Question

Which of the following statement is/are correct? (1) \(\mathrm{C}_{60}\) has a geodesic dome structure. (2) Solid \(\mathrm{C}_{60}\) has a cubic close-packed structure. (3) The name buckminsterfullerene was given to \(\mathrm{C}_{60}\) - (4) The common name for \(\mathrm{C}_{60}\) is 'bucky ball' (a) \(1,2,3\) (b) 2,3 (c) \(2,3,4\) (d) \(1,4,3,4\)

Short answer

Statements (1), (2), (3), and (4) are correct.

Step-by-step solution

Analyze Statement 1

Statement (1): \( \text{C}_{60} \) has a geodesic dome structure. \( \text{C}_{60} \) is a fullerene molecule resembling a geodesic dome structure with 60 carbon atoms arranged in a spherical shape much like a soccer ball. This statement is **correct**.

Analyze Statement 2

Statement (2): Solid \( \text{C}_{60} \) has a cubic close-packed structure. In solid state, \( \text{C}_{60} \) molecules form a cubic close-packed (ccp) lattice structure. This statement is **correct**.

Analyze Statement 3

Statement (3): The name buckminsterfullerene was given to \( \text{C}_{60} \). The molecule \( \text{C}_{60} \) was named buckminsterfullerene after architect Buckminster Fuller because its structure resembles a geodesic dome. This statement is **correct**.

Analyze Statement 4

Statement (4): The common name for \( \text{C}_{60} \) is 'bucky ball'. The \( \text{C}_{60} \) is often referred to as a 'bucky ball' due to its shape like a soccer ball. This statement is **correct**.

Determine Correct Combination

Analyze the options provided. Option (d) suggests the inclusion of statements 1, 3, and 4, yet states 4 twice. However, logically analyzing, this suggests all these statements are correct, as each statement holds true. Hence, option that includes statements 1, 3, and 4 is valid.

Key concepts

C60 molecule

Imagine a soccer ball, not for playing sports, but as a molecule composed entirely of carbon atoms. That’s the essence of the \( \text{C}_{60} \) molecule. This is a specific type of fullerene, which are molecules made purely of carbon, forming a hollow shape. The most recognized fullerene is \( \text{C}_{60} \), containing 60 interconnected carbon atoms.

Each carbon atom within the \( \text{C}_{60} \) molecule binds with others forming pentagons and hexagons. These shapes tessellate perfectly to create a symmetrical sphere, reminiscent of a communal ball structure. Due to this unique architecture, it has garnered notable interest in fields like nanotechnology and materials science for potential applications.

Geodesic dome structure

The term 'geodesic dome' might remind some of architectural designs. When applied to chemistry, particularly the \( \text{C}_{60} \) molecule, it describes the fascinating symmetry and strength of its configuration. A geodesic dome in architecture involves a network of triangles creating a sphere, allowing lightness but maintaining structural soundness.

In the \( \text{C}_{60} \) molecule, the combination of pentagons and hexagons mimics this architecture, providing stability to the spherical form. This similarity led to its comparison with the geodesic dome and hence, its attributable name. This structure isn’t trivial; it provides robustness and balance, a characteristic property of fullerenes.

Cubic close-packed structure

The arrangement of molecules within a solid determines many of its physical properties. For \( \text{C}_{60} \) in the solid state, the molecules come together in what is known as a cubic close-packed (ccp) structure.

• The ccp structure refers to how \( \text{C}_{60} \) spheres pack together in layers.
• This arrangement maximizes density as each molecule nestles into the gaps of the surrounding molecules.

Such tight packing optimizes volume usage and influences how the material might conduct electricity or heat. Each sphere in this configuration is surrounded by 12 others, consistent with the densest packing possible in a three-dimensional arrangement.

Bucky ball

Among the most endearing nicknames of \( \text{C}_{60} \) is the 'bucky ball.' Envision a tiny soccer ball, with each patch representing carbon atoms. This name isn't just a catchy term but offers an insight into the shape and form of the molecule.

Since its discovery, the resemblance to spherical geometries used in soccer provided an intuitive understanding of its configuration. The term 'bucky ball' blends scientific nomenclature with informal lingo, making it memorable. It suggests not only its shape but the dynamic potential for use in various scientific applications, similar to how balls are integral in numerous games played worldwide.

Buckminsterfullerene

The story behind the name 'buckminsterfullerene' links back to historical architecture. Renowned architect R. Buckminster Fuller was famous for his design of the geodesic dome. When the spherical \( \text{C}_{60} \) molecule was first synthesized, scientists noted its resemblance to Fuller's designs.

• This link between structure and architect inspired the name.
• It represents a homage to Fuller's legacy, highlighting the molecule's perfect symmetry and strength.

Moreover, this naming convention echoes the innovative spirit at the intersection of art, architecture, and science, underscoring how scientific discovery can be an interdisciplinary pursuit.