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Magnesium shows an oxidation state of $+2$ and bismuth shows an oxidation state of $+3$. Both do not show a negative oxidation state. Then how is magnesium bismuthide ($\ce{Mg_{3}Bi_{2}}$) formed?

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    $\begingroup$ >Both do not show a negative oxidation state. || incorrect, bot are shown to have negative oxidation state in specific circumstances. $\endgroup$ – permeakra Jun 30 '15 at 5:32
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    $\begingroup$ @permeakra while Mg3Bi2 almost certainly brings out an oxidatio state of -3 in Bi due to the great preference of Mg for +2, I am not convinced that there is a case where Mg truly forms a negative oxidation state. I would expect it to form simple alloys with the elements to the left and below it in the periodic table. $\endgroup$ – Level River St Jun 30 '15 at 7:30
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    $\begingroup$ @steveverrill Oups! mistaken it for sodium. Sodium is shown to have -1 oxidation state in, for example, salts with potassium in crown esters. Mg, indeed, is unlikely to form negative oxidation state.... Though I wouldn't bet on it in long run. $\endgroup$ – permeakra Jun 30 '15 at 7:34
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Bismuth can have any oxidation state from +1 to +5 . As it is in the same group as nitrogen and phosphorous, its most commom oxidation states with strongly oxidizing substances such as halogens and oxygen are +3 and +5.

However with a strongly electopositive (reducing) element, bismuth can have an oxidation state of -3, just as nitrogen can. While it is true that the oxidizing strength reduces as we go down the group, the "softness" (tendency to of an element to adapt its oxidation state to the preferred oxidation states of other elements) goes up.

Without definite information I can't discount the possibility that $\ce{Mg3Bi2}$ is an alloy, but the fact that it has an even stoichiometric ratio of elements suggests that it is in fact a compound in which magnesium has an oxidation state of +2 and bismuth has an oxidation state of -3.

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    $\begingroup$ Mg3Bi2 is a semiconductor, thus dismissing alloy theory. $\endgroup$ – permeakra Jun 30 '15 at 7:36

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