# Homework Help: Binding energy vs Kinetic energy

1. Jul 30, 2010

### hasan_researc

1. The problem statement, all variables and given/known data

My lecturer writes the following in his lecture notes:

" There is a binding energy between the particles.
Different states can then be characterised by the kinetic energy of the particles.
For solids, k.e. << binding energy (looks like SHM)
For liquids, single bond energy < k.e. << total binding energy
For gases, k.e. >> binding energy."

My questions are

1) What is a binding energy?
2) What is a single bond energy?
3) What energies make up the 'total binding energy' in Line 4 ?

2. Relevant equations

N/A

3. The attempt at a solution

No idea!

Any help would be greatly appreciated.

2. Jul 30, 2010

### graphene

Technically, it is the energy that a system acquired as it came together. It is better understood as the amount of energy you would have to supply to separate the constituents of the system. The system could be -
a molecule (the atoms making up the molecule would be the constituents)
an atom (the electrons and the nucleus make up the system)
a solid crystal lattice
even our solar system.

If you consider an isolated NaCl molecule, the amount of energy you'll have to supply to separate Na and Cl would be the bond energy of the ionic bond.
In case of $$CH_4$$, you'll have to supply four times the C-H bond energy to separate C and H.

As you put together different molecules that make up a system, there could be inter-molecule interactions. These interactions are additional to the interaction (bonding) within the molecule.
Have you heard of van-der Walls interactions, hydrogen bonding, dipole-dipole interactions,...? All these are interactions taking place between two different molecules. As an example, the hydrogen atoms in water are weakly bonded to the oxygen atom of neighbouring molecules (this is hydrogen bonding).

3. Jul 30, 2010

### graphene

Now see if you can understand these relations for solids, liquids and gases.

4. Jul 30, 2010

### hasan_researc

"For solids, k.e. << binding energy (looks like SHM)":
Is the binding energy a single bond energy (the smallest od all binding energies)?

"For gases, k.e. >> binding energy":
Is the binding energy the total binding energy (the largest of all binding energies)?

5. Jul 31, 2010

### graphene

In solids the atoms just vibrate about their positions. All the atoms are placed very closely, and are hence highly bonded. The high binding energy would keep an atom in its place.
No, binding energy cannot be a single bond energy, it cannot be. At atom is kept in its place by several of its neighbours.

Atoms/molecules in gases are in contrast, far apart, and loosely bonded. In fact, the ideal gas theory assumes there to be no interaction among the gas atoms/molecules. They are free to roam around within the container. Are you aware of the expression for average (kinetic) energy of gas atoms? That is much higher than the vibrational energy of atoms in a solid (at the same temp.)