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As you go left to right across a row in the periodic table, you add one proton and one electron going element to element. All of the electrons (negative charge) in that row exist in the same quantum number, or general distance away from the nucleus. However, with each proton (positive charge) you add, the electrons feel a greater attraction to the nucleus. Therefore, more energy is required to remove electrons from an element on the end of a row than one at the beginning, because of a greater attraction.
In any one row in the periodic table, all of the elements' atoms have the same number of energy levels. However, going from left to right in one row, the atomic number increases, meaning the number of protons increases. The more protons, the greater the attraction to the electrons, and therefore, the more energy required to remove an electron from the atom (which is the ionization energy).
This may not be the best way to explain it, but it can help you understand this phenomenon better. Elements toward the left of each period have less valence electrons and are more likely to lose them to establish a stable octet. For example, Na only needs to get rid of one electron to achieve a stable octet. Whereas, Cl needs to lose 7 electrons to achieve a stable octet. That's why Na has an ionization energy way lower than Cl.
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