Electromagnetic radiation and quantum phenomena (3.2.2)

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.

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.

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.

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.

When gases are heated, they emit light at specific wavelengths, resulting in a series of bright lines on a dark background. This occurs because electrons absorb energy when the gas is heated, becoming excited to a higher energy level.

Electrons cannot remain in this excited state indefinitely; they will eventually return to a lower energy level through a process called de-excitation. During de-excitation, energy must be conserved. The energy lost by the electron is emitted as a photon with a specific frequency.

In summary, this absorption/emission process occurs when an electron absorbs energy and is promoted from a lower energy level to a higher energy level. When it then transitions from a higher energy level back to a lower energy level, a photon is released.

Each time an electron transitions between energy levels, it emits photons with discrete frequencies or wavelengths. Since each atom has multiple possible electron transitions, a variety of wavelengths are emitted.

The emitted photons produce a line spectrum, which is a series of bright lines against a dark background. Each line corresponds to a specific wavelength of light emitted during electron transitions.

An emission-line spectrum serves as a unique fingerprint for each element. Since no two elements have the same energy level structure, the pattern of emission lines is unique to each element, allowing for precise identification.

By analysing these spectral lines, scientists can identify the composition of distant stars and other celestial bodies.

For example, a portion (known as the Balmer series) of the emission spectrum of hydrogen is shown above. The different coloured lines indicated the wavelengths of light that correspond to different energy changes that an electron in a hydrogen atom may experience.

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).

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.

To observe the wave nature of particles, the particles must exhibit wave behaviour, specifically producing an interference pattern. Such patterns are caused by diffraction and interference, both of which are properties of waves.

Diffraction effects are most pronounced when the de Broglie wavelength of the particles is of the same order of magnitude as the openings they pass through.

Graphite consists of layers of carbon atoms with a separation of This structure acts as an extremely fine diffraction grating, allowing the electrons to pass through and diffract.

The following experimental setup demonstrates electron diffraction.

1. Electrons are fired from an electron gun in the direction of a thin piece of graphite and accelerated by an electric field so that their de Broglie wavelength is the same order of magnitude as the carbon atom spacing.
2. The electrons diffract as they pass through the graphite in the same way as waves diffract when passing through a diffraction grating.
3. A fluorescent screen is placed behind the piece of graphite to detect the electrons that emerge from it.
4. An interference pattern consisting of concentric rings is observed due to the interference of the electrons.

Unlike a normal diffraction grating, where all openings are aligned, graphite has openings in random orientations, so overlapping diffraction from all the openings produces rings instead of discrete spots.

The setup is contained within a vacuum tube, ensuring that the electrons are not obstructed by air particles.

The de Broglie wavelength of a particle is inversely proportional to its momentum, and this can be observed in the electron diffraction experiment.

Slower electron acceleration by the electric field leads to lower momentum upon reaching the graphite grating. Consequently, the electrons exhibit a larger de Broglie wavelength, which is a closer match to the atomic spacing in the graphite. This results in increased diffraction and a broader interference pattern.

A greater momentum, which corresponds to faster electrons, leads to a smaller de Broglie wavelength. Consequently, the electrons diffract less, producing a narrower interference pattern.