How Much Energy is Needed to Separate Two Atoms in a Vibrational State?

[PolyFX]

Homework Statement

This question seems like it should be really simple but I just can't figure it out.

This diagram is the potential energy curve for the interaction of two neutral atoms. the heavy solid horizontal line indicates the two atoms are in a vibrational state.

What minimum (positive) amount of energy must be supplied to cause these two atoms to separate?

Homework Equations

Kf + Uf = Ki + Ui == > Conservation of Energy?

The Attempt at a Solution

I got the previous parts of the question correct. It asked to find K, U and K+U at the point r1.

I really don't know how to solve this part however. I know that at the minimum (lowest) point on the potential energy graph the force between the two atoms is zero. This would mean that they are neither repelling nor attracting right? Do i need to incorporate this somehow in this question?

 

[Delphi51]

Likely "separate" means to move far apart where the interaction energy is zero. Just look at the graph and see how much must be added to bring the energy up to zero.

 

[kerimek]

Yes, you are correct in thinking that at the minimum point on the potential energy graph, the force between the two atoms is zero. This means that they are in a stable equilibrium state where they are neither repelling nor attracting each other.

To determine the minimum amount of energy required to separate the atoms, we need to consider the total energy of the system. This includes both the kinetic energy (K) and the potential energy (U) of the atoms.

Based on the conservation of energy equation you provided, we can say that the initial energy (Ki + Ui) of the system must be equal to the final energy (Kf + Uf) of the system. At the minimum point on the potential energy curve, the potential energy (Uf) is at its lowest value, which we can assume to be zero. This means that the final energy (Kf + Uf) is equal to just the kinetic energy (Kf).

To separate the atoms, we need to supply enough energy to overcome the attractive forces between them and increase their kinetic energy. This means that the final kinetic energy (Kf) must be greater than the initial kinetic energy (Ki). Therefore, the minimum amount of energy required to cause the atoms to separate is equal to the difference between the final and initial kinetic energies (Kf - Ki).

In summary, the minimum amount of energy required to cause the two atoms to separate is equal to the difference between the final and initial kinetic energies, which can be calculated using the conservation of energy equation.