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Ionization energy is the energy required to lose one electron. Each atom wants to have 8 valence electrons. Fluorine has 7. Therefore, it has a very high ionization energy because it is trying to gain an electron, not remove one. To remove one electron would be extremely difficult. It will easily gain an electron but it will take an absorbent amount of energy to lose one.
Fluorine is the most electronegative element, therefore its electron affinity is high because it "desperately needs" one more electron to fill its valence shell. Similarly, because it "desperately needs" an electron, it will be very difficult to remove an electron from it, causing its ionization energy to be high as well.
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