Photoelectric Effect

In the early years of the 20th century, scientists Max Plank and Albert Einstein proposed an alternative theory for electromagnetic energy - Quantum Theory:-

Quantum theory states that light is a stream of tiny, individual "wave packets" called Quanta or Photons.

As with classical wave theory, each photon has a Velocity (v) of 3x108 ms-1 in air, a

frequency (f) measured in hertz and Wavelength (λ) measured in metres.

Unlike classical wave theory, however, the Energy of a Photon does not depend on its Amplitude, it depends on its Frequency.

The higher the Frequency, the higher the Energy.

For Example

In air, a Photon of yellow light has a Wavelength of 589nm, calculate the Energy of each Photon.

The video below gives a summary of the Photoelectric Effect, which "proves" light is a Particle (a Photon)

There are four combinations of charge and light source which must be explained in order to understand the Photoelectric Effect.

The above diagram shows the basic setup of a Gold Leaf Electroscope. To demonstrate the Photoelectric Effect we must charge the electroscope and then shine light of known wavelength upon the metal plate.


Condition 1

Positively charged electroscope

Visible Light

Condition 2

Negatively charged electroscope

Visible light

Condition 3

Positively charged electroscope

Ultra-violet Light

Condition 4

Negatively charged electroscope

Ultra-violet Light

Explanation of the Photoelectric Effect

When Photons of ultra-violet radiation are shone onto the zinc plate, they have sufficient energy to eject Electrons from the surface of the zinc. White light does not have sufficient energy, no matter the brightness, and so the electroscope does not discharge.

If light was behaving as a wave, increasing the brightness of white light should have given sufficient energy to eject electrons, but this does not work.

The only way to explain the above observations is that light is behaving as a particle, as only a Photon of sufficient Energy can cause the ejection of an Electron. Therefore the Photoelectric Effect "proves" light is a particle.


Quantum Explanation of the Photoelectric Effect


Work Function

The electrons in a metal are held on a surface by attractive forces. If an electron is to escape from the metal surface, it must overcome these attractive forces.

The Work Function of a metal is the minimum Energy which must be supplied to enable an Electron to escape from the metal surface.

If one photon of electromagnetic Energy (E = hf) strikes a metal surface, it causes one Electron to be emitted from the metal surface if the photon's energy (hf) is equal to or greater than the work function of the metal. This process is called Photoelectric Emission.

If the energy is greater than the Work Function, then the excess energy of the Photon (that has not been used to emit the electron) is converted into Kinetic Energy of the Electron.


Threshold Frequency

In order to have sufficient energy to overcome the Work Function, there is a minimum frequency that the Photon must be. This frequency is called the Threshold Frequency (f0).

It can be calculated by:-

Where:-

h = Plank's Constant = 6.63x10-34 (Js)

f = Photon Frequency (Hz)

f0 = Threshold Frequency of the Metal (Hz)

m = Mass of Electron = 9.11x10-31 (kg)

v = maximum velocity of the electron (ms-1)

By using a range of wavelength light, the following graph can be generated:-

As can be seen from the graph, once the Threshold Frequency is reached, Photoemission occurs, and after this point, the energy of the ejected electron increases with Frequency.


Photoelectric Emission and Brightness

When looking at the effect of the different sources of light earlier, we said that Brightness had no effect on Photoelectric Emission, but this is not strictly true.

1. Below Threshold Frequency - Brightness has no effect, no matter how bright the light source, there will be no emission.

2. Above Threshold Frequency - As each photon has the energy to eject an Electron, if you increase brightness, you increase number of photons, therefore increase number of ejected Electrons.