1. Interpret the assertion

To form $\mathrm{Mg}^{2+}$ from $\mathrm{Mg}$, two electrons must be removed:

The total energy required to form $\mathrm{Mg}^{2+}$ from $\mathrm{Mg}$ is:

whereas to form $\mathrm{Mg}^+$ from $\mathrm{Mg}$, only $IE_1$ is needed.

Since removing the second electron from the already positively charged ion $\mathrm{Mg}^+$ is much harder than removing the first electron, the energy needed to form $\mathrm{Mg}^{2+}$ is much higher.

So, Assertion A is true.

2. Interpret the reason

The reason says:

• $\mathrm{Mg}^{2+}$ is a smaller ion than $\mathrm{Mg}^+$
• $\mathrm{Mg}^{2+}$ carries more positive charge than $\mathrm{Mg}^+$

This is correct. Greater positive charge and smaller size mean stronger attraction between the nucleus and the remaining electrons. Therefore, removing an electron from $\mathrm{Mg}^+$ to form $\mathrm{Mg}^{2+}$ requires more energy.

So, Reason R is also true.

3. Check whether R explains A

Yes. The second electron is removed from $\mathrm{Mg}^+$, and due to higher effective attraction in the smaller/more highly charged ion, this removal requires much more energy. Hence the formation of $\mathrm{Mg}^{2+}$ from $\mathrm{Mg}$ needs much more energy than formation of $\mathrm{Mg}^+$ from $\mathrm{Mg}$.

Thus, R is the correct explanation of A.

4. Evaluate options

• A: A is false but R is true $\rightarrow$ incorrect
• B: Both A and R are correct but R is NOT the correct explanation of A $\rightarrow$ incorrect
• C: Both A and R are correct and R is the correct explanation of A $\rightarrow$ correct
• D: A is true but R is false $\rightarrow$ incorrect

Therefore, the correct option is:

5. Comparison with stored correct answer

Stored correct answer: $C$

My derived answer: $C$

They match.