Confusion about ionised atom, free electron, conduction band, donor energy level and acceptor energy level I have some confusion about the concept of some electronic bands and energy levels. Beyond valance band,
For an atom, can having at least one electron in the conduction band mean that the atom has been ionised?
Can having an electron in the donor energy level or acceptor energy level mean that the atom has been ionised?
Is free electron same as an electron in the conduction band or an electron in the acceptor or donor band?
Is an atom having a free electron an ionised atom?
I am super-super-confused...
 A: Ionization requires an atom/molecule as a whole, should have a net positive charge i.e. an electron has to be completely removed from the neutral atom/molecule. Strictly speaking, addition of electrons to a neutral atom is also a kind of ionization (and hence the name AN'ION') and so the most general definition nessesitates the requirement of a NET CHARGE on the atom/molecule.
In all the occasions you have mentioned the atom/molecule is neutral, hence not ionized. To be more precise, ionization is a extreme Excitation when the excitation energy equal (or greater than) Ionization Energy of that state.
Now all the situations you have mentioned are either ground state or excited states but not Ionized state.

Usage of the term "Free Electrons" -

*

*Free electrons/particles occur when there is no BOUND POTENTIAL in the Hamiltonian. It is commonly characterized by a infinitely whole range energy levels with no forbidden states poking around.

*Misnomer in Solid State Physics - Any solution of Schrodinger Equation that represent the Plane Wave solution is commonly called as Free Electron. It is important to note that strictly speaking these are not "free Electron" although they don't explicitly have a Potential in the Hamiltonian, the bound potential is implicitly taken into consideration in the Effective Mass. This approach simplifies the calculation, but doesn't change the physics. Hence, electrons in the various bands of the Lattice are in fact bound electrons, although some of them may be referred to as free electrons! Another effect of these bound electrons is that you have to provide some quanta of energy to release it from the lattice.

A: The band theory of solids has developed to describe the collective behavior of atoms and molecules when in the solid form.

The confusion goes away if one realizes that different quantum mechanical models have developed in order to describe different problems.

For an atom, can having at least one electron in the conduction band mean that the atom has been ionised?

In order for an electron to be considered in the conduction band, one needs a solid. Individual atoms/molecules sit at the lattice sites of the solid. The model is that the conduction band has electrons that are bound  over the whole lattice. The valence band electrons are tied on the points of the lattice where the nucleus also sits (depending on the material, whether insulator or conductor).
In the sense of the band theory model, the whole lattice is still neutral. Just the conduction band electrons have definition  over the whole lattice ( a quantum mechanical probability to be anywhere in the lattice). It has little meaning to talk about an ionized atom, because its "own electron might be away but another in the conduction band is near", (as a hand-waving explanation).

Can having an electron in the donor energy level or acceptor energy level mean that the atom has been ionised?

If for individual atoms, yes, but if the atom is part of a lattice see above.

Is free electron same as an electron in the conduction band or an electron in the acceptor or donor band?

No a free electron means there is no potential that is binding it.

Is an atom having a free electron an ionized atom?

If the atom is not in a lattice and it  attracts a floating electron, yes it will be a negatively ionize atom. If in a lattice,see above
Maybe if you read the whole link your confusion will go away.
