Final answer:
The second ionization energy of magnesium is higher than the first ionization energy. A good estimate for the second ionization energy of magnesium is approximately 1450 kJ/mol.
Step-by-step explanation:
The second ionization energy of an element refers to the energy required to remove a second electron from a singly charged ion of that element. It is generally higher than the first ionization energy because removing an electron from a positively charged ion requires more energy. In the case of magnesium (Mg), the first ionization energy is 738 kJ/mol. The second ionization energy of magnesium is always higher than the first ionization energy.
An estimate for the second ionization energy of magnesium can be obtained by looking at the general trend of ionization energies across a period. As you move from left to right across a period, the ionization energy generally increases because the effective nuclear charge increases, making it more difficult to remove an electron. Therefore, a good estimate for the second ionization energy of magnesium would be higher than the first ionization energy, but not significantly higher.
In this case, the best estimate for the second ionization energy of magnesium would be approximately 1450 kJ/mol (option b). This is higher than the first ionization energy of magnesium, but not as high as the other options provided.