Question

The number of six membered and five membered rings in Buckminster Fullerence respectively is

• A. 12, 20
• B. 20, 12
• C. 14, 18
• D. 14, 11

Answer 1

The Correct Option is A

To determine the number of six-membered and five-membered rings in Buckminsterfullerene (C₆₀), we need to understand its structure. Buckminsterfullerene is a fullerene molecule with a truncated icosahedron shape, resembling a soccer ball. It consists of 60 carbon atoms arranged in a combination of pentagonal and hexagonal rings.

1. Structure of Buckminsterfullerene:

- Buckminsterfullerene (C₆₀) has a total of 32 faces, with each face being a ring of carbon atoms.

- These faces are composed of pentagons (5-membered rings) and hexagons (6-membered rings).

- Each carbon atom is shared among three rings, and each edge is shared between two rings.

2. Counting the Rings:

- It is a well-established fact in chemistry that C₆₀ has 12 pentagonal rings and 20 hexagonal rings.

- This can be derived using Euler's formula for polyhedra, $ V - E + F = 2 $, where:

- $ V $ is the number of vertices (60 carbon atoms),
- $ E $ is the number of edges (90, since each vertex has degree 3, so $ 3V/2 = 3 \cdot 60 / 2 = 90 $),
- $ F $ is the number of faces (32, including both pentagons and hexagons).

- Let $ P $ be the number of pentagonal faces and $ H $ be the number of hexagonal faces. Then:

- $ P + H = 32 $ (total faces).

- Each pentagon has 5 edges, and each hexagon has 6 edges, but since each edge is shared between two faces, the total number of edges is given by:

$ \frac{5P + 6H}{2} = 90 \implies 5P + 6H = 180 $.
 

- Additionally, for a fullerene to be stable, it typically has exactly 12 pentagons (a property of closed carbon cages). So, $ P = 12 $.
 

- Substituting $ P = 12 $ into $ P + H = 32 $:

$ 12 + H = 32 \implies H = 20 $.
 

- Verify with the edge equation:

$ 5 \cdot 12 + 6 \cdot 20 = 60 + 120 = 180 \implies \frac{180}{2} = 90 $ edges, which is correct.

3. Conclusion:

- Buckminsterfullerene has 12 five-membered rings (pentagons) and 20 six-membered rings (hexagons).

Answer: The correct option is (A) 12, 20.

Answer 2

1. Understanding the Structure of Buckminster Fullerene:
Buckminster Fullerene (C₆₀) is a molecule made up of 60 carbon atoms arranged in a spherical shape. It consists of 12 pentagonal (five-membered) rings and 20 hexagonal (six-membered) rings, forming a structure similar to a soccer ball, also known as a truncated icosahedron.

2. Identifying the Number of Rings:
In Buckminster Fullerene, the structure is composed of 12 pentagonal rings and 20 hexagonal rings. This arrangement is fixed and unique to the C₆₀ molecule.

Final Answer:
The number of six-membered and five-membered rings in Buckminster Fullerene is (A) 12, 20.