The Mystery of Free Electron Theory

[photon79]

In free electron theory, electron doesn't feel any potential due to ions r co-electronsm they r totally free..then why don't they fly off from the metal boundaries?

 

[ZapperZ]

In free electron theory, electron doesn't feel any potential due to ions r co-electronsm they r totally free..then why don't they fly off from the metal boundaries?

Because:

1. Free electron picture is only an approximation.

2. "Free electron" doesn't necessarily mean V=0, but rather V = constant with the boundary very, very far away.

Zz.

 

[Gokul43201]

In addition (whether it's the Drude model or any of the more sophisticated models that followed), the theory tends to not venture into what happens near sample boundaries. Things often get too complicated to calculate easily when you are near a boundary.

A little further down in your study, you'll see the the idea of a sample boundary is conveniently done away with by imposing a (periodic) boundary condition that treats the sample as if it were devoid of boundaries.

Coming back to original question, the reason that the electron doesn't fly off the boundary can be separately explained in terms of a large boundary potential, known as the work function. However, the theory does not worry about the effect of this potential on the interior electrons, as they are sufficiently far away from it. The number of electrons "near" the surface, at any point of time is neglected with respect to the total number of electrons. This is not a bad approximation to make.

 

[armandowww]

A little further down in your study, you'll see the the idea of a sample boundary is conveniently done away with by imposing a (periodic) boundary condition that treats the sample as if it were devoid of boundaries.

Coming back to original question, the reason that the electron doesn't fly off the boundary can be separately explained in terms of a large boundary potential, known as the work function. However, the theory does not worry about the effect of this potential on the interior electrons, as they are sufficiently far away from it. The number of electrons "near" the surface, at any point of time is neglected with respect to the total number of electrons. This is not a bad approximation to make.

Born and von Karmann thought of this in an astonishing way (conditions for which wave function of the electron is a Bloch electron)... They also understood how to complete the Debye adjustment to the Einstein model for specific heat of a lattice at any temperature (as well as it lies beneath melting point)!
Born-von Karmann boundary conditions hold near always... let be enough boundary particles are very little compared with bulk ones:
in a fraction of mole of matter you have 10^21 circa lattice sites. Think if you have a simple cubic package... Trust in me... you'll find a so vanishing percent of atom on the surface then you feel embarrassment!
armando

 

[Modey3]

A little off topic, doesn't the basis of thermionic emission involve electrons hopping off the boundaries when the material is heated ?

Modey3

 

[ZapperZ]

A little off topic, doesn't the basis of thermionic emission involve electrons hopping off the boundaries when the material is heated ?

Modey3

Not exactly sure what you mean by "hopping off the boundaries", but thermionic emission is essentially electrons tunneling off the metal across the work function barrier. It is similar to field emission, but due to the large spread in the Fermi function at very high temperature, the electrons has an easier time escaping through the barrier.

Thermionic emission process is sufficiently described by the Richardson-Dushman model.

Zz.