Debay radius and the existence of metals

[belarus]

Our lecture on the Physics of Solid State raised a question. Professor postulated that the condition of the existence of metals is "Debay radius<Bohr radius", but the explanation was quite unclear. Could someone help me?

 

[marlon]

Isn't it the Debye length ?

http://scienceworld.wolfram.com/physics/DebyeLength.html
http://en.wikipedia.org/wiki/Electric_field_screening
marlon

 

[ZapperZ]

Our lecture on the Physics of Solid State raised a question. Professor postulated that the condition of the existence of metals is "Debay radius<Bohr radius", but the explanation was quite unclear. Could someone help me?

You did not give enough information here, so I will make a series of assumption of what I THINK you're asking:

1. Debay = Debye.

2. Debye radius = Debye length

The definition of Debye length is the length in which mobile charge carriers screen out the external electric field. This applies especially in a plasma.

3. Your prof. is trying to illustrate the fact that in a Fermi gas in a typical metal, if the Debye length is shorter than the Bohr radius, it means that the potential from the ion core is being screened out by the rest of the charge carriers in the solid. Thus the valence electron (or electrons) will not be attracted (on average) to its parent ion core and able to be "free" and join the conduction band.

Zz.