Final answer:
The statement can be true, as ionization energy generally increases with each additional electron removed, notably so when the electron comes from a stable electron configuration such as a full or half-full subshell.
Step-by-step explanation:
The statement that there is a large increase in ionization energy between the second and third ionization energies of a metal can be either true or false, depending on the metal in question. Ionization energy is the energy required to remove an electron from an atom or ion. Typically, ionization energies increase as one removes more electrons, due to a reduced electron-electron repulsion and increased attractive force between the remaining electrons and the nucleus. However, a notably large increase is observed when removing an electron from a stable electron configuration, such as a full or half-full subshell. For example, in the case of a metal like magnesium (Mg), the first two electrons removed are from the 3s orbital. The third ionization involves removing an electron from the more stable 2p orbital, resulting in a significant increase in the third ionization energy. In general, it is usually correct that the third ionization energy of a metal is significantly higher than the second, especially if the third electron removed comes from a deeper, more stable energy level.