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Why doesn't alkaline earth metals lose only one electron when they are ionized ? I know that magnesium atoms like to have the electronic configuration of neon but I don't understand the reason that we can't find $\ce{Mg+}$ atoms .

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Magnesium can definitely exist as $\ce{Mg^{+}}$. Hence the availability of first ionization energy data for magnesium.

The same goes for other metals; there are only uncommon valences, such as $\ce{Na^{3+}}$.

If you had enough energy, you could make $\ce{Na^{4+}}$ if you wanted to. It would just cost, according to the table below, 9543 + 6912 + 4562.4 + 495.8 kJ/mol.

enter image description here

I think your question is why isn't $\ce{Mg^{+}}$ more commonly encountered. That has to do with stability. Losing two electrons and becoming isoelectronic with a noble gas is more stable than having an unpaired electron. An unpaired electron is available for bond formation, and bond formation tends to be exothermic.

If you want to read up on the +1 valence of magnesium, such as in $\ce{MgH}$, you can read more here:

http://bernath.uwaterloo.ca/media/24.pdf

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  • $\begingroup$ Actually you have to add up all the IE to generate the highly charged species, so for $\ce{Na4+}$ that would take about 21500 kJ/mol. $\endgroup$ – Martin - マーチン Jun 16 '14 at 1:31
  • $\begingroup$ Good point! Will fix in text. $\endgroup$ – Dissenter Jun 16 '14 at 4:14
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How is the magnesium being ionized? If it is reacting with oxygen or another oxidizer, look at the Born-Haber cycle.

The magnesium losing electrons is endothermic. Oxygen gaining one electron is exothermic but the 2nd electron affinity of oxygen is endothermic.

$\ce{Mg^{2+}}$ and oxide making magnesium oxide is exothermic. Removing the second electron from magnesium and adding the second electron to oxygen is "paid for" by the increase in lattice energy due to having 2 doubly charged ions instead of 2 singly charged ions.

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$\ce{Mg+}$ is not commonly encountered because compounds with $\ce{Mg^{2+}}$ are more stable. This does not mean that $\ce{Mg^{2+}}$ is more stable on its own, in gas phase even $\ce{Mg+}$ is less energetically favorable than $\ce{Mg^0}$. However, when interacting with other atoms, stabilization due electrostatic interaction is much higher for $\ce{Mg^{2+}}$ than for $\ce{Mg+}$ because of much smaller radius and double charge of the former.

Still, at least some compounds of $\ce{Mg(+1)}$ are known, even if in exotic conditions, like $\ce{MgCl}$ is known in gas phase.

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