According to experimental data the band gap of semiconducting nanotube is inversely proportional to its 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 

<math>E_{g}=\frac{V}{R}</math>

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,

<math>E_{g}=0.142\frac{V}{R}</math>

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)]]