2.2.2

# The Photoelectric Effect Explanation

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## Einstein's Photon Model

Albert Einstein came up with an explanation for the photoelectric effect. Einstein suggested that light was made up of little packets of energy called photons.

### One-on-one interaction

• Einstein suggested that each photon had a one-on-one interaction with an electron.
• The electron absorbs all the energy of one photon.
• This explained why the maximum kinetic energy is independent of the intensity.
• Intensity is the number of photons arriving per second.
• It doesn't matter how many photons arrive per second because the electron only interacts with one.

### Energy depends on frequency

• Einstein also suggested that the energy of a photon is proportional to its frequency. This relationship is described in the following equation:
• The constant of proportionality is the Planck constant, h.
• $E = hf = \frac{hc}{\lambda}$
• This explained why the maximum kinetic energy of the emitted electrons is proportional to frequency.
• The higher the frequency of a photon, the more energy is transferred to an electron.

## Consequences of the Photon Model

Einstein's photon model helped explain the photoelectric effect.

### Work function

• For an electron to leave a metal surface, it needs to overcome the bonds holding it down.
• The energy needed to break these bonds is called the work function, φ.
• The work function is different for different metals.

### Threshold frequency

• We can use the threshold frequency to work out the work function of a particular metal and vice versa.
• The energy of a photon at the threshold will equal the energy needed to break the electron free from the metal (i.e. the work function).
• So $\phi = hf$
• And so threshold frequency, $f = \frac{\phi}{h}$

### Photoelectric equation

• Consider the conservation of energy.
• The electron absorbs energy $hf$ from a photon.
• The electron must lose at least the energy needed to break it free from the bonds in the metal, the work function $\phi$.
• The maximum kinetic energy of an electron is given by the photoelectric equation:
• $hf = \phi + E_{k (max)}$
• Remember that the maximum velocity of the electron can be found from:
• $E_{k (max)} = \frac{1}{2}mv_{(max)}^{2}$

### Stopping potential

• Measuring the stopping potential, Vs, can help us work out the maximum kinetic energy, $E_{k (max)}$.
• After the electrons are emitted, they pass through an electric potential.
• As the electrons are charged, they must do work, e × Vs, to move through this potential.
• The electrons will stop if all their kinetic energy is used up doing work against the potential.
• So the equation for stopping potential is:
• $eV_s = E_{k (max)}$