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.
References
Lofts, G., & Evergreen, M. J. (2023). Jacaranda science quest 9 Australian curriculum (4th ed.). John Wiley & Sons.
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