Chapter 10: Q64E (page 470)

Question: The photons emitted by an LED arise from the energy given up in electron-hole recombinations across the energy gap. How large should the energy gap be to give photons at the red end of the visible spectrum (700nm) ?

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Answer

The energy gap to give photons at the red end of the visible spectrum is 1.8 eV .

Step by step solution

Wavelength of emitted photons, $λ = 700 nm$ .

Energy corresponding to wavelength of photon is, $E = \frac{h c}{λ}$ .

Where, h is Planck's constant $= 6.64 \times 10^{- 34} J \cdot s$ .

C Is velocity of light $= 3 \times 10^{8} m / s$ .

Substitute numerical values in photon energy equation.

$E = \frac{6.64 \times 10^{- 34} J \cdot s \times 3 \times 10^{8} m / s}{700 \times 10^{- 9} m} = 0.0284 \times 10^{- 17} J = 1.8 eV$

The energy gap to give photons at the red end of the visible spectrum is 1.8eV

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