Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define half-life and decay constant.
• Calculate the half-life of a radioactive sample.
• Explain the significance of half-life in real-world applications.
• Solve problems related to half-life and radioactive decay.

Lesson summary

This lesson introduces the fundamental concept of half-life, a cornerstone of nuclear physics. We will explore how radioactive substances decay over time in a predictable way. Understanding half-life is not just for physicists; it has critical applications in medicine for treating diseases like cancer right here in Ghana (e.g., at Korle Bu Teaching Hospital), in archaeology for dating ancient artifacts from our history, and in agriculture for preserving food to reduce spoilage. We will define the key terms related to radioactive decay and learn how to perform calculations to determine the half-life of a sample.

Lesson notes

A. Introduction to Radioactive Decay

Imagine you have a large bag of "abolo" (popcorn kernels) and you start heating it. You can't predict exactly which kernel will pop at what time, but you can say with some certainty that after a minute, a certain fraction of them will have popped.

Radioactive decay is similar. An unstable atomic nucleus will spontaneously change (decay) into a more stable one by emitting radiation (alpha, beta, or gamma). We cannot predict when a *single* nucleus will decay, but for a large sample containing billions of nuclei, we can predict the *rate* of decay very accurately. B. Key Definitions Activity (A): Definition: The Activity of a radioactive sample is the rate at which its nuclei are decaying. It is the number of disintegrations (decays) per second. Analogy: If Activity is high, it's like our popcorn popping very fast. If it's low, it's popping slowly. Unit: The SI unit of Activity is the Becquerel (Bq). 1 Bq = 1 decay per second. Decay Constant (λ): Definition: The Decay Constant is the probability that a single nucleus will decay per unit time. It is a measure of how unstable a particular isotope is. Explanation: A large decay constant (λ) means a high probability of decay, so the substance decays quickly. A small λ means a low probability of decay, so it decays slowly. Unit: The unit of λ is per time, e.g., per second (s⁻¹), per minute (min⁻¹), or per year (yr⁻¹). Half-Life (T½): Definition: The Half-life of a radioactive isotope is the average time it takes for half of the original number of unstable nuclei in a sample to decay. Explanation: This is the most intuitive concept. If we start with 100g of a radioactive substance with a half-life of 10 days: After 10 days (1 half-life), 50g will remain. After another 10 days (20 days total), half of the 50g will decay, leaving 25g. After another 10 days (30 days total), half of the 25g will decay, leaving 12.5g. ...and so on. The process continues, with the amount of radioactive material halving every 10 days.

*(Teacher can sketch a similar curve on the board)* C. The Mathematical Relationship: Connecting Half-Life and Decay Constant

Evaluation guide

• Calculate the half -life of a radioa ctive sample.
• Experiential Learning
•  Let learners discuss Activity, half -life, and decay constant.
•  Assist learners in establishing the mathematical relation between half -life and decay constant.