Radioactive Decay and Radiocarbon Dating - lect 2

Radioactive Decay Types

  • Alpha Decay:

    • An element emits a helium nucleus (2 protons and 2 neutrons), equivalent to a Helium-2 plus atom (He^{2+}).

    • The equation must balance; totals on each side must be equal.

    • Example:

      • Parent Nucleus: ^{241}{92}X !\longrightarrow ! ^{237}{90}Y + ^4_2He

      • ^{241}{92}X (Thorium) decays into ^{237}{90}Y plus an alpha particle (^4_2He).

      • The number of protons (bottom number) must be the same on both sides of the equation. 92 = 90 + 2

      • The number of protons and neutrons added together (top number) must also balance. 241 = 237 + 4

      • Alpha particle decay releases two protons, the atom drops down by two.

  • Beta Decay:

    • A neutron in the nucleus is converted into a proton and an electron.

    • Neutron (^10n) deteriorates into a proton (^11p) and an electron (e^-, or \beta^--particle)

    • Equation: \ ^10n \longrightarrow \ ^11p + \ ^{-1}e or \ ^10n \longrightarrow \ ^11p + \ _{-1}^0\beta (Beta-minus decay).

      • The electron is denoted as \ ^{-1}e to balance charge (0 = 1 + (-1)).

      • The electron (e^-) has effectively zero mass (^0 at the top).

    • Carbon-14 Decay:

      • Carbon-14 (^{14}C) is important for isotopic dating.

      • Carbon has 6 protons (atomic number 6); Carbon-14 has 8 neutrons (6 + 8 = 14).

      • Carbon-14 undergoes beta-minus decay:

      • ^{14}6C \longrightarrow \ ^{14}7N + \ ^{-1}e

      • Carbon-14 becomes Nitrogen-14 by emitting an electron (\beta^--particle also known as e^-).

      • Since an electron is given off (-1 at the bottom), the atomic number increases by 1 (6 becomes 7) to balance the equation.

      • Nitrogen (N) has 7 protons and 7 neutrons in this case.

  • Positron Emission (Beta-plus Decay):

    • A proton deteriorates into a neutron plus a positive electron (positron).

    • Equation: \ ^11p \longrightarrow \ ^10n + \ ^1e or \ ^11p \longrightarrow \ ^10n + \ _{+1}^0\beta (Beta-plus decay).

      • A positive electron is denoted as \ ^1e

      • Example: Copper-64 decaying to Nickel

        • Parent Nucleus: ^{64}{29}Cu \longrightarrow \ ^{64}{28}Ni + \ ^0_1e. Number of protons goes down by one.

        • Copper (Cu) has 29 protons; copper-64 has 35 neutrons. 29 + 35 = 64

        • Giving off a positive electron reduces this number by 1 (29 -1 = 28), resulting in Nickel (Ni).

  • Electron Capture:

    • The nucleus of an atom captures an electron.

    • Equation: \ ^11p + \ ^{-1}e \longrightarrow \ ^10n

    • An electron interacts with a proton to produce a neutron.

    • Example: Potassium-40 (important for dating prehistoric materials).

      • ^{40}{19}K + \ ^{-1}e\longrightarrow \ ^{40}{18}Ar + X-rays

      • Potassium (K) has 19 protons.

      • After capturing the electron, it becomes Argon (Ar) with 18 protons.

      • Used for dating prehistoric materials due to very long half life.

  • Multiple Decay Processes:

    • Some compounds undergo multiple decay processes with specific probabilities (e.g., 80% beta decay, 20% positive emission).

    • These probabilities are generally not influenced by the environment.

    • Potassium-40, for instance, has different decay processes to adjust for in calculations when dating these compounds

  • Gamma Emission:

    • An unstable compound releases gamma radiation.

  • Spontaneous Fission:

    • Very unstable, heavy elements may spontaneously decompose into other metals and neutrons.

Isotopes of Carbon

  • There are three naturally occurring isotopes of carbon:

    • Carbon-12 (^{12}C): Makes up 99% of total carbon. 6 protons and 6 neutrons.

    • Carbon-13 (^{13}C): Approximately 1% of total carbon. 6 protons and 7 neutrons.

    • Carbon-14 (^{14}C): Trace amounts. 6 protons and 8 neutrons.

    • All isotopes of carbon has 6 protons

Radiocarbon Dating

  • Process:

    • Carbon-14 (^{14}C) is produced in the atmosphere through two main processes:

      • Naturally Occurring Process:

        • Cosmic rays interact with atoms in the atmosphere. Very high energy cosmic rays releasing neutrons.

        • Neutrons interact with Nitrogen-14 (^{14}N):

        • ^{14}7N + \ ^10n \longrightarrow \ ^{14}6C + \ ^11H

        • Neutron captured by Nitrogen-14 (^{14}N) to make Carbon-14 (^{14}C) and Hydrogen.

      • Nuclear Reactions:

        • Nuclear weapons testing and nuclear power stations also produce Nitrogen-14.

  • Incorporation into the Ecosystem:

    • Carbon-14 oxidizes to carbon monoxide (CO) and then to carbon dioxide (CO_2).

    • Carbon dioxide is absorbed by plants and animals.

    • Living organisms maintain a constant ratio of C-12, C-13 and C-14.

  • Dating:

    • Carbon-14 has a half-life of approximately 5,730 years.

    • Willard Libby won the Nobel Prize for pioneering radiocarbon dating.

    • Useful dating range: up to approximately 55,000 years (about 10 half-lives).

  • The Process Starts When An Organism Dies:

    • When an organism dies, it stops absorbing carbon 14, and the carbon 14 begins to decay.

    • After an organism dies is the origin of the decay.

    • With each 5730 years half of that carbon 14 will deteriorate.

  • Decay Process:

    • Carbon-14 decays back to Nitrogen-14 by emitting a beta particle (electron).

    • ^{14}6C \longrightarrow \ ^{14}7N + \ ^0_{-1}e (Beta Decay)

    • By measuring remaining carbon 14, its possible to determine the age and the original Carbon amount.

  • This is the equation for representing the amount of radiactivity of carbon-14, where N_0 the value when it actually dies and then the amount of carbon 14 will decay irrespective of the environment follows this curve exactly.

    *   N(t) = N_0 e^{-\lambda t}
   * t is the time elapsed since the death of the organism
   * \lambda is the decay constant, related to the half-life (T_{1/2}) by the equation by:  \lambda = \frac{ln(2)}{T_{1/2}}
  * T_{1/2}half life equals 5,730 years.

Radiocarbon Laboratory Analysis

  • Samples are analyzed through these steps

    • Sample Preparation:

      • Materials include: wood, plant remains, charcoal, bone, leather, etc.

      • Excludes geological materials (stone, glass) and samples beyond the dating range.

  • Chemical Cleaning:

    *   Isolate carbon from the sample, excluding external contaminants.
*   Washing with organic solvents to remove greases and fats.

  • Conversion to Carbon Dioxide (CO_2):

    *   Solid sample converted to carbon dioxide by combustion.

  • Conversion to Graphite:

    *   Carbon dioxide is converted to graphite for measurement in the accelerator.
*   Mixing the carbon dioxide with hydrogen inside a graphite reaction vessel.
* Copper oxide will cause the solid sample to combust, to burn, and will end up at the end of the process with carbon dioxide and a little bit of water inside the combustion tube

  • Accelerator Mass Spectrometry (AMS):
    * Graphite is pressed into an aluminum target holder.
    * A caesium beam blasts the carbon out of its target holder and into the accelerator.
    * Stream of carbon ions goes through the accelerator, being bent at certain places magnets, which serve to separate out the carbon twelve, thirteen, and 14 into separate streams. The carbon twelve and thirteen are separated out at this point, and the carbon 14 continues on through the accelerator to this point where it is detected.
    * Carbon isotopes are separated and measured.

  • The accelerator measures the ratio of carbon-14 to carbon-13.

  • Radiocarbon Age Calculation:

      *   Radiocarbon age is typically reported with a plus or minus error range to indicate the range in which carbon age can fall into.
   *   Calibration converts radiocarbon age to calendar age range, accounting for variations in atmospheric carbon-14 levels.

  1. What happens during alpha decay, and how does it affect the parent nucleus?

  2. Explain the process of beta decay, including beta-minus and beta-plus decay.

  3. How is Carbon-14 used in isotopic dating, and what happens during its decay process?

  4. Describe positron emission and provide an example of an element undergoing this type of decay.

  5. What occurs during electron capture, and how does it change the atomic number of the element?

  6. Give examples of multiple decay processes and explain what influences their probabilities.

  7. List the three naturally occurring isotopes of carbon and their respective abundances.

  8. Outline the natural and nuclear processes through which Carbon-14 is produced in the atmosphere.

  9. Explain how living organisms incorporate Carbon-14 and how this process changes upon death.

  10. What is the half-life of Carbon-14, and what equation is used to determine the age of a sample using radiocarbon dating?

  11. Describe the sample preparation and chemical cleaning steps involved in radiocarbon laboratory analysis.

  12. How is a solid sample converted to carbon dioxide and then to graphite in radiocarbon dating?

  13. Explain the Accelerator Mass Spectrometry (AMS) process and its role in measuring carbon isotopes.

  14. How is radiocarbon age calculated and calibrated to calendar age range?