Background

1. Isotopes Of Carbon
2. Isotopes Of Carbon 12

All isotopes of radium are highly radioactive, with the most stable isotope being radium-226, which has a half-life of 1600 years and decays into radon gas (specifically the isotope radon-222). When radium decays, ionizing radiation is a product, which can excite fluorescent chemicals and cause radioluminescence. Carbon is found in all living things and is the building block for organic material, there is carbon 12, 13 and 14 and they all have different properties. This isotope was discovered on February 27, 1940 by Martin Karmen and Sam Ruben and is the most radioactive out of all carbon isotopes.

¹⁴C is a radioactive isotope of carbon. It was discovered in 1934 by Grosse as an unknown activity in the mineral endialyte. In the same year, Kurie (Yale) exposed nitrogen to fast neutrons and observed long tracks in a bubble chamber. He had produced ¹⁴C. It was in atmospheric CO₂ by Libby in 1946. He determined the half life to be 5568 years. This half life has later been re-determined by Godwin. The new half life is 5730 years. Libby recognized that due to its occurrence in natural materials, ¹⁴C can be used as a dating tool for materials that contain carbon compounds derived from atmospheric CO₂ either by simple mixing processes or by carbon exchange. The mean life time of roughly 8000 years is ideal for dating of reservoirs that are a few decades to a few ten thousand yeas old. For groundwater, this means that ¹⁴C dating can be applied to aquifers that contain water formed during periods that reach well into the past glacial time. ¹⁴C is a widely used tool to establish chronologies for groundwater flow systems and climate records for the Holocene and Pleistocene. It is considered to be the most important tool for age dating of ‘old’ groundwater.

The challenge in ¹⁴C dating of groundwater is the determination of the initial ¹⁴C content of groundwater at the time of recharge, i.e., at the time when groundwater is isolated from exchange with the soil air and moves away from the water table. Electrax crack mac.

Lexmark x3550 driver windows 10. There is also a stable isotope of carbon, ¹³C. This isotope is important in that it allows us to correct for carbon isotope fractionation in nature and during analytical procedures.

Isotopes Of Carbon

Abundance of carbon isotopes in nature

12C	13C	14C
98.89 %	1.11 %	~10-12

¹³C measurements are reported in the d¹³C notation relative to a standard (PDB, or the newer VPDB standard, considered identical to PDB)
Isotope ratios are typically measured by mass spectrometry
d¹³C values cover a wide range in nature (Fig) influenced by fractionation processes analogue to what we discussed in the water isotope section
¹⁴C activities are referred to an international standard, known as as 'modern carbon'

Natural ¹⁴C production

¹⁴C is mainly produced by interaction of cosmic ray derived secondary neutrons with ¹⁴N in the atmosphere. ¹⁴N (n,p) ¹⁴C¹⁴C can also be produced by the following reaction: ¹³C(d,p)¹⁴C d: deuterium or ²H the production rate is 2.4 ± 0.2 atoms (cm² sec)^-1
The production rate has not been constant over time, comparison with tree ring chronologies and corals have shown variations in the production rate which result in an offset between calendar and ¹⁴C ages of thousands of years (Fig) (Fig)

Radioactive decay

¹⁴C decays by b^- decay with a maximum energy of 0.158 MeV.

14₆C -> 14₇N+ e^- + anti-neutrino+ Q

Its half life t is 5730 years, i.e., somewhat larger than the half life determined by Libby (5568 ys). Differnt fields tend to use different half lifes.

Natural global inventory

The global inventory of natural ¹⁴C is about 75 tons. The specific activity in pre-industrial times was 13.56 dpm (gC)^-1. dpm stands for decay per minute.

Anthropogenic ¹⁴C production

The main source of anthropogenic ¹⁴C is so-called ‘bomb’ ¹⁴C, i.e., ¹⁴C produced during atmospheric testing of nuclear weapons. At the peak of surface testing of nuclear devices in 1963, the atmospheric ¹⁴C activity had reached about twice that of natural ¹⁴C (Fig). The bomb ¹⁴C has been produced by interaction of atmospheric nitrogen with the high neutron flux from the explosion of nuclear devices (mainly thermonuclear devices). Local increases in atmospheric ¹⁴C have been observed in the vicinity of nuclear power plants.

Before bomb production began, ¹⁴C (and ¹³C) dropped due to anthopogenic emisssions of fossil carbon (Suess effect, Fig)

Notation

The notation of ¹⁴C activities is discussed in detail in Stuiver and Pollach (Radiocarbon, 19, 355-365, 1977). In short, ¹⁴C is calibrated against an NBS (National Bureau of Standards) oxalic acid standard. The internationally accepted radiocarbon dating reference is 95% of the activity, in 1950 AD, of the NBS oxalic acid normalized to d¹³C of –19.3‰ with respect to PDB. The factor of 0.95 adjusts the oxalic acid to the activity of wood from 1840 to 1860 (‘pre-industrial’). Results are reported in pmC (% modern carbon).

A_0N = 0.95 A_OX [1 – 2.3(d¹³C + 19.3)/1000]

• A_ON: ¹⁴C activity of oxalic acid normalized for ¹⁴C fractionation
• A_OX: ¹⁴C activity of oxalic acid
• The d¹³C correction of 19‰ takes into account the fractionation of ¹⁴C during the combustion of oxalic acid.

Isotopes Of Carbon 12

Generally radiocarbon concentrations of samples are normalized to a common d¹³C value of -25‰. The fractionation for 14C is 2.3 times the fractionation for 13C and therefore the enrichment in 14C due to a factionation amounts to:
2.3(d¹³C + 25‰)
Groundwater:
For groundwater studies, the pmc (percent modern carbon) notation is used.

pmc = (A_SN/A_abs) 100% = A_SN [A_ON e^l(y-1950)]^-1 100%

• A_SN: activity of sample normalized for fractionation using d¹³C
• A_ON: ¹³C normalized activity of oxalic acid
• A_abs: Absolute ¹⁴C activity of the sample
• y: year of measurement of oxalic acid

¹⁴C dating

Principle:

In the atmosphere, ¹⁴C is incorporated into ¹⁴CO₂ and takes part in the global carbon cycle. It is assimilated by plants. Except for isotope fractionation, ¹⁴C in living organic matter is the same as that in atmospheric CO₂. After organic matter dies, the ¹⁴C concentration decreases due to radioactive decay. If there is no isotope exchange, radioactive decay is the only ¹⁴C sink and if the initial ¹⁴C activity is known, an age can be calculated from the measured ¹⁴C activity of a sample.
In groundwater applications typically DIC (dissolved inorganic carbon; DIC = CO_2(aqueous) + HCO₃- + CO₃^2-) is extracted from the water a and its measured ¹⁴C activity is compared to the initial ¹⁴C activity. Determination of the initial ¹⁴C activity can be challenging and typically requires correction models that account for the carbon chemistry in the unsaturated and saturated soil zones.

¹⁴C(t) = ¹⁴C(t₀) e^{-l (t-t0)}

ln ¹⁴C(t) = ln ¹⁴C(t₀) (-l (t-t₀))

ln [¹⁴C(t)/¹⁴C(t₀)] = -l (t-t₀)

D t = (t - t₀) = -l^-1 ln [¹⁴C(t)/¹⁴C(t₀)] = T_1/2 / ln2 {ln [+C(t₀)/¹⁴C(t)]}

l: radioactive decay constant of ¹⁴C: l = t^-1; t : mean life time: t = T_1/2/ln2

Initial ¹⁴C activity in groundwater

See summary in Clark and Fritz (chapter 8) for details

In short, the ¹⁴C activity of DIC (dissolved inorganic carbon) in groundwater is determined by the following factors: (Fig. 8.6 in Clark and Fritz):

• activity in soil CO₂ (soil air and root respiration); activity » 100 pmc
• dissolution of carbonates (lime stone); activity » 0 pmc
• dissolution of carbonates can occur in the unsaturated soil zone (open system) or in the saturated soil zone (closed system).
• isotope exchange can lead to a decrease in ¹⁴C activity in addition to radioactive decay
• a variety of models can be used to estimate the initial ¹⁴C activity in groundwater. They include the very simple ‘Vogel’ model, several models that correct for carbon chemistry using chemical or ¹³C balances, and the complex NETPATH model by Plummer. The latter accounts for the chemical evolution of the groundwater along flowpaths.

¹⁴CO₂ + H₂O + CaCO₃ --> Ca²⁺ + HCO₃-

completely open system: ¹⁴C activity: » 100 pmc

completely closed system: ¹⁴C activity: » 50 pmc

Chemical and isotopc evolution in recharge zone: (Fig) (Fig) Open and closed system conditions

‘real world’ systems are somewhere in between open and closed and the correction models mentioned above and described in Clark and Fritz (chapter 8) have to be applied.

Measurement

• Technique: low-level b - counting using gas-filled proportional counters or AMS (Accelerator mass spectrometry)
• Water sample size: ca. 100 liters (low-level counting) or several hundred ml (AMS)
• Measurement precision: ± 0.2 to ± 1% (1-s error) for concentrations close to 100 pmc. This corresponds to an age resolution of about ± 16 to ± 40 years.
• Detection limit: <1% modern corresponding to ages of about 40000 years.

There are many laboratories worldwide that can measure ¹⁴C routinely. However, only few ¹⁴C laboratories have the capability to measure ¹⁴C at precisions of ± 0.2%. In groundwater studies the overall error is dominated by systematic errors and the analytical precision is not as critical as in oceanographic studies.

Resources

• Fairbanks, R. G., Mortlock, R. A., Chiu, T. C., Cao, L., Kaplan, A., Guilderson, T. P., Fairbanks, T. W., Bloom, A. L., Grootes, P. M., and Nadeau, M. J. (2005). Radiocarbon calibration curve spanning 0 to 50,000 years BP based on paired Th-230/U-234/U-238 and C-14 dates on pristine corals. Quaternary Science Reviews 24, 1781-1796.
• Reimer, P. J., Baillie, M. G. L., Bard, E., Bayliss, A., Beck, J. W., Bertrand, C. J. H., Blackwell, P. G., Buck, C. E., Burr, G. S., Cutler, K. B., Damon, P. E., Edwards, R. L., Fairbanks, R. G., Friedrich, M., Guilderson, T. P., Hogg, A. G., Hughen, K. A., Kromer, B., McCormac, G., Manning, S., Ramsey, C. B., Reimer, R. W., Remmele, S., Southon, J. R., Stuiver, M., Talamo, S., Taylor, F. W., van der Plicht, J., and Weyhenmeyer, C. E. (2004). IntCal04 terrestrial radiocarbon age calibration, 0-26 cal kyr BP. Radiocarbon 46, 1029-1058.
• Levin, I. and Hesshaimer, V. (2000) Radiocarbon - a unique tracer of global carbon cycle dynamics. Radiocarbon, 42, 1, 69-80.
  
• Fontes, J. C.; Garnier, J. M. (1979) Determination of the initial 14C activity of the total dissolved carbon; a review of the existing models and a new approach. Water Resour. Res., 15, 399-413.
• Mook, W.G. (1980) Carbon-14 in hydrogeological studies. In: Handbook of environmental isotope geochemistry (Fritz, P, and Fontes, J.C., editors), Vol 1, Elsevier Sci. Publ. Co., Amsterdam, 49-74.
• Plummer, L.N., E.C. Prestemon, and D.L. Parkhurst (1991) An interactive code (NETPATH) for modeling net geochemical reactions along a flow path. USGS Water-Resources Investigations Report,} 91-4078, USGS, Reston.
  
• Plummer, L.N., Prestemon, E.C., and Parkhurst, D.L., 1994, An interactive code (NETPATH) for modeling NET geochemical reactions along a flow PATH--version 2.0: U.S. Geological Survey Water- Resources Investigations Report 94-4169, 130 p.
• NETPATH home page
  
• Levin I, Schuchard J, Kromer B, Münnich KO (1989) The continental European Suess effect. Radiocarbon 31(3):431–40.