The energy band gap of semiconducting material to produce violet (wavelength = 4000Aᵒ ) LED is ______________ eV. (Round off to the nearest integer).

Solution

Physics sir · 3 steps

An LED emits one photon per electron-hole recombination, so the band gap is the photon energy hc/λ.

1. Gap sets colour. In an LED, an electron drops from the conduction band to the valence band and gives out one photon. That photon carries energy equal to the band gap, so E_g = hc/λ.

   E_g (eV) = hc/eλ ≈ 12400/(λ (Å))

2. Put in numbers. With λ = 4000 Å, E_g = 12400/4000 = 3.1 eV. In SI units this is (6.63 × 10⁻³⁴ × 3 × 10⁸)/(4 × 10⁻⁷) = 4.97 × 10⁻¹⁹ J, and dividing by 1.6 × 10⁻¹⁹ gives the same 3.1 eV.
3. So. The band gap is 3.1 eV, which rounds to 3.

The idea to keep. For any LED or photon question, keep hc ≈ 12400 eV Å (or 1240 eV nm) ready. Divide by the wavelength and you have the energy in eV in one step.

Answer from the NTA final answer key. Solution by PrepWiser.