Successive ionisation energies involve removing additional electrons.
Each time you remove an electron, theres a successive ionisation energy.
The second ionisation energy is the energy needed to remove 1 electron from each ion in 1 mole of gaseous 1+ ions to form 1 mole of gaseous 2+ ions.
X(n-1) (g) = X(n+) (g) + e-
Successive ionisation energies show shell structure.
Within each shell, successive ionisation energies increase. Electrons are being removed from an increasingly +ve ion - less repulsion amongst the remaining electrons, they're held more strongly by the nucleus.
The big jumps in ionisation energy happen when a new shell is broken into - an electron is being removed from a new shell closer to the nucleus.
Graphs can tell you which group of the periodic table an element belongs to - just count how many electrons are reomved before the first big jump.
Graphs can also help predict electronic structure - working from left to right, count how many points there are before each big jump to find out how many electrons are in each shell, starting with the first.
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