If x is the number of C-C sigma bonds in $C_{60}$ (fullerene) and y is number of pentagonal rings in $C_{60}$ then find out the value of $(x + 5 y)$ .
Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer.

Question

If x is the number of C-C sigma bonds in $C_{60}$ (fullerene) and y is number of pentagonal rings in $C_{60}$ then find out the value of $(x + 5 y)$ .

Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer.

TestHub · Accepted Answer

C₆₀ (Buckminsterfullerene) has 60 carbon atoms. Each carbon atom is sp² hybridized and bonded to three other carbon atoms.

Number of C-C sigma bonds (x):

The total number of bonds in C₆₀ is $(60 \times 3) /2 = 90$ . So, $x = 90$ .

Number of pentagonal rings (y):

C₆₀ has 12 pentagonal rings and 20 hexagonal rings. So, $y = 12$ .

Value of $(x + 5 y)$ :

$x + 5 y = 90 + 5 (12) = 90 + 60 = 150$ .

Sum of digits:

$1 + 5 + 0 = 6$ .

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