Stable Isotopes and Radiocarbon Dating

Stable Isotopes and Radiocarbon Dating

Introduction

• The goal is to move from a basic understanding to practical application of radiocarbon dating.
• Start with stable isotopes, then move to radiocarbon.
• Homework: Google OxCal, find the website, and sign up for an account before Thursday.
• Thursday: Dating day with dendrochronology revisited, calibration of radiocarbon dates, and building Bayesian chronological models.
• Nick Kessler will discuss blending dendrochronology with radiocarbon dating.

Stable Isotopes: Elements and Notation

• Atomic Number: The number of protons in an element.
  • Carbon has six protons.
• Atomic Mass: Protons and neutrons together.
  • The most stable form of carbon is carbon-12 ($_{12}C$), with 6 protons and 6 neutrons.
• Isotopes: Different forms of an element with varying numbers of neutrons.
  • Stable isotopes: Carbon-13 ($_{13}C$)
  • Unstable (radioactive) isotope: Carbon-14 ($_{14}C$)

Carbon Isotopes

• Carbon-13 has 7 neutrons and is heavier than carbon-12.
• Nature operates differently on the mass of isotopes through biological and geochemical processes.
• Carbon-14 is radioactive and unstable, decaying into nitrogen over time.
• The decay rate of carbon-14 is a linchpin of radiocarbon dating.

Isotope Concentrations

• Carbon-12 comprises 98.9% of carbon on the planet.
• Carbon-13 makes up 1.1%.
• Carbon-14 is less than 0.0001%, yet measurable.

Photosynthesis

• Photosynthesis equation: $CO<em>2 + H</em>2O + Sunlight \rightarrow C<em>6H</em>{12}O<em>6 + O</em>2$
• Plants take up different weights of carbon during photosynthesis through stomata.
• Plants have evolved specific ways to uptake different weights of carbon (C12, C13).

Photosynthetic Pathways

• C3 Photosynthesis:
  • Occurs in wetter, temperate areas.
  • Plants are selective about the carbon they intake, preferring lighter carbon for energy efficiency.
• C4 Photosynthesis:
  • Occurs in drier environments like deserts.
  • Plants cannot be selective and take in more of the heavy carbon due to the need to keep stomata closed to conserve water.

C3 vs. C4 Photosynthesis

• C3 photosynthesis results in 3-phosphoglyceric acid (3 carbon atoms).
• C4 photosynthesis results in oxaloacetate (4 carbon atoms).
• Harman Craig discovered C4 photosynthesis by observing land plants clustering differently on a graph measuring carbon isotopes.

Delta Carbon 13 and Delta Nitrogen 15

• Delta Carbon 13 ($\delta^{13}C$) measures the ratio of carbon-13 to carbon-12 in a sample relative to a standard (Vienna Pee Dee Belemnite).
• Equation: $\delta^{13}C = \frac{{\frac{{^{13}C}}{{^{12}C}}}<em>{sample}}{{\frac{{^{13}C}}{{^{12}C}}}</em>{standard}} - 1 * 1000$
• The result is expressed in per mil (‰).
• Higher $〖δ〗^{13}C$ values indicate more heavy carbon (carbon-13).
• Lower $〖δ〗^{13}C$ values means more light carbon (carbon-12).

Connecting Photosynthesis to $δ^{13}C$

• C4 plants have higher $δ^{13}C$ values because they take in more heavy carbon.
• C3 plants have lower $δ^{13}C$ values as they preferentially uptake lighter carbon (carbon 12).
• Archaeologists use $δ^{13}C$ to measure the presence of C4 plants like corn in different contexts.
• CAM plants (e.g., cacti) switch between C3 and C4 photosynthesis based on water availability.

Delta Nitrogen 15

• Delta Nitrogen 15 ($\delta^{15}N$) : Proxy for trophic scale.
• Tracks how high or low an organism is on the food chain.
• Organisms preferentially excrete light nitrogen (nitrogen-14). The body retains the heavy nitrogen (nitrogen-15) for tissue building.
• Consumers accumulate heavy nitrogen, so higher trophic levels have higher $δ^{15}N$ values.
• Carbon and nitrogen are the basic elements for stable isotope analysis in archaeology.

Stable Isotope Analysis: Bone Sampling

• Take a bone sample and expose it to hydrochloric acid.
• The bone will become a collagen pseudomorph, showing only the collagen portion of the bone (organic material).
• The acid removes the inorganic material (hydroxyapatite).
• Clean the collagen, extract lipids, and dry it in a freeze dryer (lyophilizer).
• Weigh a tiny piece of the dried collage using a microbalance.
• The instrument to weight this precisely costs about $23,000.

Mass Spectrometry: Counting Atoms

• Combust the sample and launch the constituent components through a flight tube with a charge (ionize).
• An electromagnet curves the flight path, separating elements by weight.
• Lighter ions hug the corner tightly, and heavier ions round the corner more loosely.
• Detectors count the elements based on their flight path.
• The number of atoms affects the per mil that is measured ($\delta^{13}C$). The higher the number of atoms, the higher the $δ^{13}C$.
• The detectors are specifically tuned for each isotope.

Isoscape Example: Bison on the Colorado Plateau

• Bison remains in the Southwest are often assumed to be traded from the plains.
• An isoscape was built using museum specimens of bison and their $δ^{13}C$ values.
• The isoscape model takes elevation into account.
• The model can predict the likelihood of samples coming from specific areas.
• Results: Haney bison specimens did not originate from the plains, suggesting local populations of bison existed.

Radiocarbon Dating: Introduction

• Martin Common discovered carbon-14 in 1940.
• Willard Libby won the Nobel Prize in 1960 for the method of radiocarbon dating.
• Radiocarbon dating relies on the half-life of carbon-14.

Radiocarbon Dating: Process

• Plants eat carbon from the atmosphere.
• Carbon-14: created naturally in the biosphere,lithosphere and atmosphere
• Cosmic radiation from the sun collides with nitrogen in the atmosphere, knocking off a proton and creating carbon-14.
• Carbon-14 combines with oxygen to form carbon dioxide.
• Plants take in carbon-14 through photosynthesis.
• Living organisms are in equilibrium, theoretically, with the environment, and when an organism dies, it falls out of equilibrium with the environment.
• Carbon-14 decays back to nitrogen-14 through beta decay.
• Half-life of carbon-14: approximately 5,700 years.

Assumptions of Radiocarbon Dating

• Assumption 1: The concentration of carbon-14 remains constant in reservoirs through time.
• Reservoir: A spot in the environment where carbon is distributed in a very specific way.
• Types of reservoirs:
  • Terrestrial systems
  • Marine systems
  • Freshwater systems
• This is also key for pathologies. If there is a turbulent amount of C14 then the time it takes for half of it to decrease will be dependent on what you have.
• If you don't know how much carbon is supposed to be naturally in the system, then you can't know how much carbon-14 there ought to be.

Fluctuations in Carbon-14 Concentration

• Ice cores are used to measure carbon isotope values in the atmosphere through time.
• The industrial revolution caused a drop in carbon-13 levels due to the burning of fossil fuels.
• Correcting for these changes in atmospheric carbon levels is crucial for accurate dating.

Radiocarbon Dating: Example

• Living things current have 100 carbon-14 atoms in their tissues.
• An archaeological sample has 75 carbon-14 atoms.
• Half-life is 5,700 years.
• The sample is 2,850 years old (half of a half-life or $5700/2$).

Calibration Curves

• The amount of radiocarbon is tracked with the tree rings.
• Trees put on things every single year reliably or somewhat reliably.
• Radiocarbon years typically underestimate calendar years.
• Calibration curves, such as IntCal20, are used to correct radiocarbon dates.
• Calibration curves show the relationship between calendar years and radiocarbon years.
• Paul Reimer created IntCal20.