1.4.2—Equations to represent first, second

Successive ionisation energies are the energies required to remove one mole of electrons, one electron-removal step at a time, from the same element as its gaseous ion becomes more positive. The second step starts from X⁺(g), the third from X²⁺(g), and so on.

Write each gaseous species explicitly: X⁺(g) → X²⁺(g) + e⁻ for the second ionisation, then X²⁺(g) → X³⁺(g) + e⁻ for the third. As electrons are removed, shielding decreases and the proton-to-electron ratio increases, so the remaining electrons are generally more strongly attracted to the nucleus and successive values increase.

Interpret the sequence by locating a large jump between successive values. The jump means the next electron is being removed from a new inner shell, closer to the nucleus and more strongly attracted; the number of electrons removed before the jump gives the outer-shell count in the supported s- and p-block inference.

Do not compare successive values as if each came from a fresh neutral atom, and do not remove several electrons in one step. Keep the gaseous state and changing positive charge in every equation; use the jump as evidence about shell structure, not as a standalone claim about an unsupported element or configuration.