Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The energy required to form Mg$$^{2+}$$ from Mg is much higher than that required to produce Mg$$^+$$
Reason R: Mg$$^{2+}$$ is small ion and carry more charge than Mg$$^+$$
In the light of the above statements, choose the correct answer from the options given below.

We need to evaluate both the Assertion and the Reason.

Assertion A: The energy required to form $$Mg^{2+}$$ from $$Mg$$ is much higher than that required to produce $$Mg^{+}$$.

To form $$Mg^{+}$$ from $$Mg$$, we need the first ionization energy ($$IE_1$$):

$$ Mg \rightarrow Mg^{+} + e^{-} \quad (IE_1 = 737.7 \text{ kJ/mol}) $$

To form $$Mg^{2+}$$ from $$Mg$$, we need both the first and second ionization energies ($$IE_1 + IE_2$$):

$$ Mg \rightarrow Mg^{2+} + 2e^{-} \quad (IE_1 + IE_2 = 737.7 + 1450.7 = 2188.4 \text{ kJ/mol}) $$

Since $$IE_1 + IE_2$$ is much greater than $$IE_1$$ alone, the energy required to form $$Mg^{2+}$$ from $$Mg$$ is indeed much higher than that required to form $$Mg^{+}$$. Assertion A is true.

Reason R: $$Mg^{2+}$$ is a smaller ion and carries more charge than $$Mg^{+}$$.

After removing the first electron, $$Mg^{+}$$ has the electronic configuration $$1s^2 2s^2 2p^6 3s^1$$. Removing the second electron from $$Mg^{+}$$ to form $$Mg^{2+}$$ requires more energy because:

• $$Mg^{+}$$ already has a net positive charge, so the remaining electrons experience a greater effective nuclear charge ($$Z_{eff}$$).
• $$Mg^{2+}$$ (with configuration $$1s^2 2s^2 2p^6$$) is smaller in size than $$Mg^{+}$$, meaning the electron being removed is held more tightly by the nucleus.

The fact that $$Mg^{2+}$$ is smaller and carries more charge than $$Mg^{+}$$ directly explains why the second ionization energy is higher, and therefore why forming $$Mg^{2+}$$ requires much more total energy. Reason R is true and is the correct explanation of A.

The correct answer is Option D: Both A and R are true and R is the correct explanation of A.