# How to graph potential energy for 2 atoms in diatomic molecule w/ 3 unknowns

• collin2012
In summary, the conversation discusses finding the force F(r) on one atom in a diatomic molecule, represented by the potential energy function U(r)=a/r^12 - b/r^6. The equation for F(r) is derived to be (12a/r^13) - (6b/r^7), but the values of a and b are unknown. The conversation also mentions creating graphs for U(r) and F(r) versus r, but without knowing a and b, it is difficult to do so. It is noted that U(r) is a simplified version of the Lennard-Jones potential, but the process of obtaining the graph is still unclear. Further explanation is requested.
collin2012

## Homework Statement

The potential energy of two atoms in a diatomic molecule is approximated by

U(r)=a/r^12 - b/r^6,

where r is the spacing between the atoms and a and b are positive constants.

Find the force F(r) on one atom as a function of r.

Make two graphs one of U(r) versus r and one of F(r) versus r.

F(r) = -(dU/dr)

## The Attempt at a Solution

I know F(r) = -(dU/dr).

So, F(r) = (12a/r^13) - (6b/r^7)

And then I get stuck. I don't know how to make a plot of U(r) vs r and F(r) vs r when I don't know a and b.

I want to plug values of r=[0.1, 0.2, 0.3, ...] into the F(r) equation, but I have no idea what to do about a and b.

This question has been asked before on this forum and I have looked at the hints, but I am still completely lost.

Could someone please get me pointed in the right direction.

Thanks.

So I figured out that U(r) = a/r^12 - b/r^6 is a simplified version of the Lennard-Jones potential and I know what the graph looks like now, but I still don't understand how you get it. I am so lost. Could someone please explain. Thanks.

## 1. How do I determine the potential energy for a diatomic molecule with 3 unknowns?

To graph the potential energy for a diatomic molecule with 3 unknowns, you will need to use a mathematical model such as the Morse potential or the Lennard-Jones potential. These models take into account the distance between the two atoms, the strength of their interaction, and any other relevant parameters to calculate the potential energy.

## 2. What is the purpose of graphing potential energy for a diatomic molecule?

The potential energy graph allows us to visualize the interactions between the two atoms in a diatomic molecule. It helps us understand the stability and potential energy changes as the distance between the two atoms changes.

## 3. How do I determine the unknown parameters for the potential energy graph?

The unknown parameters can be determined through experimental data or by using theoretical calculations based on the properties of the atoms in the molecule. These parameters can also be adjusted to fit the experimental data more accurately.

## 4. Can the potential energy graph predict the behavior of a diatomic molecule?

Yes, the potential energy graph can predict the behavior of a diatomic molecule by showing the energy changes as the distance between the two atoms changes. It can also help determine the bond strength and stability of the molecule.

## 5. Are there any limitations to graphing potential energy for a diatomic molecule?

One limitation is that the potential energy graph only considers the interactions between two atoms and does not take into account the influence of other molecules or external factors. Additionally, the accuracy of the graph may be affected by the assumptions and simplifications made in the mathematical models used.

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