使Cl-,Si2-, K+, Ar 中每個氣態粒子除去一粒電子,其所需的能量的遞增次序應怎樣排列?還有這樣排的原因是什麼

First, let's look at the electronic configuration:
Cl-: [Ar]
Si2-: [Ne] 3d10 4s2 4p4
Ar: [Ar]
K+: [Ar]

Please note that Cl- and K+ have the same electronic structure as Ar. We many consider the stability due to the octet structure as similar in magnitude among these three species. However, since the removal of electron from a negatively charged ion would be more favorable than that in a neutral or even positively charged species, so we may speculate that the ionization energy for K+>Ar>Cl-.
For Si2-, as it is a doubly negatively charged ion, its I.E. would probably be low. Also, as the resulted species Si- posses half-fill stability in the 4p orbital, we may expect the removal of one electron from Si2- would be much favorable than thatin Cl-. Therefore, the species in ascending order of I.E. would be Si2-, Cl-, Ar and K+.

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When considering the I.E. of a chemical species, two factors are to be concern.
First is the charge of the species concern. The more negative the species, (generally) more favorable the removal of electron.
Second is the extra stability brought about by the some specific electronic structure.
That is all you can think of.