Unit #1

Activity 6
It Takes Two to Tango: Modeling Two Atoms in a Box

Activity Overview

Collisions between two atoms result in a transfer of kinetic energy [energy of motion] from one atom to the other, and demonstrate that the total kinetic energy of the two atoms is the same before and after the collision.

Students use Workbench software to observe and measure the interaction between two atoms. By colliding atoms and graphing their kinetic energy, they learn that total kinetic energy is conserved.

Learning Objectives

Students will:

• Predict what will happen to the kinetic energy of two atoms before and after a collision.
• Apply the rule of energy conservation to explain what happens when something seems to "loose" energy.

Conceptual Prologue

Macro-Micro Connection

The many atoms of the hot air balloon are constantly moving around and interacting. Until this point, only the behavior of a single atom has been explored. Even the tiniest visible piece of something has an uncountably large number of atoms. To better understand how the behavior of atoms can explain what we observe with our eyes, we need to study the behavior of how two atoms interact with each other. This activity will explore the simplest case - interaction between two atoms.

Other Macro connections:

• When playing pool, some or all of the energy of the cue ball is transferred to the ball being hit, causing it to slow down and the other balls to speed up or start moving. (Why don’t these balls bounce around the table forever? To what other forms of energy is the kinetic energy converted?)

Science Concepts

Energy cannot be created or destroyed. It can be transferred from one object to another or it can be converted into other forms of energy.

Collisions between atoms are 100% elastic, which means that none of their energy is converted to other forms when colliding.* This means that the total kinetic energy of the two atoms will be the same before and after the collision. Each atom may have a different kinetic energy than before the collision, but if one atom gained energy, the other lost energy, leaving the total unchanged.

*Actually, during the collision, some (or all in the case of a collision in which the centers of the atoms are perfectly aligned) of the kinetic energy is converted to electrostatic potential energy before being converted back into kinetic energy. For now, the graphs of kinetic energy will not show this loss and recovery of kinetic energy. The current model has been simplified to show instantaneous changes in energy as if the atoms are made of perfectly hard spheres.

Naive Conceptions

• Energy is not conserved.

Energy is conserved as explained above.

Activity Design and Execution

Major Science Concepts:	• Kinetic energy • Conservation of energy
Assumed Previous Knowledge:	• That atoms don't convert any of their kinetic energy to other forms during collisions.
Time:	• Approximately 50 minutes
Materials:	• Computers with Workbench Software
Advanced Preparation: (if any)	• None.

Investigative Question: What happens to the kinetic energy when two atoms collide?

1. Have students use Workbench software to bring up the "Two Atoms in a Box" activity.
2. The software will then explain the controls and graph to the students (you may also want to demo this on an LCD projector if possible).
3. The software will then ask students to experiment with the model for a while and answer the following questions:
   • Make both atoms have the same mass and answer the following question: One atom always seems to give some of its energy to another atom. Which atom usually loses energy and which one gains it?
   • Make Atom A the lightest kind of atom and Atom B the heaviest. What do you notice when you compare their velocities and their kinetic energies?
   • Try to arrange a collision in which atom A and atom B each have the same energies after the collision as they had before the collision. What do you think has to be true for this to happen?
   • List two ways to set up a collision in which energy is exchanged between the atoms.
   • Is there ever any case where the TOTAL energy of the two atoms is NOT conserved (the same)? Try to see if you can make this happen.
4. Discuss their answers.
5. Explain to them that their previous model of how an atom behaves didn't include any rules on how two atoms interact. Ask them to come up with additional rules they would have to add to the model they created for how atoms work from the previous activity, in order for it to behave like the one with which they have been experimenting.

Assessment

Have students write several things in their notebooks:

1. What are the two ways something can seem to "lose" energy?
2. Things that roll come to a stop. You feel tired at the end of the day. Gasoline needs to be put into a car on a regular basis. Why do most things seem to lose energy? What happens to this energy?
3. Imagine that you could easily measure all different kinds of energy (heat, sound, kinetic, etc.) Now, let's say you dropped a rubber ball and let it bounce until it stopped, keeping track of all the energy around the ball, including the ball. Would you expect the TOTAL energy (ball and its surroundings) to be more, less or the same when comparing the beginning of the experiment to the end of the experiment? Why?
4. In the last activity you described the rules necessary for a model of one atom bouncing around in a box. Take out that piece of paper and add some new rules. Now that we have two atoms, what new rules are necessary for the model to describe how two atoms interact with each other?

Internal Notes:
• See computer lab B for the mock up of this activity.