Light Emitting Diode

A light emitting diode emits light when electrons injected into the junction recombine with holes, releasing the energy difference as photons. In an ideal LED the photon energy equals the band gap, so (E_g = h\nu = hc/\lambda). Rearranging gives the wavelength (\lambda = hc/E_g). Using the convenient relation that (hc \approx 1240,\text{eV nm}), the wavelength is (\lambda = 1240 / 2.0 = 620,\text{nm}), which lies in the orange-red part of the visible spectrum. This inverse relationship between band gap and wavelength explains why different LED materials emit different colours: a wider gap pushes the emission toward blue and violet, while a narrower gap shifts it into the red and infrared. The value 310 nm comes from doubling the energy or halving the constant, placing it wrongly in the ultraviolet. The value 1240 nm results from omitting the band gap value entirely, giving an infrared answer. The value 414 nm corresponds to a 3.0 eV gap, not the stated 2.0 eV. As a final check, a 2.0 eV gap should yield visible light, and 620 nm sits squarely within the 400-700 nm visible range, confirming the calculation is physically reasonable.