Apply Einstein’s energy equation and interpret linear photoelectric data.
Method and worked examples
A metal can emit photoelectrons when each incident photon has enough energy to overcome its work function W. Einstein’s equation is Kmax =hf−W. The threshold frequency is f0=hW. Below threshold, increasing intensity does not release electrons in the simple single-photon model. Above threshold, higher intensity increases emission rate while higher frequency increases maximum kinetic energy.
The stopping-voltage magnitude Vs satisfies eVs= Kmax. A graph of Kmax against f has gradient h, vertical intercept −W and frequency intercept f0. If energy is plotted in eV instead of joules, the numerical gradient uses eV s rather than Js. Use the maximum energy, because emitted electrons need not all leave with the same kinetic energy.
Example 1
Photon energy is 5.00 eV and the work function is 2.00 eV. Find Kmax and stopping voltage.
Kmax =5.00−2.00=3.00 eV. For electrons, this is stopped by a voltage magnitude 3.00V.
Example 2
Use h=6.63×10−34Js and W=3.315×10−19J. Find threshold frequency.
f0=hW=5.00×1014 Hz.
Watch out:In the ordinary single-photon model, photon energy must meet the work function; intensity alone cannot overcome a frequency below threshold.
6. Photoelectric thresholds and stopping voltage | Year 12 Physics | Ascent Arcade