In the periodic table the metallic character with increase in atomic number

decreases in a period and increases in a group

The correct answer is option 1. decreases in a period and increases in a group.

Let us delve into the concept of metallic character and how it varies across the periodic table.

Metallic character refers to the tendency of an element to exhibit properties associated with metals, such as:

Good conductivity of heat and electricity

Malleability (ability to be hammered into thin sheets)

Ductility (ability to be drawn into wires)

Metallic luster

Formation of basic oxides

Trends in Metallic Character

Across a Period (Horizontal Trend)

As you move across a period (from left to right) in the periodic table:

Atomic Size: Generally decreases. This is because as you move across a period, you are adding more protons to the nucleus, increasing the nuclear charge. This increased nuclear charge pulls the electrons closer to the nucleus, thereby reducing the atomic radius.

Effective Nuclear Charge \((Z_{eff})\): Increases. The increasing number of protons in the nucleus leads to a stronger attraction between the nucleus and the outermost electrons. This makes it harder for atoms to lose electrons and exhibit metallic properties like conductivity.

Increases. Ionization energy is the energy required to remove an electron from a gaseous atom or ion. Across a period, as the effective nuclear charge increases, it becomes more difficult to remove electrons, thus increasing the ionization energy.

Electronegativity: Increases. Electronegativity is the tendency of an atom to attract shared electrons towards itself in a chemical bond. Across a period, atoms have higher electronegativity because they have a stronger pull on electrons due to increased nuclear charge.

Due to these factors, metallic character decreases across a period because elements tend to exhibit more non-metallic properties as you move from left to right.

Down a Group (Vertical Trend)

As you move down a group (from top to bottom) in the periodic table:

Atomic Size: Generally increases. This is because each subsequent element in a group has an additional electron shell (principal quantum number increases), leading to larger atomic radii.

Effective Nuclear Charge \((Z_{eff})\): Decreases. Despite an increase in atomic number and nuclear charge, the shielding effect of inner electrons increases significantly. Outer electrons experience less attraction to the nucleus due to this shielding effect, making it easier for them to be lost or shared in chemical bonding.

Ionization Energy: Decreases. With larger atomic size and decreased effective nuclear charge, the outermost electrons are farther from the nucleus and experience less attraction. Therefore, less energy is required to remove an electron.

Electronegativity: Decreases. Similar to ionization energy, electronegativity decreases down a group because outer electrons are farther from the nucleus and less strongly attracted.

Because of these trends, metallic character increases down a group as elements have larger atomic radii, lower ionization energies, and lower electronegativities, making it easier for them to lose electrons and exhibit metallic properties.

Given these trends, the correct option regarding the variation of metallic character with atomic number is (1) decreases in a period and increases in a group.

This option correctly reflects that metallic character generally decreases across a period due to increasing effective nuclear charge and increases down a group due to increasing atomic size and decreasing effective nuclear charge.