The elements in the same period in the periodic table show increase in

Electronegativity with increase in atomic number

The correct answer is option 3. Electronegativity with increase in atomic number.

As we move across a period from left to right in the periodic table, several properties of elements change systematically. This is due to the increasing number of protons in the nucleus (atomic number) and the corresponding increase in the number of electrons in the outer shell.

Trends in Key Properties Across a Period

Metallic Character:

Trend: Decreases from left to right.

Reason: Elements on the left (like alkali metals) have fewer valence electrons and lose them easily to form positive ions (cations), exhibiting metallic properties. As we move right, elements have more valence electrons and are less likely to lose them, culminating in the non-metals which gain electrons to form negative ions (anions).

Electronegativity:

Trend: Increases from left to right.

Reason: Electronegativity is the tendency of an atom to attract electrons towards itself in a chemical bond. As you move across a period, the effective nuclear charge increases because the number of protons increases while the shielding effect remains relatively constant. This stronger nuclear attraction pulls electrons closer, increasing electronegativity.

Electropositivity:

Trend: Decreases from left to right.

Reason: Electropositivity refers to the ability of an atom to donate electrons. As you move across a period, atoms hold onto their electrons more tightly due to increasing nuclear charge, making them less likely to donate electrons and thus less electropositive.

Analysis of Each Option

1. Metallic nature with increase in atomic number: This is incorrect because, as explained, metallic character decreases across a period as you move from left to right.

2. Electronegativity with increase in metallic character: This is incorrect because metallic character decreases while electronegativity increases across a period. They are inversely related.

3. Electronegativity with increase in atomic number: This is correct. As the atomic number increases across a period, the number of protons in the nucleus increases, leading to a greater effective nuclear charge. This greater pull on the electrons makes atoms more electronegative.

4. Electropositivity with increase in atomic number: This is incorrect because electropositivity decreases across a period as the atomic number increases. Elements become less likely to lose electrons and more likely to attract them.

The correct statement, reflecting the trend that is consistently observed across periods in the periodic table, is: Electronegativity with increase in atomic number

This captures the increase in an atom's ability to attract electrons as the atomic number increases across a period.