For atoms to bond either ionically or covalently with one another, the key requirement is:
a. The valence shells of all atoms must be filled after the bonding occurs.
This principle is rooted in the octet rule, which states that atoms tend to bond in such a way that each atom has eight electrons in its valence shell, achieving a stable electronic configuration similar to that of noble gases.
Here's a brief evaluation of the other options:
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b. The chemical properties of the atoms must be satisfied. This statement is vague and not a definitive requirement for bonding.
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c. The ions must have different charges. This is specific to ionic bonding; while it is true for ionic compounds that form through the attraction of oppositely charged ions, it doesn't apply to covalent bonding.
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d. The resulting compound must follow ionic naming conventions. This is specific to ionic compounds and is not a requirement for all types of bonding, including covalent bonding.
Thus, option a is the most accurate and general requirement for bonding.