Why is the energy of an atom with one electron missing greater than that of the neutral atom?
The energy of "ion + electron far away" is greater than the energy of the atom with the electron nearby. The reason is just the electrostatic force - the positive ion attracts the electron, and you need energy to separate them.
Aw, thank you!
Consider that if you put a neutral atom in between the electron and the ion, the electron will accelerate towards the ion and impact the atom, performing work on it. When work is performed energy is transferred, so this requires that the energy of the separated electron and ion be higher than when they are together, otherwise there would be no energy to transfer in the first place!
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