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SAM E1 Model 1
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The Potential Energy of Two Atoms
Any time there is force that depends only on the distance, there is a potential energy.
How does the the potential energy between atoms depend on distance?
Potential energy is the energy of position and is always related to a force. Gravitational potential exists because of the force of gravity. A spring can have potential energy if a force has been applied to stretch or compress it. An atom has potential energy because of the Lennard-Jones force.
Potential energy is a very powerful concept. It provides a shortcut for solving problems and leads to deeper understanding of complex systems.
The model below makes a graph of the potential energy of the red atom as a function of its distance from the green atom.
One again, the green ball is nailed down and the red ball is free to move back and forth in the blue region.
Do this:
Before running the model, predict what the graph will look like.
Run the model.
Use the "tape" controls below the model to explore the relationship between the model and the graph.
Take a snapshot of the graph. (Use the camera icon in the menubar.)
Show on the snapshot where on the graph the force is a) repulsive, b) zero, and c) attractive.
Show on the snapshot where the force is greatest and weakest.
The potential energy curve you have calculated is so important, it has a name: the Lennard-Jones potential.
The Lennard-Jones potential has an attractive part and a repulsive part.
Between the attractive and repulsive parts, there is a minimum where there is no force.
Be sure you can point out where the attractive, repulsive, and no-force parts are.
Some important points about energy units:
We use electronvolts (eV) as the unit of energy.
This is defined as the energy required to move an electron against a one-volt potential difference.
In a common 1.5 V battery, every electron going through the battery picks up 1.5 eV of energy.
An eV is tiny amount of energy equal to about 1.6 x 10^19 Joules or .16 aJ.
Some important points about potential energy (PE):
PE for atoms is defined as zero when they are far apart.
The PE becomes negative when there is an attractive force.
That 10^-3 in the upper corner of the graph tells you to divide the values by 1000. So, 400 indicates 0.4 eV.
The vertical axis on the graph runs from -0.7 eV to 0 eV.
Challenges:
Next, explore a skateboard model to see how potential and kinetic energies are related
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Place your snapshot of PE here.
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What is the smallest energy recorded on your graph?
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Start the red atom from rest closer to the green one. Try starting at 8, 7, and 6 Angstroms. Take snapshots of your results. Write below three conclusions from your experiments.
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1. Part of the same potential energy curve is graphed.
2. The atom always has negative PE.
3. The atom is trapped.
4. The atom can only climb as high on the curve as its starting point.
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Try starting the atom using the "High Speed Start" button. How does this change the potential energy?
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No. PE depends only on position.
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