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.

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

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.

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:

Question	Answer
What is the work function of a metal?	The work function (\phi) is the minimum amount of energy required to bring an electron from inside the metal to its surface.
What happens if the incident photon has less energy than the work function?	The photon transfers its energy to the electron, but it isn’t enough for the electron to escape the metal, so no electrons are released.
What happens if the incident photon has more energy than the work function?	The photon transfers its energy to the electron; some energy (at least the work function) is used to escape, and the remainder is given as kinetic energy.
What is the equation for the maximum kinetic energy of an emitted electron?	E_{\text{max}} = E_{photon} - \phi or E_{\text{max}} = hf - \phi
How can you find the work function of a metal from a graph of maximum kinetic energy vs. incident light frequency?	The y-intercept of the graph is the negative of the work function. For example, if the intercept is -2.5\times10^{-19} \text{ J}, the work function is 2.5\times10^{-19} \text{ J}.
What is the equation linking the work function and the threshold frequency?	$$
In the equation \phi = hf_0, what does f_0 represent?	f_0 is the threshold frequency of the metal (in hertz).