Forbidden energy gap in an atom is the gap between the:

Forbidden energy gap (ΔEg): Energy gap between the conduction band and valence band is known as the forbidden energy gap i.e.,

ΔEg = (C.B)min - (V.B)max

• No free electron is present in the forbidden energy gap.
• Width of the forbidden energy gap depends upon the nature of the substance.
• As temperature increases, the forbidden energy gap decreases very slightly.

Important:

• In a conductor, the conduction band is partially filled and the valence band is partially empty or when the conduction and valance bands overlap. When there is overlap electrons from the valence band can easily move into the conduction band. 

• In an insulator, there exists a large bandgap between the conduction band and valence band Eg (Eg > 3 eV). 
• The valance band is fully filled with electrons.
• There are no electrons in the conduction band, and therefore no electrical conduction is possible.

• Semiconductors can be defined as those materials that have almost an empty conduction band and almost filled valence band with a very narrow energy gap between the conduction and valence band.
• In a semiconductor, there exists a finite but very small band gap between the conduction band and valence band (Eg < 3 eV). Because of the small bandgap, at room temperature, some electrons from the valence band can acquire enough energy to cross the energy gap and enter the conduction band.