Remember that we model an electron as being at the bottom of the well. In the model, energy is needed to work against gravitational attraction in the same that energy is needed to work against eectrostatic attraction between the positive nucleus and the negative electron.The work function is the minimum energy required to escape from the atom.
It is possible to give more energy. That just means that the escaping electrons have extra kinetic energy.
That extra kinetic energy is measured in a circuit like this:
Notice the weird extra battery positioned at the top of the circuit. It is the wrong way round. Any electrons that are realeased by the light are pulled back across the gap, stopping the flow so the ammeter reads zero.
The more kinetic energy given to the electons the bigger the backwards voltage V needed to stop the current. This is called the stopping potential.
This is the graph that is produced by this equipment. Change the frequency of the light and measure the stopping potential in eV. Turn that into Joules to give you the kinetic energy. The threshold frequency is obvious.
