LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is 1.9 eV. Calculate the wavelength of light emitted and its colour.
[h = 6.63 × 10⁻³⁴ Js and c = 3 × 10⁸ ms⁻¹]

Solution

Physics sir · 4 steps

The photon carries exactly the band-gap energy, so λ = hc/E_g. Just convert eV to joules first.

1. Photon energy. In an LED an electron drops across the band gap and gives out one photon of energy E_g. So E_g = hc/λ.

   λ = hc/E_g = (6.63 × 10⁻³⁴ × 3 × 10⁸)/(1.9 × 1.6 × 10⁻¹⁹) m

2. Put in numbers. The top is 1.989 × 10⁻²⁵ J m and the bottom is 3.04 × 10⁻¹⁹ J. That gives λ = 6.54 × 10⁻⁷ m ≈ 654 nm.
3. Find the colour. Red light runs from about 620 to 750 nm, and orange sits around 590 to 620 nm. So 654 nm is red.
4. So. The LED emits light of about 654 nm, which is red: option (b).

The idea to keep. For photon problems use λ (nm) ≈ 1240/(E (eV)) as a quick check. A small band gap means a long wavelength, towards the red end.

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