1. Check the Reason (R): Are $O^{2-}$ and $Mg^{2+}$ isoelectronic?

• Oxygen has atomic number $8$.

• In $O^{2-}$, it gains $2$ electrons: $8 + 2 = 10 \text{ electrons}$

• Magnesium has atomic number $12$.

• In $Mg^{2+}$, it loses $2$ electrons: $12 - 2 = 10 \text{ electrons}$

So, both ions have $10$ electrons.

Therefore, $O^{2-}$ and $Mg^{2+}$ are isoelectronic species.

Hence, Reason (R) is true.

2. Check the Assertion (A): Are the ionic radii of $O^{2-}$ and $Mg^{2+}$ same?

Although they are isoelectronic, isoelectronic species do not necessarily have the same radius.

For an isoelectronic series, radius depends on nuclear charge:

• Greater nuclear charge $\Rightarrow$ stronger attraction on the same number of electrons
• Hence, smaller radius

Now compare nuclear charges:

• For $O^{2-}$: nuclear charge = $8$
• For $Mg^{2+}$: nuclear charge = $12$

Since $Mg^{2+}$ has much higher nuclear charge, it pulls the same 10 electrons more strongly. Thus, $r(Mg^{2+}) < r(O^{2-})$

So, their ionic radii are not same.

Hence, Assertion (A) is false.

3. Evaluate the options

• A: Both true, and R explains A $\rightarrow$ False
• B: Both true, but R not explanation $\rightarrow$ False
• C: A true, R false $\rightarrow$ False
• D: A false, R true $\rightarrow$ Correct

4. Final Answer

The correct option is: $\boxed{D}$

5. Comparison with stored correct answer

Stored correct answer: $D$

My derived answer also is $D$, so they agree.