Explain why the first ionization energy of lithium is much larger than the first ionization energy of cesium.

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In general, ionization energies get larger as you move left to right on the Periodic Table, as the current valences get filled; but they get smaller as you move down the Periodic Table, as new valences are added that are more weakly bound or "further away" from the nucleus (I put that in scare quotes because quantum mechanics is a fickle beast; typically both the highest and lowest orbitals will actually have nonzero wavefunction density very close to the nucleus).

It comes down to the fact that it gets harder to remove electrons when you have a lot of electrons already in your valence orbital, but it is easier to remove electrons from higher valences than lower valences.

Since lithium and cesium are both in the same column (group) of the Periodic Table, but cesium is further down, we should expect that cesium would have lower ionization energies than lithium; and indeed it does. Conceptually, cesium's valence orbital has the same number of electrons as lithium's (1), but cesium's valence is much higher and thus less strongly bound to the nucleus.

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