkey=46cfd76e3a379c03df7ab1b2770d5998df824535&keytype2=tf_ipsecsha
- ↑ D.J. Minson, M.M. Ludlow and J.H. Troughton, Differences in natural carbon isotope ratios of milk and hair from cattle grazing tropical and temperate pastures, Nature 256 (1975), p. 602.