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 (Group 14) as atomic number increases, we will analyze each property mentioned in the question step by step.

### Step 1: Understand the Group 14 Elements
The elements in the carbon family (Group 14) include Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), and Lead (Pb). As we move down the group, the atomic number increases.

**Hint:** Familiarize yourself with the elements in Group 14 and their positions in the periodic table.

### Step 2: Analyze Catenation
Catenation is the ability of an element to form chains with itself. Carbon has a high tendency for catenation due to its small size and strong C-C bonds. As we move down the group, the tendency for catenation decreases because the bond strength decreases and larger atoms are less capable of forming long chains.

**Hint:** Remember that smaller atoms generally form stronger bonds with themselves compared to larger atoms.

### Step 3: Examine Oxidation States
The oxidation states of Group 14 elements can vary. Carbon typically shows a +4 oxidation state, while heavier elements like lead can show +2 oxidation states due to the inert pair effect. As we go down the group, the tendency to show the +2 oxidation state increases because the s-electrons become less available for bonding.

**Hint:** Consider how the inert pair effect influences the availability of electrons for bonding as you move down the group.

### Step 4: Assess Metallic Character
Metallic character generally increases as we move down a group in the periodic table. Carbon and silicon are non-metals, germanium is a metalloid, while tin and lead are metals. Therefore, as we go down the group, the metallic character increases.

**Hint:** Recall that metallic character is associated with the ability to lose electrons easily, which increases down the group.

### Step 5: Consider Covalency Higher than 4
The ability to form complexes with covalency higher than 4 is influenced by the availability of d-orbitals in heavier elements. As we move down the group, the availability of d-orbitals increases, allowing for more complex bonding.

**Hint:** Keep in mind that d-orbitals become available in heavier elements, enhancing their ability to form complex compounds.

### Conclusion
Based on the analysis:
1. Catenation decreases down the group.
2. The tendency to show +2 oxidation state increases down the group.
3. Metallic character increases down the group.
4. The tendency to form complexes with covalency higher than 4 increases down the group.

Thus, the correct statement regarding the trend in properties of the carbon family with increasing atomic number is that the tendency to show +2 oxidation state increases.

**Final Answer:** The correct option is that the tendency to show +2 oxidation state increases with an increase in atomic number in the carbon family.