The photoelectric effect demonstrates the relationship between photon frequency and energy. When light of a certain minimum frequency shines on a metal surface, electrons are emitted. The maximum kinetic energy of the emitted electrons depends on the frequency of absorbed light based on Einstein's equation, which relates the photon frequency, stopping potential, and metal's work function. The photoelectric effect provided evidence that light behaves as discrete packets of energy called photons rather than as a wave.

1. Where can we see the relationship between photon frequency and energy? The Photoelectric Effect

2. LEDs emit photons of a particular frequency They start to do this when provided with enough energy from a power supply We can measure the amount of energy required by measuring the voltage when it just starts to ‘shine’ To review

3. LEDs and Quantum Behaviour

4. But what other ways are there of demonstrating this phenomenon?

5. Photo Electric Effect

6. Photo Electric Effect Here the frequency of the absorbed light is compared with the potential difference needed to stop electrons emitted from clean metal surfaces. The photoelectrons are emitted from a photocathode on the left-hand side of the photocell shown above and they just climb a potential hill described as ∆ V in the diagram. Note that ∆ V is adjusted until the current in the circuit just drops to zero. We call the ∆ V the stopping p.d. In the photoelectric effect a single photon transfers all of its energy to a single electron within the metal. However, the electron will not emerge with the full photon energy because some energy is required to remove an electron from the metal. If the electron receives its energy when it is at the surface of the metal the energy required to remove it is known as the work function which is given the symbol φ . Each metal has its own unique work function. For this electron we can say that hf = e ∆ V + φ

7. That means that electron will emerge with the maximum kinetic energy which is measured by e ∆ V. By conservation of energy this is equal to hf - φ If the electron receives its energy when it is below the surface of the metal, some kinetic energy is lost as the electron travels to the surface and the electron has less than the maximum amount of kinetic energy when it is released from the surface. In this case the electron will emerge with a kinetic energy hf – φ – energy lost as electron travels to surface The experiment above is designed to measure just the maximum kinetic energy of the emerging electron. For this situation we have the equation e ∆ V= hf - φ which was first published by Albert Einstein in one of his famous 1905 papers. This equation is testable as indicated by the diagram above, since ∆ V and f are both measurable.

8. You should note that a minimum frequency of radiation, f 0, is needed to eject an electron from a metal. If the frequency of the radiation is below this, no electrons will be ejected. If the frequency is above this value the number of electrons ejected per second will depend on the intensity of the radiation since a brighter light means more photons falling on the metal per second. However, the maximum kinetic energy of the ejected electrons will be independent of intensity. This follows from Einstein’s equation above and is easily confirmed by experiment. The bottom right-hand panel of the diagram above shows that graphs for different metals will have identical gradients but different intercepts. The gradient equals the Planck constant, h , which is a fundamental constant. The intercept is related to the work function, φ.

9. Spectral Lines and Energy Levels