Question

${{C}_{60}}$ , an allotrope of carbon contains:
[A] 20 hexagons and 12 pentagons
[B] 12 hexagons and 20 pentagons
[C] 18 hexagons and 14 pentagons
[D] 16 hexagons and 16 pentagons

Answer 1

HINT: To answer this, think about the allotrope of carbon that looks like a soccer ball made up of hexagon and pentagons. Remember that no two pentagons in this structure share an edge. You can use this to find out the correct answer.

COMPLETE STEP BY STEP SOLUTION: We know that carbon is capable of forming several carbon-containing compounds having different properties due to its valence electrons. These structures are known as allotropes. We know that diamond and graphite are well known allotropes of carbon. However, a recent allotrope of carbon, ${{C}_{60}}$ named fullerene was found. So, to answer this question let’s discuss fullerene. Fullerene is an aromatic allotrope of carbon. It was named after the scientist called BuckminsterFullerene has 2 variants- ${{C}_{60}}$ and ${{C}_{70}}$. However, ${{C}_{60}}$ is the closed fullerene. It has a closed, ball-like structure and thus is also known as ‘buckyballs’. In buckminsterfullerene, or simply known as fullerene, carbon atoms are closely bonded by double and single bonds to form a closed structure and with the rings fused with five to seven carbon atoms. It might be a hollow sphere or a tube like structure. ${{C}_{60}}$ is the smallest fullerene molecule and it contains hexagonal and pentagonal rings but any two pentagonal rings do not share any edge as it would be destabilizing. Its structure is known as a truncated icosahedron which looks like a soccer ball. It is made up of 20 hexagons and 12 pentagons. There’s a carbon atom at the vertices of every polygon and a bond along the polygon edges. We can understand from the above discussion that ${{C}_{60}}$ contains 20 hexagons and 12 pentagons.

Therefore, the correct answer is option [A] 20 hexagons and 12 pentagons.

NOTE: There are other common allotropes of carbon named diamond and graphite. Although they are made up of the same element i.e. carbon, they differ in physical as well as chemical properties like texture, strength etc.
Diamond is composed entirely of the element carbon. Each carbon atom is connected to four other carbon atoms. In graphite, the carbon atoms are arranged in a hexagonal structure. Each carbon atom is attached to three other carbon atoms covalently and thus there is one free delocalised electron.