# Photoelectric Effect

September 01, 2016

The Photoelectric Effect

Albert Einstein won his first Nobel Prize for his work on the Photoelectric Effect, which demonstrated the particle nature of light. This demonstration stood in contrast to the Young’s Double Slit experiment and observed diffraction, which demonstrated the wave nature of light.

Einstein worked with a metal plate with light incident on it. He measured how many electrons were emitted from the plate and also the kinetic energy of the electrons. The electrons in the plate need energy to first be liberated from the plate – this is called the work function. Any remaining energy will be found in the kinetic energy of the electrons.

If light behaved as a wave, one would expect the energy to be built up slowly until the electrons had energy equal to the work function. One would expect a constant stream of electrons, regardless of the frequency or colour of the light. Equally, if the intensity of the light were to increase, one would expect the electrons to have a higher kinetic energy. This was not observed in the experiment.

It was observed in the experiment that no electrons were emitted when the light was below a particular frequency, called the Threshold Frequency. So, for example, infrared light produced no electrons, whereas UV light did. The kinetic energy of the electrons then increased with increasing frequency. Another key finding was that increasing the intensity of the light did not increase the kinetic energy of the electrons, but only the number of electrons emitted (so long as the frequency was above the threshold frequency). Einstein proposed that these phenomena occurred because light is not actual a wave, but rather a stream of particles, known as photons. A photon is a quantum of energy of electromagnetic radiation, with energy E=hf. Key findings:

• Electrons need a certain amount of energy to ‘escape’ the metal. This is known as the work function.
• The energy of a photon is proportional to frequency. (E=hf)
• Therefore only photons with frequency higher than the threshold frequency will have energy equal or greater than the work function.
• Any extra energy is found in the kinetic energy of the electrons. This is due to the conservation of energy when a photon interacts with an electron.
• An increase in frequency, above the threshold frequency, increases the kinetic energy of the electrons.
• An increase in intensity increases the number of liberated electrons (due to more photons incident on the metal).

We can write the observations of the photoelectric effect mathematically.

• Each photon has energy
• The work function for an electron is denoted ϕ, which is the minimum energy required to remove a delocalised electron from the surface of a metal
• The kinetic energy of the electron is denoted KEmax

Due to conservation of energy:

hf = ϕ + KEmax

Demonstrating the photoelectric effect using a zinc plate attached to gold-leaf electroscope

Description:

The clean zinc plate is mounted on the cap of a gold-leaf electroscope and negatively charged. The gold leaves will repel each other. Under white light, there is no change to the repulsion between the gold leaves, even if the intensity is increased. However, the gold leaves collapse when a U-V lamp is shone on the plate. The experiment therefore shows the emission of negative charge/electrons from the plate.