Lesson Notes By Weeks and Term v4 - SHS 2
NUCLEAR PHYSICS
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NUCLEAR PHYSICS
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Subject: Physics
Class: SHS 2
Term: 2nd Term
Week: 20
Grade code: 2.4.2.LI.3
Strand code: 4
Sub-strand code: 2
Content standard code: 2.4.2.CS.1
Indicator code: 2.4.2.LI.3
Theme: ATOMIC AND NUCLEAR PHYSICS
Subtheme: NUCLEAR PHYSICS
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This lesson explores one of the most fascinating applications of nuclear physics: radioactive dating. We often hear about archaeologists discovering ancient bones or artifacts, like those displayed at the National Museum in Accra, and declaring them to be thousands of years old. How do they know the exact age? The answer lies in the "nuclear clock" that is ticking inside these objects. We will focus on Carbon-14 dating, a powerful technique used to determine the age of organic materials.
This topic builds on our previous understanding of radioactivity and half-life. Let's start with a quick review and then dive into the details of carbon dating. A. Recap: Radioactivity and Half-Life Radioactive Decay: The spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation (alpha, beta, gamma). The original nucleus transforms into a different nucleus. Half-Life (T½): The time it takes for half of the radioactive nuclei in a given sample to decay. For example, if we start with 100g of a substance with a half-life of 10 years, after 10 years we will have 50g left. After another 10 years, we'll have 25g left, and so on. B. The Principle of Carbon-14 Dating
Carbon-14 (¹⁴C) dating is a method for determining the age of an object containing organic material. Creation of Carbon-14: High-energy cosmic rays from space strike nitrogen-14 (¹⁴N) atoms in the upper atmosphere, converting them into carbon-14 (¹⁴C) atoms, which are radioactive. `¹⁴N + neutron → ¹⁴C + proton` Incorporation into Living Things: This radioactive ¹⁴C combines with oxygen to form carbon dioxide (CO₂). Plants absorb this CO₂ during photosynthesis. Animals then eat the plants (or other animals that eat plants), incorporating ¹⁴C into their bodies. Constant Ratio: As long as an organism is alive, it continuously exchanges carbon with the environment. Therefore, the ratio of radioactive ¹⁴C to stable carbon-12 (¹²C) in its body is nearly the same as the ratio in the atmosphere. The Clock Starts at Death: When the organism (e.g., a tree, an animal, a person) dies, it stops taking in new carbon. The stable ¹²C in its remains stays constant, but the radioactive ¹⁴C begins to decay back into nitrogen-14 through beta decay, with a half-life of approximately 5730 years. `¹⁴C → ¹⁴N + β⁻ + antineutrino` Measuring the Age: By measuring the remaining ¹⁴C/¹²C ratio in a sample (like a bone or a piece of wood) and comparing it to the ratio in a living organism, scientists can calculate how long the organism has been dead. The less ¹⁴C found, the older the sample. C. The Mathematics of Radioactive Dating
We use two main formulas to perform these calculations.
Formula 1: The Half-Life Fraction Method (for simple cases)