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Blue transitions motivate wide-bandgap semiconductors, but a large band gap alone cannot guarantee efficient emission. Gallium nitride has a direct band gap; indium gallium nitride composition tunes the transition energy.^[ref]

For an emitted photon, with frequency $\nu$ and vacuum wavelength $\lambda$,where $h$ is the Planck constant and $c$ the vacuum speed of light. Multiplying energy by wavelength gives $hc=1239.841984\mathrm{eV}\mathrm{nm}$. Thus chosen wavelengths $450\mathrm{nm}$ and $630\mathrm{nm}$ correspond to $2.75520\mathrm{eV}$ and $1.96800\mathrm{eV}$: blue requires more energy per photon than red. A stipulated transition energy $3.40\mathrm{eV}$ instead gives $364.659\mathrm{nm}$, in the ultraviolet. These are conversions, not measured emission lines.

For near-edge emission, $E_{\gamma }\approx E_g$ estimates the photon energy from the emitting material's band gap. Quantum well confinement or impurity transitions can change it. The 1994 blue light-emitting diode used zinc-doped indium gallium nitride, emitting below its near-edge transition.^[ref]

The measured forward terminal electric potential difference $V_f$ is also not fixed by $E_g/q$, where $q$ is the elementary charge. It depends on electric current, temperature, contacts and series electrical resistance. Even the simple Shockley diode equation with series electrical resistance has $V_f=V_j+I{R}_s$, whereas an optical transition does not acquire an extra energy $qI{R}_s$ merely because the contact drop increases. Consequently, extracting a band gap from one terminal-voltage reading is not justified.

Graphite: each carbon forms three strong in-plane sigma bonds in an sp${}^2$ honeycomb layer. The remaining p orbitals form delocalized pi bands, allowing electrical conduction especially along the layers. Much weaker interlayer attraction permits sliding, explaining softness without implying weak in-plane C-C bonds.

Carborundum is silicon carbide, SiC. A suitable structure is a three-dimensional, tetrahedrally coordinated covalent network: each Si has four C neighbors and each C four Si neighbors. Strong directional bonding in all directions resists slip and gives hardness. Its filled bonding states are separated from empty states by a substantial band gap, giving low conductivity when pure and undoped.

“Non-conductor” is the intended contrast with graphite; SiC is more precisely a wide-bandgap semiconductor, whose conductivity can change with doping and temperature.

HgS and ${\mathrm{C}}_3{\mathrm{N}}_4$ are semiconductors; $\mathrm{Hg}(\mathrm{SCN}{)}_2$ is a wider-gap, insulating material under the stated conditions. None is a metallic conductor. Their finite electronvolt-scale gaps and very low measured conductivities exclude a partially filled, highly conducting metallic band picture.

The insulator/semiconductor boundary is conventional rather than a sharp universal gap cutoff. Calling the $3.2\mathrm{eV}$ material a wide-bandgap semiconductor is also physically reasonable; the table alone does not establish a unique naming boundary. Conductivity is $\sigma =e(n{\mu }_n+p{\mu }_p)$, so its ordering need not follow gap size alone: carrier density, defects, trapping and mobility also matter.