Which of the following arrangements represents the increasing order (smallest to largest) of ionic radii of the given species O$$^{2-}$$, S$$^{2-}$$, N$$^{3-}$$, P$$^{3-}$$?

To determine the increasing order of ionic radii for the species O2-, S2-, N3-, and P3-, we need to analyze their positions in the periodic table and their electron configurations. Ionic radius depends on the number of electrons and the effective nuclear charge.

First, let's find the electron count for each ion:

• Oxygen (atomic number 8) in O2- has 8 + 2 = 10 electrons.
• Sulfur (atomic number 16) in S2- has 16 + 2 = 18 electrons.
• Nitrogen (atomic number 7) in N3- has 7 + 3 = 10 electrons.
• Phosphorus (atomic number 15) in P3- has 15 + 3 = 18 electrons.

This shows that O2- and N3- are isoelectronic (both have 10 electrons, like neon), while S2- and P3- are isoelectronic (both have 18 electrons, like argon).

For isoelectronic species, ionic radius decreases as nuclear charge (atomic number) increases because a higher nuclear charge pulls the electron cloud closer. Comparing O2- (atomic number 8) and N3- (atomic number 7):

• N3- has lower nuclear charge (7) than O2- (8), so N3- has a larger ionic radius than O2-.
• Thus, O2- < N3-.

Similarly, comparing S2- (atomic number 16) and P3- (atomic number 15):

• P3- has lower nuclear charge (15) than S2- (16), so P3- has a larger ionic radius than S2-.
• Thus, S2- < P3-.

Now, we compare across the two groups. O2- and N3- are in period 2 (principal quantum number n=2), while S2- and P3- are in period 3 (n=3). Ions in higher periods have larger radii due to more electron shells. Therefore, both S2- and P3- are larger than O2- and N3-.

Combining the comparisons:

• O2- is the smallest (period 2, highest nuclear charge in its group).
• N3- is next (period 2, larger than O2- due to lower nuclear charge).
• S2- is next (period 3, smaller than P3- due to higher nuclear charge).
• P3- is the largest (period 3, lowest nuclear charge in its group).

So the order is: O2- < N3- < S2- < P3-.

Comparing with the options:

• A: O2- < N3- < S2- < P3-
• B: O2- < P3- < N3- < S2-
• C: N3- < O2- < P3- < S2-
• D: N3- < S2- < O2- < P3-

Option A matches our derived order.

Hence, the correct answer is Option A.