Problem — Fermi estimate, photons from an LED

Problem

A $10$ W white LED bulb emits about $30\%$ as visible light (the rest as heat). Estimating an average wavelength of $550$ nm, how many photons per second does it emit?

Solution

Step 1 — Useful light power. Only $30\%$ of the $10$ W becomes visible light:

$P_\text{light} = 0{,}30\cdot 10\;\text{W} = 3\;\text{W} = 3\;\text{J/s}$

Step 2 — Energy of an average photon.

$E_f = \frac{hc}{\lambda} = \frac{1240\;\text{eV·nm}}{550\;\text{nm}} \approx 2{,}25\;\text{eV} = 2{,}25\cdot 1{,}6\cdot 10^{-19} \approx 3{,}6\cdot 10^{-19}\;\text{J}$

Step 3 — Photons per second.

$\frac{N}{t} = \frac{P_\text{light}}{E_f} = \frac{3}{3{,}6\cdot 10^{-19}} \approx 8\cdot 10^{18}\;\text{photons/s}$

$\ev{N/t \sim 8\cdot 10^{18}\;\text{ph/s}}$

Billions of billions of photons per second: the flux is so dense that light appears continuous to us, with no trace of its grainy nature. The quantisation of light manifests itself only with detectors sensitive to single photons or at extremely low intensities.

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Topics: Fisica quantistica Concepts: Fotone Skills: Stime di Fermi · Conversione di unità