Metallic bond

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When individual atoms bond to form a metal lattice, the total energy decreases, but does the kinetic energy of the electrons increase or decrease? What about the potential energy? Does it increase due to pauli exclusion or decrease due to the decrease in distance between the ion and electron? Thanks a lot!
 

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Kinetic energy goes up when atoms bond. If you think of it from a tight-binding perspective, as atoms move closer together the overlap of the electron's wavefunctions increase, which increases the ability for the electrons to hop from one atom to another.

Potential energy will both increase due to Pauli exclusion and decrease due to the decreasing the ion-electron distance. When going from isolated atoms to bonded atoms, the ionic attraction wins over Pauli exclusion. But if you increase pressure and compress the system, then the increasing kinetic energy and exclusion principle will increase the total energy more the electrostatic potential will decrease it.
 
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Mapes
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But if you increase pressure and compress the system, then the increasing kinetic energy and exclusion principle will increase the total energy more the electrostatic potential will decrease it.
This part doesn't seem right. If the energy is higher in the bonded state than the unbonded state due to increased pressure, then the metal will turn into a gas. Can you give an example of this happening?

Increasing the pressure should favor the formation of solid bonds, rather than the reverse. That is, the decrease in electrostatic potential energy should always win out.
 

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