Question

The number of six membered carbon rings and five membered carbon rings present in Buckminsterfullerene are \(x\) and \(y\) respectively. The sum of \(x\) and \(y\) is:

• A. \(32\)
• B. \(23\)
• C. \(30\)
• D. \(42\)

Hint:

Buckminsterfullerene \((C_{60})\) contains: \[ 12 \text{ pentagons and } 20 \text{ hexagons} \] similar to a soccer ball structure.

Answer 1

The Correct Option is A

Step 1: Recall the structure of C60.
Buckminsterfullerene is \( C_{60} \), shaped like a football. It has both pentagonal and hexagonal carbon rings fused together.
Step 2: Count five-membered rings.
Like a football, \( C_{60} \) has 12 five-membered (pentagonal) rings. So \( y = 12 \).
Step 3: Count six-membered rings.
\( C_{60} \) also has 20 six-membered (hexagonal) rings. So \( x = 20 \).
Step 4: Calculate the sum.
\[ x + y = 20 + 12 = 32 \]
Step 5: Verify using Euler formula.
For \( C_{60} \): vertices V = 60, edges E = 90, faces F = 32. Euler gives \( V - E + F = 60 - 90 + 32 = 2 \), which confirms correctness.
Step 6: Match with options.
The sum 32 matches option 1. \[ \boxed{32} \]