Final answer:
The second ionization energy of sodium is greater than the second ionization energy of magnesium due to sodium's smaller atomic radius.
Step-by-step explanation:
The second ionization energy of sodium is greater than the second ionization energy of magnesium because sodium has a smaller atomic radius than magnesium. The second ionization energy refers to the energy required to remove a second electron from an atom. Since sodium has a smaller atomic radius, it has a stronger attraction between the positively charged nucleus and the negatively charged electrons, making it more difficult to remove a second electron compared to magnesium.