22.2 Photoelectric effect

The photoelectric effect is emission of electrons from a metal when incident photons have enough energy to overcome the surface work function.

Increasing intensity above threshold increases the number of emitted electrons, while frequency controls each photon’s energy and maximum electron speed.

Dim ultraviolet light can eject electrons while bright red light may not if red photon energy is below threshold.

Photoemission is not caused by accumulating energy over time from sub-threshold photons in the simple model.

Threshold frequency f₀ is the minimum photon frequency that ejects electrons; threshold wavelength λ₀ is the maximum wavelength, related by c=f₀λ₀.

Below f₀ or above λ₀ no electrons are emitted regardless of intensity in the ideal model.

A metal with threshold frequency 6.0×10¹⁴ Hz has threshold wavelength about 500 nm.

Threshold frequency is not the frequency of emitted electrons, and higher intensity cannot compensate for lower photon frequency.

A photon ejects an electron if hf≥Φ, where Φ is the work function; any excess becomes the electron’s kinetic energy.

Use Φ as the minimum energy needed to escape the surface and connect it to threshold frequency via Φ=hf₀.

Increasing frequency above threshold increases maximum photoelectron kinetic energy by the excess photon energy.

Work function is not the same as binding energy of every electron in the bulk and does not depend on beam intensity in this model.

Einstein’s photoelectric equation balances one photon’s energy: hf=Φ+½mv_max².

Use the maximum kinetic energy, not an average, and rearrange to find threshold, speed or stopping potential.

A plot of maximum kinetic energy against frequency has gradient h and intercept −Φ.

Increasing intensity raises photocurrent but not maximum kinetic energy when frequency is fixed.

For photoelectrons, the maximum kinetic energy is set by the energy of one incident photon: K_max=hf−Φ.

At a fixed frequency above threshold, raising intensity sends more photons per second, so the photocurrent can rise, but each photon still supplies the same energy and K_max is unchanged.

Doubling the intensity of ultraviolet light doubles the possible emission rate in an ideal experiment, not the stopping potential.

Intensity is not a substitute for frequency: sub-threshold photons do not eject electrons simply because the beam is brighter.