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In class we talked about how the 2nd electron is always harder to remove (ionization energy for the 2nd electron is always higher than for the 1st electron), but I was wondering if this includes atoms like Mg and Ca, in group 2. Since taking off the 2nd electron would give them a full octet of valence electrons wouldn't they be more loosely held onto?
Yes, the second ionization is always higher regardless of whether the electron would gain a full octet or not. The second ionization is always higher because it takes more energy to remove an electron positively charged ion( since one electron has already been removed) rather than a neutral atom.
Conceptually, the 2nd ionization energy is higher than the first because there is less electron-electron repulsion present in the atom, which results in the remaining electrons being "held" onto tighter. Similarly, the 3rd ionization energy will always be higher than the 2nd, and so on.
Even though removing a second electron would give those atoms a full octet, remember that the cation formed from removing the first electron has less electron-electron repulsion so the remaining single electron in the valence shell is held tighter by the nucleus. This makes it harder to pull off, so the 2nd ionization energy is higher.
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