One of the most fascinating developments in Modern chemistry has been the synthesis of Buckminister fullerence, `C_(60)` Identify the correct options about `C_(60)`

Options

A. It cosists of fused `5` and `6` membered carbon rings.
B. All atoms are not-equivalent
C. All bonds are not-equivalent
D. `C-C` bond lengths at the fusion of two `6`-membered rings are shorter with the `C-C` bond length at the fusion of `5`-and `6`-membered rings.

Answer

To identify the correct options about Buckminster fullerene, \( C_{60} \), let's analyze each statement step by step.

### Step 1: Analyze the structure of \( C_{60} \)
- Buckminster fullerene, \( C_{60} \), is a molecule composed of carbon atoms arranged in a spherical shape. It consists of fused pentagons (5-membered rings) and hexagons (6-membered rings).

**Hint**: Remember that the structure of \( C_{60} \) resembles a soccer ball, which is made up of hexagons and pentagons.

### Step 2: Check if it consists of fused 5 and 6-membered carbon rings
- The statement that \( C_{60} \) consists of fused 5 and 6-membered carbon rings is **correct**. In fact, there are 12 pentagons and 20 hexagons in its structure.

**Hint**: Visualize the arrangement of pentagons and hexagons in \( C_{60} \) to understand how they are fused.

### Step 3: Evaluate if all atoms are equal
- The statement that not all atoms in \( C_{60} \) are equal is also **correct**. In the structure, the carbon atoms in the pentagons are in a different environment compared to those in the hexagons.

**Hint**: Consider the hybridization and bonding environment of carbon atoms in different types of rings.

### Step 4: Assess if all bonds are equal
- The statement that not all bonds in \( C_{60} \) are equal is **correct**. The bond lengths and angles differ between the bonds in the pentagons and hexagons due to their different geometries.

**Hint**: Recall that bond lengths can vary based on the type of ring and the hybridization of the carbon atoms involved.

### Step 5: Compare C-C bond lengths at the fusion of rings
- The statement regarding the C-C bond length at the fusion of two six-membered rings being shorter than the C-C bonds at the fusion of five and six-membered rings is **correct**. The bonds formed between two hexagons are generally shorter due to the nature of the bonding and the geometry involved.

**Hint**: Think about how bond lengths can be influenced by the type of ring fusion and the overall molecular structure.

### Conclusion
After analyzing all the statements, we conclude that all the options regarding \( C_{60} \) are correct. Therefore, the correct answer includes options A, B, C, and D.

### Final Answer
All statements about \( C_{60} \) are correct: A, B, C, and D.