Radioactive Decay and Half-Life: Carbon-14 Lab Report
This laboratory report investigates the principles of radioactive decay and half-life through a simulated experiment using Carbon-14 and Uranium-238 isotopes. The study examines how half-life remains constant regardless of sample size, calculates decay constants and rates of decay for each isotope, and applies radiocarbon dating to estimate the ages of six artifact samples — including a living tree, animal skull, wooden cup, bone, fish bones, and a rock. Results confirm that half-life is determined solely by nuclear configuration, that Uranium-238 decays more slowly than Carbon-14, and that carbon concentration decreases predictably with sample age.
- Introduction: Background theory on radioactive decay and carbon-14 dating
- Materials and Methods: Simulation steps and data collection procedure
- Data: Tables of Nt values, decay rates, and artifact ages
- Discussion: Interpretation of half-life constancy and carbon dating results
- Conclusion: Summary of findings against lab objectives
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What makes this paper effective
- Clearly states two focused objectives at the outset and returns to both in the conclusion, giving the report a coherent frame.
- Presents data in well-organized tables and interprets each table systematically in the discussion, linking observations back to underlying nuclear physics principles.
- Draws explicit connections between theoretical concepts (half-life independence from mass, nuclear proton/neutron configuration) and empirical simulation results.
Key academic technique demonstrated
The report exemplifies the scientific lab-report format: it moves logically from background theory and equations through a step-by-step methodology, raw data tables, interpretive discussion, and a summary conclusion. Quantitative reasoning is foregrounded throughout — decay constants and rates are calculated from first principles using the half-life equations introduced in the introduction, then applied directly to artifact dating in Part Two.
Structure breakdown
The report opens with a theoretical introduction covering radioactive decay, the Carbon-14 cycle, and the half-life equation. The Materials and Methods section is divided into lab preparation, experiment execution, and two data-collection phases. The Data section presents three tables covering Nt values, decay constants/rates, and radiocarbon dating results. The Discussion interprets each table in turn, and the Conclusion synthesizes findings against the original objectives.
Introduction
This laboratory explored the concept of radioactive decay. Radioactive decay is the process by which unstable atomic nuclei undergo radiation, emitting energy and other elements in the process (Lofts & Evergreen, 2023). Materials with unstable atomic nuclei are called radioactive materials. An important application of radioactive decay is its use in dating samples to determine when organisms lived on Earth and to make predictions about environmental conditions at that time.
Carbon-14 is a radioactive isotope of carbon commonly used to estimate the age of organic material through the process of radiocarbon dating. Carbon-14 is formed in the environment when cosmic rays interact with nitrogen atoms (N) and nitrogen molecules (N₂) (Lofts & Evergreen, 2023). It undergoes rapid oxidization in the atmosphere to form carbon dioxide (CO₂). Living organisms continually replenish their carbon-14 content by exchanging carbon dioxide with the biosphere. This exchange stops when an organism dies, and its carbon-14 content begins to decline over time as it undergoes radioactive decay to form Nitrogen-14 atoms (Lofts & Evergreen, 2023). Thus, the older the artifact, the lower its carbon-14 concentration. The process of determining an artifact's age by examining its carbon-14 content is referred to as radiocarbon dating.
The number of carbon-14 atoms decaying per unit of time is referred to as the rate of radioactive decay. It is calculated using the formula:
Rate of radioactive decay = k × Nt (Equation 1)
Where Nt is the number of radioactive atoms in the sample at time t, and k is the radioactive decay constant.
The time it takes for one half of the radioactive atoms to decay is defined as the artifact's half-life (denoted as t1/2). It is calculated as:
t1/2 = ln2 / k (Equation 2)
t1/2 = 0.693 / k; where k is the radioactive decay constant.
Carbon-14 has a half-life of 5,730 years. This implies that the concentration of carbon-14 in an artifact is halved over the course of 5,730 years. This laboratory uses experimental simulation data to determine the age of sampled artifacts. It has two primary objectives:
(i) To understand the concepts of radioactive decay and half-life.
(ii) To become familiar with the half-life curve.
Materials and Methods
(i) Access the simulation environment through the "Radioactive Dating Game" tab on the course home page.
(ii) In the simulation environment, choose the "Half Life" tab and click on "Carbon-14" from the right menu.
(iii) Examine the graph that loads and record the estimated half-life.
(iv) From the bucket, select and move 10 carbon-14 atoms to the workspace to examine how many undergo radioactive decay before the half-life point. Record this number in Table 1.
(v) Repeat step (iv) with 20, 30, and 40 carbon-14 atoms.
(vi) Return to the bucket, select uranium, and move 10 atoms to the workspace. Record the estimated half-life from the graph, and record how many atoms decay before the half-life point.
(vii) Repeat step (vi) using 20, 30, and 40 atoms.
(viii) Calculate the average Nt value for both Carbon-14 and Uranium-238 and record in Table 1.
(ix) Use the half-life equation (Equation 2) to obtain the decay constant and record the values in Table 2.
(x) Using Equation 1, calculate the rate of decay for each element and record the values in Table 2.
(xi) In the simulation environment, select "Dating Game." This phase of data collection uses carbon dating to determine the age of various samples.
(xii) From the list of samples, drag the probe to the "Living Tree" sample until a dialogue box appears showing the carbon percentage in the sample. Record this value in Table 3.
(xiii) Repeat step (xii) for the remaining five samples: Animal Skull, Wooden Cup, Bone, Fish Bones, and Rock 5.
(xiv) Use the percentage of carbon present in each sample to predict the sample's age.
(xv) Prepare a report for the observations made.
Discussion
The data in Table 1 examine how half-life changes with the mass of an element. The results indicate that the half-life of both Carbon-14 and Uranium-238 remains constant regardless of the number of atoms in the sample. This confirms that half-life is independent of an element's mass. The decay process is radioactive in nature and does not depend on the element's stoichiometric properties. Half-life is determined purely by the configuration of neutrons and protons in an isotope's nucleus, which governs nuclear stability and, consequently, the probability that radioactive decay will occur.
Comparing the two isotopes in Table 2, Uranium-238 decays at a slower rate than Carbon-14 and therefore has a significantly longer half-life. This is because Uranium-238's nucleus is more stable than that of Carbon-14 and disintegrates at a lower rate.
As hypothesized at the start of the lab, the results in Table 3 indicate an inverse relationship between carbon concentration and age. Samples with lower carbon concentrations are generally older, since carbon-14 decays over time and its concentration decreases as an artifact ages after the death of the organism. The fish bone sample has the lowest carbon concentration and is estimated to be over 16,000 years old. The living tree records 100% carbon-14 concentration because living plants continually replenish their carbon-14 supply through the uptake of carbon dioxide during photosynthesis. The carbon decay process begins only when an organism dies and ceases to exchange carbon-14 with the biosphere.
Rock 5 registered 0.0% carbon remaining, making its age indeterminate using radiocarbon dating alone. This is consistent with the known limitations of the radiocarbon method: samples older than approximately 50,000 years contain too little Carbon-14 to yield a reliable date, and rocks are typically dated using other radiometric methods such as uranium-lead dating.
Conclusion
This laboratory sought to examine the concepts of radioactive decay and half-life and to become familiar with the half-life curve. The half-life of two isotopes — Carbon-14 and Uranium-238 — was estimated using different quantities of atoms of each isotope. The results showed that an isotope's half-life remained constant regardless of the mass of the tested sample, since the decay process is purely radioactive and is dictated by the configuration of protons and neutrons in the nucleus rather than by physical or stoichiometric properties. Uranium-238 exhibited a longer half-life than Carbon-14 because its nucleus has a more stable configuration and thus decays at a slower rate.
In the second phase of the experiment, the carbon content of six samples was examined and used to predict each sample's age. The results supported the hypothesis that an isotope's carbon content declines over time; older samples generally have lower carbon contents. Living samples, by contrast, maintain 100% carbon-14 content because they continuously replenish their carbon-14 concentrations from the biosphere. Decay begins only upon death, when an organism no longer participates in the global carbon cycle.
References
Lofts, G., & Evergreen, M. J. (2023). Jacaranda science quest 9 Australian curriculum (4th ed.). John Wiley & Sons.
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