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Ok this question is a little tricky question. Let us answer this question based on concept of band theory. let us look at group 1 metals. Take the example of Na. It has only one valance electron. Hence the band diagram will be incomplete when sketched and due to this the nature of the element that is Na is metallic and also it exhibits good conductivity.

Now let us take the case of group 2 metals. Since the valence electron will be two and both of them will be filled, there will be an overlap of band. This will give it metallic nature but on the contrary since there will not be empty states it will be a poor conductor when compared to group 1.

Note: Group 2 metals exhibit conductivity but on a comparative scale with group 1 and 3 they are bad conductors.

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