The correct statement regarding metallic character is: Metallic character decreases across a period and increases down a group.

This trend is explained by considering the atomic structure and the factors affecting metallic bonding. Across a period (from left to right on the periodic table), the number of protons in the nucleus increases, while the principal quantum number remains constant. This leads to a stronger effective nuclear charge, pulling the valence electrons closer to the nucleus and making them less readily available for metallic bonding. Consequently, metallic character decreases.

Down a group (from top to bottom), the principal quantum number increases, and the atomic size increases significantly. This results in a shielding effect, where inner electrons reduce the attractive force of the nucleus on valence electrons. The larger atomic radius and weaker nuclear attraction cause valence electrons to be more loosely held, and thus, more readily available for metallic bonding. Therefore, metallic character increases down a group.

Options 2, 3, and 4 are incorrect because they contradict the established periodic trends of metallic character. They don't accurately reflect the interplay between effective nuclear charge, shielding effect, and atomic size.