Can two metallic atoms of the same type form a bond?  For example: K and K, two potassium atoms

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The goal of chemical bonding is to fulfill the octet rule. The octet rule states that main group atoms are most content with eight valence electrons (the electrons that are found in their outermost shells/orbits), the electron configuration of noble gasses. Atoms will behave (and form bonds) in a way to obtain this octet. Covalent bonds occur between two nonmetals. During a covalent bond, the atoms involved share their electrons to reach the desired octet. Any electron that is shared goes towards each of the sharing atoms' octet. A chemical bond between a metal and a nonmetal is called an ionic bond.  Metals, which have 1 or 2 or 3 valence, will "donate" all their current valence electrons so they can drop down to the next lower orbital that is already full, and satisfy the octet rule. Conversely, nonmetals that have 5 or 6 or 7 valence electrons will take those that are being given by these metals in order to reach their desired octet. Transition metals have what are called delocalized electrons that can "swim" from one transition metal to another in order to fulfill octets. This is called metallic bonding 

So, using your example, each K has one valence electron. K is not a transition metal, so delocalization of electrons does not apply. It would be near impossible to obtain an octet using either ionic or covalent bonding. 

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