Final answer:
The first ionization energy of magnesium is lower than fluorine due to the higher effective nuclear charge in fluorine. The third ionization energy of magnesium is higher than fluorine because it involves the removal of an inner electron.
Step-by-step explanation:
The first ionization energy of magnesium is lower than that of fluorine because of the higher effective nuclear charge experienced by the valence electrons in fluorine compared to magnesium. Fluorine has a higher atomic number and more protons in its nucleus, which leads to a stronger attraction between the positively charged nucleus and the negatively charged valence electrons. Therefore, it requires more energy to remove an electron from fluorine compared to magnesium.
The third ionization energy of magnesium is higher than that of fluorine because the third ionization energy involves the removal of an inner electron. Inner electrons are closer to the nucleus and are more tightly held than valence electrons. Since fluorine has a smaller atomic radius than magnesium, its inner electrons are even closer to the nucleus, making them more difficult to remove. As a result, it requires more energy to remove an inner electron from fluorine compared to magnesium.