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What is the relationship between the ionization energy of the electron and its initial potential energy...

What is the relationship between the ionization energy of the electron and its initial potential energy in the atom?

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When the potential energy of the electron in the atom increases, the ionization energy decreases. We have the total energy E of the electron in a circular orbit (which is half of potential energy) is:

The potential energy of the electron increases with quantum number n, in the periodic table this occurs from left to right and from top to bottom. On the other hand the ionization energy increases in the periodic table from left to right and from bottom to top.

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