The general trend in the properties of elements of carbon family shows that with increase in atomic number

Options

A. the tendency towards catenation increases
B. the tendency to show `+2` oxidation state increases
C. metallic character decreases
D. the tendency to form complexes with covalency higher than four decreases

Answer

To solve the question regarding the general trend in the properties of elements of the carbon family as atomic number increases, we can follow these steps:

### Step 1: Identify the Carbon Family
The carbon family consists of the elements in Group 14 of the periodic table: Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), and Lead (Pb).

### Step 2: Analyze Catenation
Catenation refers to the ability of an element to form chains of atoms. Carbon has a strong tendency to catenate due to its ability to form strong covalent bonds with itself. As we move down the group from Carbon to Lead, the strength of the carbon-carbon bond decreases, leading to a decrease in catenation.

**Conclusion**: The tendency towards catenation decreases down the group.

### Step 3: Examine Oxidation States
The oxidation states of the carbon family elements can vary. Carbon typically shows a +4 oxidation state, while heavier elements can show +2 and +4 states. As we move down the group, the +2 oxidation state becomes more stable due to the inert pair effect, which refers to the reluctance of the s-electrons to participate in bonding.

**Conclusion**: The tendency to show the +2 oxidation state increases down the group.

### Step 4: Assess Metallic Character
Metallic character generally increases down a group in the periodic table. Carbon is a non-metal, Silicon is a metalloid, Germanium is a semi-metal, and both Tin and Lead are metals.

**Conclusion**: The metallic character increases down the group.

### Step 5: Complex Formation
Carbon does not have d-orbitals available for bonding, which limits its ability to form complexes with covalency higher than 4. In contrast, the heavier elements of the carbon family have d-orbitals and can form such complexes.

**Conclusion**: The tendency to form complexes with covalency higher than 4 increases down the group.

### Final Conclusion
Based on the analysis:
- Catenation decreases
- The tendency to show +2 oxidation state increases
- Metallic character increases
- The tendency to form complexes with covalency higher than 4 increases

Thus, the correct answer to the question is that the tendency to show the +2 oxidation state increases with an increase in atomic number.