AQA A-Level Physics/Photoelectric effect

Key Definitions
The Photoelectric Effect: The emission of electrons from a surface when it is illuminated by electromagnetic radiation above a certain threshold frequency (typically in the UV range).

Threshold Frequency: The minimum frequency of electromagnetic radiation such that it carries enough energy to dislodge (or remove) an electron from the surface.

Work Function ($$\phi$$): The minimum work that must be done to remove an electron from the surface.

Stopping Potential ($$V_s$$): The applied potential difference required to stop the fastest moving photoelectrons.

What Happens During the Photoelectric Effect
In Einstein's photon model, electromagnetic (EM) radiation is made up of packets of energy called photons. When a surface (usually metal) is illuminated with EM radiation, each photon has a one on one interaction with each electron on the surface.

Removing an electron from the surface
Supposing the photon has the objective of removing an electron from the surface. What energy would it require?

Going back to our definitions, this energy is called the work function. Hence, to complete its objective, the photon must have the same energy as the work function of the material.

It may not seem obvious at first, but this links perfectly to the threshold frequency through the equation $$E = hf$$, where $$h = 6.63 \times 10^{-34}$$ and is called Planck's constant.

Hence, the energy that the photon has (in this case, the work function) has a corresponding frequency, in this case, called the threshold frequency.

To release the electron from the surface, the photon must have energy $$hf = \phi$$.

Removing an electron from the surface with kinetic energy
Consider the case where the objective of the photon is to not only release the electron from the surface but to give it a certain velocity, $$v$$ away from the surface.

Because the electron has a velocity, it must have kinetic energy. As a result, the total energy that the photon must deliver can be summarised by this equation:

Photon Energy = Work Function + Kinetic Energy

Or $$hf = \phi + E_{k(max)}$$

Maximum Kinetic Energy
The surface of a material contains many layers of electrons. The further the electron is from the surface layer, the more energy is required to remove it from the material. This can be thought of as an increase in work function.

Going back to our equation $$E_{k} = hf - \phi$$, we can see that increasing $$\phi$$ decreases our kinetic energy.

Hence, the maximum kinetic energy $$K_{e(max)}$$ of an electron occurs when the electron is on the very top layer of the surface.