Particle nature of light (Topic 5D)

In the 1800s, electromagnetic (EM) radiation was solely viewed as continuous waves.

Many phenomena involving electromagnetic radiation can be explained by a wave model:

• EM waves diffract around objects. For example, radio waves diffract around hills.

• EM waves interfere. For example, in Young’s double slit experiment, the waves passing through each slit interfere to produce an interference pattern on a screen. Young’s double slit experiment also demonstrates diffraction of EM waves.

In 1900, our understanding of electromagnetic radiation underwent a revolution. German physicist Max Planck studied the blackbody emission spectrum, which is the spread of wavelengths of EM radiation emitted by an idealised object due to its temperature.

All blackbody emission spectra have the same characteristic shape. The peak wavelength corresponds to the wavelength of light that is emitted most strongly.

The peak wavelength does not necessarily correspond to the colour we see. For example, a blackbody can appear white even if its peak emission is green because its broad spectrum includes significant red and blue light, which, when combined, the brain perceives as white.

The temperature of a blackbody determines its peak wavelength and hence its colour, as shown below for blue, green and red blackbodies, where the intensity is presented in arbitrary units, a.u.

The shape of blackbody spectra could not be explained by the wave model of EM radiation. Instead, Planck postulated the photon model, which states that EM radiation is made up of individual particles rather than continuous waves. We now know these particles as photons.

Photons are discrete wave-packets of energy.

Photons demonstrate the discrete nature of energy, meaning that energy cannot be divided into smaller portions indefinitely.

For example, an electron in an atom can absorb a photon, thereby gaining energy. The electron cannot absorb ‘part’ of the photon. It can only gain the whole energy of the photon or none at all.

As an analogy, consider a person walking up a set of stairs. His height above the ground increases in discrete steps, and he cannot be at any height in between the steps. On the other hand, if they walk up a slope, then their height increases continuously.

• On a small scale, energy is discrete, as seen in the case of an electron absorbing a photon.

• On a large scale, energy can be seen as continuous. For example, a car gains kinetic energy as it speeds up, and the kinetic energy is observed to increase continuously.

The wave model could not explain blackbody spectra because it predicted an infinite energy of radiation at low wavelengths (or high frequencies) and became known as the ultraviolet catastrophe or Rayleigh–Jeans catastrophe.

The graph below shows the blackbody spectrum predicted by the wave model (in red) compared to the experimentally observed spectrum shown in black.

Planck’s photon model was able to reproduce the observed spectrum. Planck postulated that the energy emitted at each wavelength was discrete, not continuous.

• The total energy at each wavelength is equal to the energy of the photons emitted, which are small packets of energy.
• At low wavelengths, each of these photons has such a high energy that a blackbody cannot produce them at all, explaining the dip in the spectrum.

In different circumstances, electromagnetic radiation can be considered as either a wave or a photon. Since a photon is a particle, this is known as the wave–particle duality of EM radiation.

When EM radiation propagates through space, it should be modelled as a continuous wave:

• The wave model of EM radiation describes the diffraction and interference of waves.

When EM radiation interacts with matter, it should be modelled as a particle:

• Electrons exist in energy levels in atoms. When these electrons absorb a photon, they can transition to a higher energy level. This cannot be explained by considering EM radiation as continuous waves.

Electromagnetic waves exhibit wave–particle duality.

The photoelectric effect provides evidence for light behaving as a particle. When light of high enough frequency is incident on a metal’s surface, electrons are emitted. This can only be explained by the light behaving as a stream of particles (photons).

Photons can also demonstrate wave properties. Light will diffract around obstacles and slits; it can also interfere with itself constructively and destructively, producing interference patterns.

Electrons also exhibit wave–particle duality, showing both particle-like and wave-like behaviour in different circumstances.

When behaving as particles, electrons can be accelerated by electric and magnetic fields due to their charges, and their motion can be described using classical mechanics.

Electrons can also display wave properties. When a beam of electrons is fired through very narrow openings, they can diffract and produce interference patterns.

When electromagnetic (EM) radiation of sufficient energy is shone on the surface of a metal, electrons are emitted from the surface. This is known as the photoelectric effect.

The electrons emitted due to the photoelectric effect are called photoelectrons. It is important to note that photoelectrons are just normal electrons.

For most metals, ultraviolet (UV) light has enough energy to cause the photoelectric effect.

The photoelectric effect can be demonstrated using a gold leaf electroscope, which consists of a metal rod attached to a strip of gold leaf.

1. The gold leaf is placed inside a box to shield it from air draughts.
2. A negatively-charged zinc plate is attached to the top of the electroscope. The negative charges spread out between the metal rod and the gold leaf, causing the gold leaf to repel the strip and move away.
3. If UV radiation is shone on the zinc plate, the gold leaf gradually falls back down towards the metal rod.

The UV radiation causes photoelectrons to be emitted from the zinc by the photoelectric effect, so that the metal rod and gold leaf slowly lose their charge and no longer repel.

The photoelectric effect is evidence for the photon model of EM radiation.

Each photon incident on a metal surface can only transfer its energy to an electron in a one-to-one interaction. The diagram below shows this interaction at the atomic level.

Each electron requires a certain amount of energy to escape the metal. If the energy absorbed from the photon is greater than the required energy, the electron escapes.

Since the surface electrons undergo one-to-one interactions with the incident photons, the intensity of incident radiation – the number of photons – does not affect whether electrons are emitted.

Electrons are emitted from a metal surface by the photoelectric effect when radiation with a frequency higher than the threshold frequency is incident on the surface.

• Increasing the intensity of radiation does not change the maximum kinetic energy of the photoelectrons.
• The rate of emission of photoelectrons due to incident radiation with a frequency above the threshold frequency is directly proportional to the intensity of the incident radiation.

Increasing the intensity of radiation increases the number of photons incident on the metal surface per second. More electrons absorb energy from a photon and leave the surface, so the rate of emission of photoelectrons increases.

When monochromatic photons with uniform energy encounter electrons in a metal, each electron gains the same amount of energy from each photon, but the emitted photoelectrons have a range of kinetic energies (KE). This is because work must be done on the electrons for them to leave the metal.

The minimum energy required to free an electron from a metal surface is the work function,

• Surface electrons absorb a photon and lose an amount of energy equal to the work function before being released. The remaining energy from the absorbed photon is converted to KE.

• Deeper electrons require more energy to escape, so less of the absorbed photon energy is converted to KE upon emission.

The minimum energy required to free an electron from a metal surface is the work function Different metals have different work functions, which are in the range of a few electronvolts.

The conversion between electronvolts and joules is:

The table below gives the work functions of some common metals.

The work function of a metal can vary depending on its surface conditions, which is why the work functions above are given as a range. Examples of factors that change the work function of a metal include:

• Surface contamination can either increase or decrease the work function.
• Surface structure: roughened surfaces often have lower work functions than smooth surfaces.
• Surface defects reduce the work function.

Einstein’s photoelectric equation can be written in terms of the threshold frequency, as:

A plot of the maximum kinetic energy, against the frequency, of incident radiation is shown below.

The gradient of the straight line graph is equal to

The threshold frequency is the X axis intercept. This can be seen by setting which leads to:

A negative kinetic energy is unphysical, so the graph shows that no electrons are emitted for incident radiation below,

Additionally, the Y axis intercept is equal to the negative of the metal work function. Setting gives:

Einstein’s photoelectric equation can be written in terms of the threshold frequency, :

A plot of the maximum kinetic energy against the frequency for two different metals is shown below.

The gradient of the graph is equal to Planck’s constant, so it remains the same for any metal. Plots for different metals demonstrate how a higher work function results in a higher threshold frequency.

In the example above, metal 2 has a higher work function and higher threshold frequency than metal 1.

The larger the work function, the greater the energy of incident photons required to emit photoelectrons. From the equation higher energy photons have a higher frequency.

A continuous spectrum is a type of light spectrum where you can observe all possible frequencies of light, spread smoothly over a wide range. It’s like seeing the full range of colours in a rainbow without any gaps.

For example: If you were to look at the spectrum of light produced by a white-hot filament, you would see a continuous blend of colours from red to violet without any missing sections.

Even though the Sun’s light appears white, its spectrum is not continuous.

When we examine it closely, we see dark lines in the Sun’s absorption spectrum called absorption lines where some frequencies are missing. These gaps are caused by elements in the Sun’s outer layers absorbing certain specific wavelengths of light.

Bohr’s atomic model:

• Electrons orbit the nucleus: Similar to how planets orbit the Sun, electrons circle around the nucleus, but they can only exist in specific orbits.

• Electrons have specific, quantized energy levels: Electrons cannot just orbit anywhere. They are confined to certain paths or energy levels that correspond to particular energies. These paths are called electron shells.

• Energy transitions: Electrons can move between these orbits, but to do so, they must either absorb energy to move to a higher shell or release energy to transition to a lower shell.

Picture an electron moving up or down steps in a building. Each step represents a specific, discrete energy level – the electron cannot stop in between the steps, only on one or the other. This means their energy is quantized, meaning they are limited to specific values.

Bohr used the idea of photons (particles of light) to explain the phenomenon of spectral lines. He explained that atoms emit or absorb light at specific, discrete frequencies, producing spectral lines instead of a continuous range of colours.

These lines correspond to specific energies associated with the energy levels electrons may occupy in an atom. This is because photons are either emitted or absorbed when electrons in the atom move between energy levels.

Excitation occurs when an electron gains energy and jumps from a lower energy level (closer to the nucleus) to a higher energy level (farther from the nucleus). This requires the electron to absorb a specific amount of energy.

The energy needed for this can come from various sources.

• Photon absorption: The electron can absorb a photon (a packet of light energy) with exactly the right amount of energy corresponding to the difference between two energy levels.
• Heat energy: Energy from the surroundings can also excite electrons, such as heating a gas.
• Electric field: Applying an electric field can provide energy to excite electrons.

De-excitation occurs when an electron loses energy and falls from a higher energy level to a lower energy level. When this happens, the electron releases the energy it no longer needs. This energy is emitted as electromagnetic radiation (usually visible light or other forms of radiation, depending on the atom).

The frequency of the emitted radiation is directly related to the energy difference between the higher and lower energy levels. This is why atoms emit light at specific frequencies, which we can observe as spectral lines.

Absorption when an electron absorbs energy (such as from a photon), it moves to a higher energy level. This is also called excitation.

Only photons with exactly the right amount of energy – the difference between two energy levels – can be absorbed. If the photon doesn’t match, the electron won’t move. Thus, only specific frequencies of light are absorbed.

Emission occurs when the electron drops back to a lower energy level, it emits a photon with energy exactly equal to the difference between the two levels.

This process is the basis for the emission spectra of elements.

Energy levels within an atom are given as negative values. This is because external energy must be supplied to transition an electron from one energy level to another, or to move it to a point far from the nucleus where its energy is zero.

The negative energy represents how much energy an electron is ‘missing’ compared to being free. The more negative the value, the more tightly the electron is bound to the nucleus.

The value of a given energy level tells you the amount of energy required to remove the electron from that specific energy level and move it to infinity, where it is free of the atom.

Think of the negative energy as the depth of a well. To pull the electron out of the well, you need to add enough energy to overcome its negative value.

The energy level with the most negative value is the ground state, This is the lowest energy level an electron can occupy in an atom.

It is the most stable position for the electron and requires the most energy to remove the electron from the atom compared to any other energy level.

In a hydrogen atom, the energy of the ground state is This means you would need to supply of energy to completely remove the electron from a hydrogen atom.

This complete removal of an electron from an atom is called ionisation.

The wavelength of the emitted photon is inversely proportional to the energy of the transition.

• Larger energy transitions result in photons with shorter wavelengths (higher frequency).
• Smaller energy transitions produce longer wavelength photons (lower frequency).

For example, transitions to different energy levels in the hydrogen atom produce photons with different characteristics:

• Transition to (ground state): Photons emitted are in the ultraviolet range (short wavelength, high energy, high frequency).

• Transition to Photons emitted are in the visible light range.
• Violet light corresponds to the highest energy (shorter wavelength).
  • Red light corresponds to the lowest energy (longer wavelength).

• Transition to Photons emitted are in the infrared range (long wavelength, lower energy, lower frequency).

Continuous spectra

• A continuous emission spectrum is one that contains light across all wavelengths of the electromagnetic spectrum.
• This type of spectrum is produced by hot, dense objects, such as the cores of stars.
• Photons emitted from these sources include all possible wavelengths and frequencies, creating a seamless spectrum without gaps.

Emission line spectra

• An emission line spectrum occurs when electrons transition from higher to lower energy levels, releasing photons.
• Each transition corresponds to a specific wavelength, producing coloured lines on a black background.
• This type of spectrum is characteristic of hot, low-pressure gases.

Absorption spectra

• Absorption spectra arise when an atom absorbs specific wavelengths of light, resulting in missing lines.
• When a continuous spectrum passes through a cool, low-pressure gas, specific wavelengths of light are absorbed, leading to a spectrum with missing wavelengths.
• This spectrum consists of a continuous background with dark lines where certain wavelengths have been absorbed.

The missing wavelengths in an absorption spectrum correspond exactly to the wavelengths emitted in the emission spectrum of the same element. When electrons return to lower energy levels, they emit photons in all directions, which is why some wavelengths appear absent.

The three kinds of spectra you should be familiar with:

• Continuous spectra: Contains all possible wavelengths and frequencies
• Emission line spectra: Discrete coloured lines on a dark background
• Absorption line spectra: Discrete dark lines on a continuous background

The key differences between how these spectra are produced and what they look like are shown in the image below: