Dissociation Energy (Modern physics)

[Pedro Roman]

Homework Statement

Hello, the question is, does the binding energy of a molecule is greater than or equal to the dissociation energy?

Homework Equations

A molecule exists because its energy is less than that of the system of separate noninteracting atoms:

Mc²∠Ʃ m_i c²

Here M is the mass of the molecule, m_i is the mass of the ith atom constituting the molecule, and c is the speed of the light.

The total potential energy U of two atoms the system often approximated by the expression

U = -A/rⁿ + B/r^m

where r is the intermolecular separation distance between the two atoms, A and B are constant, and n y m are small integers.

The Attempt at a Solution

Because the potential has an absolute minimum U_min when the intermolecular distance is small, the energy of the molecule is less than the energy of the separated atoms. This means that the energy of dissociation is -U_min, ie, when U = 0, since the atoms before forming molecule were far away from each other, the energy was larger than zero, therefore dissociation energy is less than the binding energy. Is my reasoning correct?

Thanks a lot.

 

[mark726]

Your reasoning is partially correct. The binding energy of a molecule is indeed greater than the dissociation energy, but not for the reason you have stated. The binding energy of a molecule is the difference between the total energy of the molecule and the energy of its separated atoms. This includes both the potential energy and the kinetic energy of the atoms.

The dissociation energy, on the other hand, is the energy required to break the bonds between the atoms and separate them completely. This only takes into account the potential energy of the atoms, as they have no kinetic energy when they are separated.

Therefore, the binding energy will always be greater than the dissociation energy, as it takes into account both the potential and kinetic energy of the atoms in a molecule.

I hope this helps clarify the difference between the two energies. Let me know if you have any further questions.