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I always encounter assertions similar to the following quote:

The electrons in the conduction band have higher energy than those in the valence band of a semiconductor.

We know by definition the conduction band is much more further away from the nucleus comparing to the valance band.

But in contrast to the quote above, below plot shows an energy of an electron versus its distance form the nucleus:

enter image description here

[Blue is curve shows the total energy]

The curve shows the absolute value of the total electron energy is getting closer to zero hence decreasing with distance from nucleolus.

However in band gap theory the energy is shown as if it is increasing by distance as shown here:

enter image description here [As you see above the energy increases with y-axis where y-axis also depicts the distance from mucleus]

Why the electron energy with respect to distance from nucleus in Bohr atom model doesn't match the one in band theory? Or am I getting something wrong here?

As you see in the equation the total electron energy absolute value goes to zero by n where n increases with distance from the nucleus.

enter image description here

GNZ
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  • Probably better to ask on physics.se – Andy aka Jan 11 '23 at 19:59
  • @Andyaka Please move it to physics.se if you are able to. – GNZ Jan 11 '23 at 20:05
  • I'm pretty sure that's the energy needed to fully ionize the electron, or, alternately, the energy is negative (with respect to an electron at infinite distance). The [Wikipedia article the Bohr model](https://en.wikipedia.org/wiki/Bohr_model) shows the energy as _negative_ and _inversely proportional to radius_. So in absolute terms, conduction electrons have higher energy (less negative energy) than valance electrons. – TimWescott Jan 11 '23 at 20:14

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