Understanding Buckminster Fullerene and Allotropes

The question asks about Buckminster fullerene, which is described as looking like a football and being an allotropic form of a certain element. Let's explore what allotropes are and specifically look at the element that forms Buckminster fullerene.

An allotrope is a different structural form of the same element. The element exists in two or more different forms in the same physical state. These different forms arise due to differences in how the atoms are bonded together or how they are arranged spatially.

Common examples of elements with allotropes include Carbon, Sulfur, Phosphorus, and Tin, which are conveniently listed in the options provided. Let's examine the allotropes of each element listed in the options.

Analyzing Allotropes of the Given Options

Phosphorus Allotropes

Phosphorus exists in several allotropic forms, including white phosphorus (${P_4}$), red phosphorus, and black phosphorus. These forms have different physical and chemical properties due to the varying arrangements of phosphorus atoms.

White phosphorus consists of discrete tetrahedral molecules (${P_4}$). Red phosphorus has a polymeric structure. Black phosphorus is the most stable allotrope and has a layered structure similar to graphite.

However, none of these forms resemble a football or are known as Buckminster fullerene.

Sulfur Allotropes

Sulfur also exhibits allotropy. The two most common crystalline forms are rhombic sulfur ($\alpha$-sulfur) and monoclinic sulfur ($\beta$-sulfur). Both consist of ${S_8}$ rings, but the arrangement of these rings in the crystal lattice differs.

Rhombic sulfur is the stable form at room temperature, while monoclinic sulfur is stable at temperatures above ${95.5^\circ C}$. Sulfur also has amorphous allotropes like plastic sulfur.

None of sulfur's allotropes are Buckminster fullerene or have a football-like structure.

Carbon Allotropes

Carbon is well-known for its diverse allotropic forms, which include:

• Diamond (a very hard, crystalline structure)
• Graphite (a soft, layered structure)
• Fullerenes (molecular forms)
• Carbon nanotubes (cylindrical forms)
• Graphene (a single layer of graphite)
• Amorphous carbon (like charcoal, soot)

Fullerenes are a class of carbon allotropes whose molecules are spheres, ellipsoids, tubes, and many other shapes. They are made entirely of carbon atoms, arranged in hollow structures with pentagonal and hexagonal faces.

The most famous and stable fullerene is Buckminster fullerene, which has the chemical formula ${C_{60}}$. Its structure is a truncated icosahedron, consisting of 12 pentagons and 20 hexagons. This structure closely resembles a standard football (soccer ball), which is typically made from panels stitched together in a pattern of pentagons and hexagons.

The discovery of fullerenes, including ${C_{60}}$, earned the Nobel Prize in Chemistry in 1996. Their unique structure gives them interesting physical and chemical properties, leading to research in various applications.

Tin Allotropes

Tin exists in two main allotropic forms at atmospheric pressure: grey tin ($\alpha$-tin) and white tin ($\beta$-tin).

Grey tin has a diamond cubic structure and is stable below ${13.2^\circ C}$. It is brittle and looks like a grey powder. White tin has a tetragonal structure and is stable above ${13.2^\circ C}$. It is a silvery-white metallic solid and is the common form of tin.

Neither of tin's common allotropes is Buckminster fullerene or has a football shape.

Conclusion

Based on the analysis of the allotropes of Phosphorus, Sulfur, Carbon, and Tin, it is clear that Buckminster fullerene, known for its football-like structure, is a specific allotropic form of Carbon.

Therefore, the correct answer is Carbon.

Revision Table: Key Concepts

Additional Information: Fullerenes and Carbon Allotropy

Fullerenes represent a fascinating class of carbon structures beyond the traditional diamond and graphite. They were first theorized before their experimental discovery in 1985.

• Buckminster fullerene (${C_{60}}$) is the most abundant fullerene and is considered the parent molecule for many fullerene derivatives.
• Other fullerenes exist, such as ${C_{70}}$ (which is more elongated) and larger ones.
• The term "fullerene" is named after architect R. Buckminster Fuller, known for designing geodesic domes that resemble the structure of ${C_{60}}$.
• Fullerenes have potential applications in materials science, medicine (e.g., drug delivery), and electronics due to their unique cage structure and properties.
• Understanding carbon allotropy is crucial in materials science as different forms exhibit drastically different properties (e.g., hardness, conductivity, reactivity).