Work function

The work function of a metal is the minimum amount of energy required to bring an electron from inside the metal, to its surface.

What if the incident photon has less energy than the work function?

• Then the photon will transfer its energy to the electron, but that isn’t enough.
• It won’t have enough energy to escape the metal.
• So no electrons will be released from the metal.

What if the incident photon has more energy than the work function?

• The photon will transfer its energy to the electron.
• Some of that energy (a value of at least the work function) will be used to escape the metal.
• Whatever is left of the energy will be given to the electron as kinetic energy.
• So the kinetic energy of the electron will be equal to the energy of the photon, minus the work function of the metal.
  • E_{\text{\space max}}=E_{photon}-\phi
  • E_{\text{\space max}}=hf-\phi

Finding the work function of a metal

• If we plot a graph of the maximum kinetic energy of the emitted electrons against the frequency of the incident light, we can find the work function of the metal.
• The y-intercept of the graph will be the negative of the work function of the metal.
  • So, if the y-intercept of the graph is -2.5\times10^{-19}J, for example, then the work function of the metal is 2.5\times10^{-19}J.
• There’s a note for this graph! See photoelectric effect graph.

Work function and threshold frequency

If we know the work function or the threshold frequency of a metal, we can find the other one using the equation:

\phi = hf_0

Where:

• \phi is the work function of the metal (in joules),
• h is Planck’s constant (6.63 \times 10^{-34} Js),
• f_0 is the threshold frequency of the metal (in hertz).