Given below are two statements:
Statement I: The correct order in terms of atomic/ionic radii is $$Al >Mg > Mg^{2+} >Al^{3+}$$
Statement II: The correct order in terms of the magnitude of electron gain enthalpy is Cl > Br >S >O.
In the light of the above statements, choose the correct answer from the options given below:

We need to evaluate two statements about atomic/ionic radii and electron gain enthalpy.

Statement I claims the order in terms of atomic/ionic radii is $$Al > Mg > Mg^{2+} > Al^{3+}$$. Comparing atomic radii of Al and Mg shows that Mg (Z = 12) has an atomic radius of about 160 pm, while Al (Z = 13) has an atomic radius of about 143 pm. As one moves from left to right across a period, the atomic radius decreases due to increasing nuclear charge with the same number of electron shells; thus Mg > Al, making the assertion Al > Mg incorrect. For the ionic radii, $$Mg^{2+}$$ (10 electrons, Z = 12) has a radius of approximately 72 pm, and $$Al^{3+}$$ (10 electrons, Z = 13) has a radius of approximately 53.5 pm. Both ions are isoelectronic, but the higher nuclear charge in $$Al^{3+}$$ leads to a smaller radius, so $$Mg^{2+} > Al^{3+}$$ is correct. Since the first part of the statement is wrong, Statement I is false.

Statement II asserts the order of the magnitude of electron gain enthalpy as $$Cl > Br > S > O$$. The electron gain enthalpy $$\Delta_{eg}H$$ represents the enthalpy change when a gaseous atom gains an electron. The magnitudes of the electron gain enthalpies are |-349| = 349 kJ/mol for Cl, |-325| = 325 kJ/mol for Br, |-200| = 200 kJ/mol for S, and |-141| = 141 kJ/mol for O. Oxygen shows a lower magnitude than expected because its small 2p subshell results in significant electron-electron repulsion when an extra electron is added. Therefore, the order $$Cl > Br > S > O$$ is correct, and Statement II is true.

Hence, the correct answer is Option (1): Statement I is false but Statement II is true.