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Fluorine is the most electronegative atom because it has 7 valence electrons (5 in the 2 p shell) and therefore is close to the optimal electron configuration, making it have a higher affinity for gaining another electron to reach the stable octet configuration.
The rule for increasing electronegativity is that it increases across a period and up a group. Since the noble gases don't apply to this rule (they have completely full shells), fluorine is the uppermost and rightmost element on the periodic table.
Adding to that, ignoring noble gases, fluorine also has little shielding effect since its electrons are close to the nucleus in the n=2 shell. Thus, the protons in the nucleus have a stronger pull on the electrons than in any other element.
Fluorine only has electrons in the n=2 shell, meaning there are no higher layers to "shield" the positive charge from attracting electrons. It also has the highest number of protons in its period, making the nucleus attract electrons very strongly.
The higher the electronegativity of an atom, the greater its ability to attract shared electrons. The electronegativity of atoms increases as you move from left to right across a period in the periodic table. If you look at the periodic table, Florine is one of the most electronegative atoms because it is the farthest up and the farthest to the right.
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