What is the difference between a conduction and valence band ? How an electron will behave different in conduction and valence bands ? When an electron leaves an atom the atom becomes ion. Does it mean that during conduction those atoms become ions whose electrons are taking part in conduction ? Are free electrons are electrons which take part in conduction ?
One has to keep in mind that electrons and atoms belong to the realm of quantum mechanics.
In quantum mechanics one has possible solution of the appropriate QM equations with the correct boundary conditions and potentials. Some are approximate models,like the band theory for solids, but they have been very successful in describing and predicting the behavior of solid state matter built up in lattices.
The basic premise in the band theory is that the whole ensemble of mocules and atoms are in one quantum mechanical state, where some of the electrons are bound to the atoms/molecules in the lattice positions, and some are shared by the whole lattice.
What is the difference between a conduction and valence band ?
The assignment of mobility to the higher energy levels of the lattice solution, as in the image.
How an electron will behave different in conduction and valence bands ?
Because the electron in the valence band is not shared with the whole lattice but is localized at the lattice points. One has to study the mathematics to get a true understanding.
When an electron leaves an atom the atom becomes ion.
That is true for free atoms.
Does it mean that during conduction those atoms become ions whose electrons are taking part in conduction ?
Handwaving: the atom shares the conduction electrons that leave its neighbors in the lattice.
Are free electrons are electrons which take part in conduction ?
There are no free electrons in a solid. Just some electrons are bound by the whole solid lattice and shared with the atoms/molecules (conduction band) and the rest are localized at the lattice site of the atom (valence).
Firstly, valance band and conduction bands are a part of the electronic band structure ans so not defined for a single atom.
When the valance electron of an atom is removed , the atom is said to be ionized. But the same structure of orbitals is not defined for a molecule or in this case a crystal lattice of the metal.
Similar to the MO theory where molecular orbitals are formed, here too we have a huge number of energy levels. But, from a farther view we see that the levels can be grouped into energy bands. Then, we define valance and conduction bands accordingly.
So the valance band here is not the same as a valance electron for a single atom. They are terms of two different cases and theories.
First, the Fermi level is chemical potential for electrons, of a body is a thermodynamic quantity, it is the work required to add an electron to the body.
In solid state physics, the valence band and conduction band are the closest to the Fermi level and determine the conductivity of the solid.
In non-metals, the valence band is the highest level of energies at which the electrons are present at absolute zero temperature. The conduction band is the lowest level of vacant electronic states.
The valence band is located below the Fermi level, and the conduction band is above it. This is not important in metals, where conduction occurs in one or more partially filled bands, taking on the properties of both the conduction and valence bands.
A band gap in a solid is where no electron energy levels can exist.
The shade follows the Fermi Dirac distribution, black is all states filled, white is no states filled. In metals, the Fermi level lies inside at least one of the bands. In insulators the Fermi level is inside the band gap. In semiconductors, the bands are near, and the Fermi level is thermally populated by electrons or holes.
Now your question of free electrons, a metal consists of a lattice of atoms, and their outer shell of electrons can freely dissociate from their parent atoms and travel through the lattice. This sea of dissociable electrons allows the metal to conduct electric current.