By definition, the first ionization energy is the energy required to produce one mole of gaseous cations, and one mole of electrons, from one mole of gaseous atoms:
#M(g) + Delta_1 rarrM^(+)(g) + e^-#
As is typical, #Delta# increases across a Period, from left to right as we face the Table, and decreases down a Group. The increase is due to the increased nuclear charge; the decrease is due to the separation of the valence electron from the nuclear charge.
The second ionization energy, #Delta_2#, relates to the formation of dications from the given cation:
#M^+(g) + Delta_2 rarrM^(2+)(g) + e^-#
#Delta_2# should be intrinsically greater than #Delta_1# inasmuch as it should require more energy to abstract an electron from a positively charged particle than from a neutral one.
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