# Half-life

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## Objective

Students will be able to solve problems related to half-life.

#### Big Idea

Half-life, the amount of time it takes for one half of a radioactive substance to decay, varies for different isotopes.

## Introduction

Unit Overview: This unit, called Passion, Power, and Peril, is an inter-disciplinary unit between two classes—English and Chemistry. In Chemistry class, students will learn about nuclear chemistry, but they will also research a specific aspect of the nuclear power industry. They will use this research in three ways. First, they will write a one-page paper for a Chemistry grade that explains how nuclear chemistry connects to the research topic. Second, students will write an informative/explanatory research paper that answers your research question by showing the complexity of the issue for an English grade. Finally, students will use their research and writing to create a piece of artwork for a multimedia art display designed to challenge the audience with weighing the costs and benefits of nuclear technology.

In this process we would like students to consider the following questions: How does society evaluate costs and benefits of a technology?  What are the costs and benefits of nuclear power plants?

Lesson Overview: In this lesson students will be able to explain what half-life is and how it is used to calculate problems involving mass and time.

This lesson aligns to the NGSS Disciplinary Core Idea of HS-PS1-8. Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decay because it shows how changes in a sample of atoms occur over time.

It aligns to the NGSS Practice of the Scientist of Using mathematics and computational thinking because students are required to approach half-life problems from different perspectives.

It aligns to the NGSS Crosscutting Concept of Stability and Change because half-life  is about how rates of change can be quantified and modeled over very short or very long periods of time.

In terms of prior knowledge or skills, students should have a basic understanding of radioactivity and nuclear decay as found in this lesson and this lesson.

There are no special materials needed for this lesson.

## Do Now/Activator

10 minutes

Do Now: I start class by asking students to make some observations at their tables about a bar graph that shows nuclear decay over time, and a table that shows the half-lives of various elements.

I reason that this is a good way to start class because I want students to start thinking about both the diminishing of a sample over time, but also the fact that the rate varies depending on the substance.

Activator: I then tell students that we are going to learn how people can tell how old an Egyptian mummy is, and show this video about carbon dating.

I have chosen this approach because I want students to see that half-life has real world applications, of which dating objects is but one. I find that this video engages students and leads to interesting conversations. One student started a conversation about the Bible and how it contradicts what science tells us. (I discuss the Bible as allegory and am happy that I have him thinking about things).

## Mini-lesson and Guided Practice

15 minutes

Mini-lesson: I begin the lesson by explaining that there are certain things students should look for when solving half-life problems. They should identify any masses that are given, the half-life of the substance in question, and any times that are given. I note that a t-chart is a useful tool for solving simple half-life problems, and that time and mass should comprise the two columns. I use this information then to solve the first half-life problem from the Half-Life Problems for classwork.

Guided Practice: I ask students whether they understand what I have presented. They respond affirmatively, so I ask them to try to do the next problem.

I chose this particular focus so that each student can check for their own understanding, and then ask questions. Sometimes getting stuck is a great way to learn because it creates an opportunity to get unstuck.

Once students have had a chance to work the problem, I ask for a volunteer to explain his work, as shown in this video where a student explains the solution to half-life problem #2.

## Application

25 minutes

Student Activity: During this time students work on half-life problems. I circulate around the room and encourage them. Because this new and there is not an obvious way for them to check their work, I find myself letting students know that they are doing their work correctly a lot.

Catch and Release Opportunities: One of the more interesting problems involves a medical isotope with a short half-life. I model what working with such a substance might look like in the work place. I pretend to go to the reactor and pick up the isotope. However, on my way back to the procedure room I run into an old friend and get to talking. By the time I get back to the procedure room all of my radioactive isotope has converted into a useless substance. I then remind students that half-lives can be measured in milliseconds or billions of years.

## Debrief

10 minutes

To wrap this lesson up I review with students some things that they need to look for when solving half-life problems:

• any masses that are given
• the half-life of the substance in question,
• any times that are given

I note that the t-chart should have time in multiples of the half-life, and the mass dividing in half at each half-life. I assign Half-life homework problems so that students have more of an opportunity to practice.