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As you remove more electrons from an atom, the attraction between electrons and the nucleus increase because repulsion decreases. So as you go through successive ionization energies, more energy is required to remove electrons due to the lack of repulsion.
Electrons repel each other so the more electrons you have the greater the repulsion you have from the nuclear. By that logic, if you start to remove electrons the attractive forces between the surrounding electrons and the nucleus increases because there are less forces which repel the electrons. Therefore, as you increase in ionization energies, there is more energy required to remove electrons since there are less repulsive forces working to expel the electron.
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