Problem 139 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

Statements (a), (b), and (d) are correct.

Step 1: Understanding the Statements

Read each statement carefully: (a) C_{60} has a geodesic dome structure; (b) Solid C_{60} has a cubic close-packed structure; (c) The name buckminsterfullerene was given to C_{60^{-}}; (d) The common name for C_{60} is 'bucky ball.' The goal is to identify which of these statements are factually correct.

Step 2: Analyzing Statement (a)

Statement (a) suggests that C_{60} has a geodesic dome structure. C_{60}, known as Buckminsterfullerene, resembles a soccer ball shape composed of pentagons and hexagons, similar to the geodesic domes popularized by architect Buckminster Fuller. Thus, statement (a) is correct.

Step 3: Analyzing Statement (b)

Statement (b) states that solid C_{60} has a cubic close-packed structure. C_{60} molecules in solid form often form a face-centered cubic (FCC) crystal structure, which is also known as cubic close-packed (CCP). Therefore, this statement is correct too.

Step 4: Analyzing Statement (c)

Statement (c) claims that the name buckminsterfullerene was assigned to C_{60^{-}}. In reality, the name buckminsterfullerene refers to the neutral molecule C_{60}, inspired by the shape reminiscent of a geodesic dome. "C_{60^{-}}" refers to a negatively charged ion, not commonly named buckminsterfullerene. Thus, statement (c) is incorrect.

Step 5: Analyzing Statement (d)

Statement (d) asserts that the common name for C_{60} is 'bucky ball.' C_{60} molecules are indeed commonly referred to as "bucky balls" due to their shape, which resembles a small soccer ball. Hence, this statement is correct.

Key Concepts

C60 Molecule Structure

The \(C_{60}\) molecule, also known as buckminsterfullerene, is an iconic representation of a class of molecules called fullerenes. This unique structure consists of 60 carbon atoms arranged in a hollow sphere. It closely resembles a classic soccer ball. This spherical arrangement occurs because the carbon atoms are organized into a network of 12 pentagons and 20 hexagons.
These polygons fit together in a specific pattern, creating a stable, closed shell that is highly symmetrical. \(C_{60}\) is renowned for its remarkable symmetry and is one of the first fullerene molecules to be discovered, marking a significant milestone in the field of nanostructures. Such a structure offers interesting properties, including the ability to trap atoms inside its hollow core.

Geodesic Dome Structure

The concept of a geodesic dome, popularized by architect Buckminster Fuller, finds a surprising natural analogy in the structure of \(C_{60}\). Geodesic domes showcase robust architectural designs that distribute structural stress evenly across the surface, much like the \(C_{60}\) molecule distributes molecular forces.
The molecules are arranged similarly to the tessellated pattern seen in these domes, with a balance of pentagons and hexagons creating a spherical surface that minimizes potential energy. This efficient use of materials makes both geodesic domes and the \(C_{60}\) molecule incredibly stable and lightweight. This insightful comparison helps understand how molecular arrangements can draw inspiration from architectural designs while offering insights into molecular stability.

Cubic Close-Packed Structure

In its solid state, \(C_{60}\) molecules arrange into a cubic close-packed structure (CCP), also known as face-centered cubic (FCC). This means that the spheres, or molecules, pack densely together, occupying the smallest possible volume.
In this arrangement, each molecule is in contact with twelve others, resulting in a highly efficient packing arrangement. This structure is significant in materials science, as it influences the properties of the material, such as its density and strength. It's a common structure observed in many metals and alloys, which further demonstrates the versatility and adaptability of the \(C_{60}\) molecule in forming complex solid arrangements.

Buckyball Common Name

The term "buckyball" is a playful nickname derived from the molecule \(C_{60}\)'s resemblance to a soccer ball. This name not only highlights the shape but also pays homage to Buckminster Fuller, whose geodesic domes share similarities in their construction.
Buckyballs have garnered significant interest due to their unique spherical shape and the potential applications in materials science, electronics, and nanotechnology. The name has become widely used when referring to these molecules, emphasizing the connection between scientific nanostructures and creative design. With advancements in nanoscience, buckyballs hold promise for future innovations, capturing the imagination of scientists and students alike.