Electron Band Structure

Okay here's my doubt and i need help : A metal conductor has big atoms so the distance of the electrons in the outer most shell from the centre of the atom is large and hence, they tend to de attach. RIGHt or WRONG ? Next, if electrons do get deattached from the atom then a positive ion shud be formed i guess, but many people say its not true. Now my major doubt is: Do electrons that deatach from the atom (in a conductor) move freely on the surface of the conductor OR is that the electrons jump from one atom's outermost shell to the others ? * if electrons do jump then I guess the net charge of the atom will be zero and hence no ions will be formed, which is in favor of what most people say. Please help if can, i just want to know the truth :)
- Tanvir Singh Manku (age 15)
New Delhi, India

What happens is that the quantum states with sharply defined energies change as the atoms come together. Instead of having separate states on the separate atoms, you get new "band" states that are spread across all the atoms.  In a metal, the conduction electrons are in these spread-out band states. So although they aren't attached to individual atoms, there is still the same average electron density around each atom. The region around each atom stays electrically neutral. Unlike in some other materials, there aren't localized charges hopping around. These conduction electrons do not migrate to the surface, which would create a charge imbalance and increase the net energy. They are present throughout the metal.

You might wonder why the quantum states are spread out. For a quantum wave, the momentum and kinetic energy depend on how much the state changes from place to place. Thus a spread-out quantum state can have different energy than a localized one. In a simple case, take an electron near two atoms. A state with the electron wave spread symmetrically over both is more spread out and thus has lower kinetic energy than a state localized on either atom. Another type of spread-out state has the wave-function changing sign (anti-symmetric) between the atoms. Since the wave function is changing more rapidly there, it has higher kinetic energy than the localized states. In a metal, the low-energy versions of the spread-out states fill up with electrons and the high-energy ones are empty.

Mike W.

(published on 06/02/2014)