To determine which ion has a stable valence electron configuration, we should refer to the concept of achieving a full outer shell of electrons, which is typically associated with having eight electrons in the outer shell (an octet) for main group elements.
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Potassium (K): Potassium has an atomic number of 19 and has the electron configuration of [Ar] 4s¹. When it loses one electron to form a \( K^+ \) ion, it achieves the electron configuration of Argon, which has a complete outer shell.
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Fluorine (F): Fluorine has an atomic number of 9 and an electron configuration of [He] 2s² 2p⁵. When it gains one electron to form a \( F^- \) ion, it achieves the electron configuration of Neon, which also has a complete outer shell.
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Magnesium (Mg): Magnesium has an atomic number of 12, with an electron configuration of [Ne] 3s². When it loses two electrons to form a \( Mg^{2+} \) ion, it achieves the electron configuration of Neon, which is stable.
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Sulfur (S): Sulfur has an atomic number of 16, with an electron configuration of [Ne] 3s² 3p⁴. When it gains two electrons to form a \( S^{2-} \) ion, it achieves the electron configuration of Argon, which is also stable.
Among the provided options, both potassium (K) with a \( 1+ \) charge and fluorine (F) with a \( 1- \) charge form ions with stable configurations. However, the question requires the identification of a single correct answer based on the context of achieving stable configuration via gaining or losing electrons.
The best final answer to the question, particularly focusing on the options you provided, is:
- Fluorine (F) with a 1− charge.
Fluorine achieves a stable configuration by gaining one electron (gaining an electron makes it a \( F^- \) ion), reaching a noble gas configuration (Neon), thereby satisfying the conditions for stability in the periodic table context.