According to experimental data the band gap of semiconducting nanotube is inversely proportional to its radius. The simple analytical model also explained in solution for homework Problem 3 indicates that the prefactor V in this dependence is the absolute value of the nearest neighbor tight-binding element in the pi-orbital approximation
$$E_{g}=\frac{V}{R}$$
Here CNT radius R is measured in the units of carbon-carbon bond length. If R is expressed in nanometers,
$$E_{g}=0.142\frac{V}{R}$$
The plot below, which collects data from CNTBands pi-orbital tight-binding simulations (dark-blue circles) demonstrates that this is indeed the case. The solid red line is the inverse dependence given by the equation above.
