The photon energy and wavelength are related by the Planck–Einstein relation $$ E = h\,f = \frac{h c}{\lambda}. $$ If an electron transitions across a semiconductor bandgap with energy $E_g$ (in eV), an emitted photon (if radiative) will have energy approximately $E \approx E_g$ and thus $$ \lambda\,[\mathrm{nm}] = \frac{h c}{E}\frac{1}{\mathrm{eV}} \approx \frac{1240.8}{E_g\,[\mathrm{eV}]}. $$

Interactive widget

Drag the slider to change the bandgap and see the corresponding dominant optical wavelength. The swatch approximates the visible color for 380–780 nm.

Background and notes

• The numerical constant 1240.8 comes from $h c$ expressed in eV·nm: $h c \approx 1240.8\,\mathrm{eV\cdot nm}$.
• For indirect bandgap semiconductors (e.g., Si), radiative recombination is weak; the relation still connects an energy scale to a wavelength.
• Visible light spans roughly 380–780 nm. Outside this range, the color swatch is left transparent.