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Mar10-12, 12:03 PM
P: 44
The idea of a band gap normally refers to the difference in energy between an entirely full (valence) band and an entirely empty (conduction) band. Here, since you have a half-filled band, the system would be metallic if you believe the simplified band structure diagram you’ve attached. (In fact, one-dimensional metals will spontaneously undergo a distortion that makes them insulating – google “Peierls distortion” for more on this if you’re interested.)

As for your second questions: where do you think the Fermi level would fall in a hypothetical chain of F+ ions? (Note of course that this would be unstable in real life since it would carry an infinite amount of charge!)