[Nitin_Naudiyal]

Band Theory assumes that the atomic orbital of the atom in a crystal combine to form molecular orbitals which are spread over the complete crystal structure.
With increase in the participating atom of the crystal the number of Molecular orbital containing electron increases.
As the number of molecular orbitals increases the energy difference between the adjacent orbitals i.e. energy level decreases.
Until the energy gap becomes very small and molecular discrete energy level merge into one another to form continuous band of molecular orbitals

I have the following questions:

1) How does the energy level decreases as a result in the increase in the number of molecular orbitals?
2)Do the molecular orbitals merge or only the gap between the orbitals decreases?

Thanking you in Advance.

[Borek]

1) How does the energy level decreases as a result in the increase in the number of molecular orbitals?

Energy level doesn't decrease - difference between energy levels of MOs decreases. Technically you try to put many of them into some range - no wonder they have to be packed tight, with small distances between them.

2)Do the molecular orbitals merge or only the gap between the orbitals decreases?

I don't think they can merge, that would mean violation of Pauli's exclusion principle.

[Corribus]

1) How does the energy level decreases as a result in the increase in the number of molecular orbitals?

You’ve got some ambiguity in your language that makes it hard to know exactly what you are asking about.  How does the energy level of what decrease?  Energy of the HOMO increases (destabilizes) and energy of the LUMO decreases (stabilizes).  The band gap decreases because the band gap is the energy difference between the HOMO energy and LUMO level.

2)Do the molecular orbitals merge or only the gap between the orbitals decreases?

The answer is both, not one or the other - if I understand your use of the word "merge".  I'm not really sure how much detail you need or want here, but... The orbitals merge in the sense that they interact with each other and create new orbitals - or at least, that's how the molecular orbitals are modelled theoretically.  In LCAO-MO theory, molecular orbitals are approximated as linear combinations of atomic orbitals.  In band theory, the "bands" are formed by linear combinations of the individual molecular orbitals.  The combinations that are allowed are determined by symmetry. 

However there are maximum and minimum energy values the orbital combinations can have.  Explaining why would take some effort on my part and I’m not sure it’s important to what you want to understand.  The important thing is that these extrema impose boundaries on the “bands” in the extrapolation to an infinite number of orbitals.  As the number of combining orbitals grow, they get closer together because they have to fit into a finite space.  In the infinite limit, they are infinitely close together, or “bands”.

The gap between the HOMO and LUMO shrinks like the gap between every other pair of orbitals.  In a metallic substance, this gap approaches zero and there is essentially one big band that includes all bonding and antibonding orbitals.  In a semiconductor, the gap asymptotically approaches a nonzero limit.  This is the band gap of the material.

[Nitin_Naudiyal]

Thank you for your replies.

[Nitin_Naudiyal]

As the number of molecular orbitals increases the energy difference between the adjacent orbitals i.e. energy level decreases.

Why does the energy difference between the adjacent orbitals i.e. energy level decreases with the increase in the number of Molecular Orbitals.

[Corribus]

Because there are more of them, and they must fit within a finite amount of energy space.  There is a maximum and minimum energy the new molecular orbitals can have.

It's like people crowding in a bus - the more people get on, the closer together they are because there's only so much room available.

[Nitin_Naudiyal]

Thank you Corribus for the explanation.