Which one among the following is the correct arrangement in increasing

Which one among the following is the correct arrangement in increasing order of ionic radii of O²⁻, F⁻, Na⁺, Mg²⁺ ?

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UPSC Geoscientist – 2024
The correct arrangement in increasing order of ionic radii is Mg²⁺ < Na⁺ < F⁻ < O²⁻.
The given ions O²⁻, F⁻, Na⁺, and Mg²⁺ are isoelectronic species, meaning they all have the same number of electrons (10 electrons, with the electronic configuration $1s^2 2s^2 2p^6$).
For isoelectronic species, the ionic radius decreases as the nuclear charge (atomic number) increases. A higher nuclear charge exerts a stronger attraction on the same number of electrons, pulling them closer to the nucleus and reducing the ionic size.
The atomic numbers are: Oxygen (O) = 8, Fluorine (F) = 9, Sodium (Na) = 11, Magnesium (Mg) = 12.
The effective nuclear charges are approximately +8 for O²⁻, +9 for F⁻, +11 for Na⁺, and +12 for Mg²⁺.
As the nuclear charge increases (from +8 to +12), the attraction on the 10 electrons increases, leading to a decrease in ionic size.
Order of increasing nuclear charge: O²⁻ (+8) < F⁻ (+9) < Na⁺ (+11) < Mg²⁺ (+12). Order of decreasing ionic radii: O²⁻ > F⁻ > Na⁺ > Mg²⁺.
Order of increasing ionic radii: Mg²⁺ < Na⁺ < F⁻ < O²⁻.
Cations are generally smaller than their parent atoms because they lose valence electrons and the remaining electrons are held more tightly by the nucleus. Anions are generally larger than their parent atoms because they gain electrons, increasing electron-electron repulsion and expanding the electron cloud. Among isoelectronic species, negative ions are larger than positive ions, and within negative ions, the size increases with increasing negative charge. Within positive ions, the size decreases with increasing positive charge.
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