The photoelectric effect

In a nutshell

When electromagnetic radiation is shone onto a metal, electrons are emitted from the surface of that metal. This is called the photoelectric effect. The photoelectric effect can be demonstrated using a gold-leaf electroscope and is key evidence for the particulate nature of light.

Definitions

The gold-leaf electroscope

The photoelectric effect can be demonstrated using the gold-leaf electroscope, which is a zinc plate on top of a negatively charged stem, with a negatively-charged gold leaf attached. Once the electroscope has been charged, the negative charge of the plate will spread to the stem and gold leaf, which will develop a negative charge and repel each other.

If a clean plate of zinc is then placed on the negatively charged electroscope, and UV light is incident on its surface, free electrons will be emitted from the zinc. These free electrons will cause the negative charge to be lost and the gold leaf will fall back towards the stem. 

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Three conclusions from the photoelectric effect

The gold-leaf electroscope experiment was repeated with different frequencies of electromagnetic radiation, and three key conclusions were drawn:

1. Electrons were only emitted above a certain frequency, the threshold frequency. Below this, not a single electron was emitted no matter the intensity of light shone on the surface. For example, when visible light is shone on the surface, electrons will never be emitted, as all frequencies of visible light are below the threshold frequency. 
   
2. When the radiation is above the threshold frequency, emission of electrons is instantaneous. For example, when UV light is shone on the electroscope, electrons are emitted straight away, there is no time delay. 
3. If the frequency is above the threshold frequency, increasing the intensity will not increase the kinetic energy of the emitted electrons. An increase in intensity will instead lead to an increase in the number of electrons emitted. To increase the kinetic energy of emitted electrons, the incident frequency must be increased.

These observations do not correspond with the wave model of electromagnetic radiation. In this model, the rate of energy transferred is dependent on its intensity, and it was therefore vital in proving the particulate nature of photons.

Einstein's explanation

Each electron on the surface of the metal requires a certain amount of energy in order to escape. Each photon transfers all its energy to an electron. The excess amount, after energy is used to escape the electron, being transferred into kinetic energy of the electron.

Due to the one-to-one interactions between photons and electrons, there is no time delay. This is because there is no accumulation of energy from multiple photons. Depending on the position of electrons relative to positive ions in the metal, they require different amounts of energy to free them.  

There must be a constant for each metal, the work function $$\Phi$$​, which is the minimum energy required to free an electron from the surface of a metal. Each photon must have energy at least as great as the work function in order to free an electron from the metal. This relates to the threshold frequency as energy is directly proportional to frequency.

UV light has a higher frequency than visible light, hence it was above the threshold frequency. This meant electrons were released in the gold-leaf electroscope experiment, whereas for visible light they were not.