Intense red photon and work function

Problem

True or false? “A photon of very intense red light extracts electrons from a metal with work function $W = 4\;\text{eV}$, provided the intensity is sufficient.” Justify your answer.

Solution

False. In the photoelectric effect each electron absorbs only one photon: what matters is the energy of the single quantum $hf$, not the intensity (which is just the number of photons per second).

A photon of red light ($\lambda \approx 650\;\text{nm}$) has energy

$E = \frac{hc}{\lambda} = \frac{1240}{650} \approx 1{,}9\;\text{eV} < W = 4\;\text{eV}$

Since $1{,}9\;\text{eV} < 4\;\text{eV}$, no electron is extracted, however intense the light is: increasing the intensity only increases the number of photons, each still too low in energy. Light of sufficient frequency (blue/UV) with $hf \geq W$ is needed.

$\ev{\text{False: below the threshold } hf < W \text{ no intensity extracts electrons}}$

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Topics: Fisica quantistica Concepts: Effetto fotoelettrico · Fotone