Problem 1

Q: Arrange in order of decreasing ionic radius: $\text{Mg}^{2+},\, \text{Na}^+,\, \text{F}^-,\, \text{O}^{2-},\, \text{N}^{3-}$

Step 1: Count electrons in each ion.

• $N^{3-}$: 7 − (−3) = 10 $e^{-}$; $Na^{+}$: 11 − 1 = 10 $e^{-}$; $Mg^{2+}$: 12 − 2 = 10 $e^{-}$; $F^{-}$: 9 + 1 = 10 $e^{-}$; $O^{2-}$: 8 + 2 = 10 $e^{-}$
• All have 10 electrons → isoelectronic series

Step 2: For isoelectronic species, radius $\propto 1/Z$. List proton counts: N(7), O(8), F(9), Na(11), Mg(12)

Step 3: Arrange decreasing radius = increasing proton count (descending radius): $r(\text{N}^{3-}) > r(\text{O}^{2-}) > r(\text{F}^-) > r(\text{Na}^+) > r(\text{Mg}^{2+})$

Answer: $N^{3-}$ (146 pm) > $O^{2-}$ (140 pm) > $F^{-}$ (133 pm) > $Na^{+}$ (98 pm) > $Mg^{2+}$ (66 pm)