The Photoelectric Effect
When electromagnetic radiation, such as light, hits the surface of a metal electrons are emitted. These electrons are called photoelectrons and this phenomenon is called the photoelectric effect – as illustrated in the diagram below.
Photoelectrons – Amplitude and Frequency
If light (or any other form of electromagnetic radiation) travelled through space purely as a wave the following effects would be observed when altering the amplitude or frequency:
- Increasing amplitude – increases the kinetic energy of photoelectrons.
- Increasing frequency – increases the rate of photoelectron emission.
However, experiments show that these observations do not occur. Instead the following happens:
- Increasing amplitude – the kinetic energy of photoelectrons remains constant and the rate of photoelectron emission increases.
- Increasing frequency – increases the kinetic energy of photoelectrons but the rate of photoelectron emission remains constant.
These observations lead Einstein to develop a model in which electromagnetic radiation can sometimes behave as particles of electromagnetic energy – now called photons.
These packets of energy are what cause the electrons to be emitted from the metal surface and any remaining energy becomes the kinetic energy of the photoelectron.
Photons – Planck’s Equation
Photon – a quantum of electromagnetic radiation (a discrete packet of energy).
The energy of a photon can be calculated using Planck’s Equation:
Where h is Planck’s constant measured in joule seconds (Js) and f is the frequency of the electromagnetic radiation measured in hertz (Hz).
The value of Planck’s constant is approximately 6.626 x10-34 Js.
From this equation you can see that the frequency of the electromagnetic radiation is directly proportional to the energy of a photon.
Einstein’s Photoelectric Equation
Due to the conservation of energy the total energy of the photon must be equal to the energy needed to release the electron and any kinetic energy the electron has.
The energy required to release an electron from a metal is called the work function:
Work Function (Φ) – the minimum amount of energy required to eject an electron from the surface of a particular metal.
The value of the work function varies depending on the type of metal.
From this we get Einstein’s Photoelectric equation:
Where E is the energy of the photon, Φ is the work function of the metal and KE is the kinetic energy of the photoelectron – all measured in joules.
If we substitute in the equations to calculate the energy of a photon and kinetic energy this can also be expressed as:
Where h is Planck’s constant, f is the frequency of the electromagnetic radiation, m is the mass of the photoelectron measured in kilograms (kg) and v is the velocity of the photoelectron measured in metres per second (ms-1).
Threshold Frequency and Amplitude
From Planck’s equation we can see that the energy of a photon is equal to Planck’s constant multiplied by the frequency of the radiation. As Planck’s constant cannot change the energy of photons can only be varied by changing the frequency of the radiation.
When photons hit an electron, they must have enough energy (equal to the work function) to release them. If photons don’t have enough energy, the frequency must be too low. By increasing the frequency, the energy of the photons will increase and the electrons can be released.
The frequency at which the photons have enough energy to meet the work function of a metal is called the threshold frequency.
Threshold Frequency – the minimum frequency required for radiation to release an electron from the surface of a metal.
If the amplitude of the electromagnetic radiation is increased, the number of photons hitting the surface of the metal increases. This means that the rate of electron emission increases (more electrons are released per unit time). For this to happen though the frequency of the radiation must be at least equal to the threshold frequency.
Worked Examples
In each of the questions below use 6.63 x10-34Js for Planck’s constant and give all answers to three significant figures.
Example 1
Calculate the energy of a photon of light with a frequency of 4 x1014Hz.
Example 2
Radiation with a frequency of 3.13 x1016 Hz releases an electron from a copper plate. The kinetic energy of the electron is 2 x10-17J. Calculate the work function of the plate.
Example 3
An electron is emitted from an iron plate with a velocity of 5 x106ms-1. The work function of iron is approximately 7.2 x10-19J. Calculate the frequency of the radiation required to emit this electron. Use m = 9.11 x10-31kg for the mass of the electron.
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