Lesson Notes By Weeks and Term v4 - SHS 3
NUCLEAR PHYSICS
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NUCLEAR PHYSICS
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Subject: Physics
Class: SHS 3
Term: 1st Term
Week: 2
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 will learn how scientists can act like detectives, using the predictable decay of radioactive atoms to determine the age of ancient objects. This isn't just abstract science; it's how we know the age of fossils, ancient human settlements in Ghana like the Kintampo culture, and how we can understand the history of our planet. By understanding this "atomic clock," we can unlock secrets from the past. We will focus on the most famous method, Carbon-14 dating, and learn the calculations involved.
A. The Foundation: Radioactivity and Half-Life Radioactivity: The spontaneous, random process by which an unstable atomic nucleus loses energy by emitting radiation (alpha particles, beta particles, or gamma rays). This process is also called radioactive decay. Half-Life (T½ or T): The time taken for half of the radioactive nuclei in a given sample to decay. This is a constant value for each specific radioactive isotope. It does not matter how much of the substance you start with; after one half-life, 50% will remain. Analogy: Imagine you have a bowl of 100 pieces of Gari. The half-life is 1 minute. After 1 min (1 half-life), you will have 50 pieces left. After 2 mins (2 half-lives), you will have 25 pieces left. After 3 mins (3 half-lives), you will have 12.5 pieces left (conceptually). The key takeaway is that the decay is exponential, not linear. 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: Cosmic rays from space strike nitrogen-14 (¹⁴N) atoms in the upper atmosphere, converting them into carbon-14 (¹⁴C). ¹⁴N + n → ¹⁴C + p Absorption by Living Things: This radioactive ¹⁴C combines with oxygen to form carbon dioxide (CO₂). Plants absorb this CO₂ during photosynthesis. Animals 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 ¹²C in its body remains constant and is the same as the ratio in the atmosphere. The Clock Starts: When the organism dies (e.g., a tree is cut down, an animal dies), it stops taking in new carbon. The stable ¹²C remains, but the radioactive ¹⁴C begins to decay back into ¹⁴N through beta decay, with a half-life of approximately 5,730 years. ¹⁴C → ¹⁴N + e⁻ + ν̅ₑ (Beta decay) Measuring the Age: By measuring the remaining ratio of ¹⁴C to ¹²C in a sample (like a bone, piece of wood, or charcoal) and comparing it to the original atmospheric ratio, scientists can calculate how long ago the organism died. C. The Mathematics of Radioactive Decay
The law of radioactive decay can be expressed using the concept of half-life.
Let: N₀ = Initial number of radioactive nuclei (at time t = 0) N(t) = Number of radioactive nuclei remaining at time t t = time elapsed T = The half-life of the isotope n = number of half-lives that have passed (n = t/T)