According to experimental data the band gaps of semiconducting nanotubes are inversely proportional to their radius. The simple [http://prl.aps.org/abstract/PRL/v68/i5/p631_1 analytical model] also explained in solution for [/topics/CNTBandsProblems homework Problem 3] indicates that the dependence is
if the CNT radius is measured in the units of carbon-carbon bond length. '''''V''''' is the absolute value of the nearest neighbor tight-binding element in the pi-orbital approximation. If '''''R''''' is measured in nanometers,
The plot below, which collects data from pi-orbital tight-binding simulations from ''CNTBands'' (dark-blue circles) demonstrates that this is indeed the case. The solid red line is the inverse dependence given by the equation above.
[[Image(CNTBandgap_vs_Radius.png)]]