Question

How does the band gap of a semiconducting chiral carbon nanotube change as its diameter increases?

• A. The band gap increases
• B. The band gap decreases
• C. The band gap remains constant
• D. The band gap becomes zero

Hint:

Band gap of CNT $\propto \frac{1}{\text{diameter}}$
Larger nanotube → Smaller band gap

Answer 1

The Correct Option is B

Concept:
Carbon nanotubes (CNTs) are cylindrical nanostructures derived from graphene sheets. Their electronic properties depend strongly on their chirality and diameter. Depending on these structural parameters, carbon nanotubes can behave as either metallic or semiconducting materials. The band gap is the energy difference between the valence band and the conduction band of a material, and it determines whether a material behaves as a conductor, semiconductor, or insulator.
Step 1:Relation between diameter and band gap.
For semiconducting carbon nanotubes, the band gap is inversely proportional to the nanotube diameter. This relationship can be approximately expressed as: \[ E_g \propto \frac{1}{d} \] where:

• $E_g$ = band gap energy
• $d$ = diameter of the nanotube

Step 2:Effect of increasing diameter.
As the diameter of the nanotube increases, the curvature of the graphene sheet decreases. This causes the electronic structure to become closer to that of graphene, which has a very small or zero band gap.
Step 3:Resulting behavior.
Because of this inverse relationship, when the diameter increases, the band gap becomes smaller. Conclusion:
Therefore, the band gap of a semiconducting chiral carbon nanotube decreases as its diameter increases.