To determine which pair of ions is not iso-electronic, we need to calculate the number of electrons in each ion.$\\$Iso-electronic species have the same number of electrons. Let's analyze each option:$\\$Option 1: $$O$^{2-},$F$^{-} \\$• Oxygen (O) has an atomic number of 8, so a neutral O atom has 8 electrons.$\\$• $$O$^{2-}$ gains 2 electrons, so it has $8 + 2 = 10$ electrons.$\\$• Fluorine (F) has an atomic number of 9, so a neutral F atom has 9 electrons.$\\$• $$F$^{-}$ gains 1 electron, so it has $9 + 1 = 10$ electrons.$\\$Both ions have 10 electrons, so they are iso-electronic.$\\$Option 2: $$Na$^{+},$Mg$^{2+} \\$• Sodium (Na) has an atomic number of 11, so a neutral Na atom has 11 electrons.$\\$• $$Na$^{+}$ loses 1 electron, so it has $11 - 1 = 10$ electrons.$\\$• Magnesium (Mg) has an atomic number of 12, so a neutral Mg atom has 12 electrons.$\\$• $$Mg$^{2+}$ loses 2 electrons, so it has $12 - 2 = 10$ electrons.$\\$Both ions have 10 electrons, so they are iso-electronic.$\\$Option 3: $$Mn$^{2+},$Fe$^{3+} \\$• Manganese (Mn) has an atomic number of 25, so a neutral Mn atom has 25 electrons.$\\$• $$Mn$^{2+}$ loses 2 electrons, so it has $25 - 2 = 23$ electrons.$\\$• Iron (Fe) has an atomic number of 26, so a neutral Fe atom has 26 electrons.$\\$• $$Fe$^{3+}$ loses 3 electrons, so it has $26 - 3 = 23$ electrons.$\\$Both ions have 23 electrons, so they are iso-electronic.$\\$Option 4: $$Fe$^{2+},$Mn$^{2+} \\$• $$Fe$^{2+}$ has $26 - 2 = 24$ electrons.$\\$• $$Mn$^{2+}$ has $25 - 2 = 23$ electrons.$\\$These ions have different numbers of electrons, so they are not iso-electronic.$\\$Therefore, the pair that is not iso-electronic is Option 4: $$Fe$^{2+},$Mn$^{2+}.$