The Photoelectric Effect

The Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from the surface of a metal upon the absorption of electromagnetic radiation. Electrons removed in this manner are known as photoelectrons. This effect provides critical evidence that light is quantised, or carried in discrete packets. Each electron can absorb only a single photon, meaning only the frequencies of light above a threshold frequency will emit a photoelectron.

The Particle Nature of Light

In classical wave theory, electromagnetic (EM) radiation is presumed to behave as a wave, evidenced by phenomena such as diffraction and interference. However, experiments from the last century, including the photoelectric effect and atomic line spectra, can only be explained if EM radiation is understood as behaving like particles.

The Development of Quantum Physics

The field of quantum mechanics has evolved relatively recently compared to classical mechanics (Newton’s laws, wave theory, etc.). Around 1900, discoveries such as the electron and the gamma photon began to challenge existing models of matter. Pioneers of Quantum Theory, including Max Planck, Niels Bohr, and Albert Einstein, began to propose new theories about the nature of matter.

Demonstrating the Photoelectric Effect

The photoelectric effect can be demonstrated using a gold leaf electroscope. Here’s how it works:

• A metal plate, typically zinc, is attached to a gold leaf that initially carries a negative charge, repelling it from a negatively charged central rod.

• Negative charge (electrons) accumulates on the zinc plate.

• When UV light is shone onto the metal plate, photoelectrons are emitted, resulting in the removal of extra electrons from the central rod and gold leaf. Consequently, the gold leaf falls back towards the rod as it becomes less negatively charged and thus repels less.

Observations of the Gold Leaf Experiment

• Closer UV Light Source: The gold leaf falls more quickly due to increased intensity, resulting in more photoelectrons emitted per second.

• Higher Frequency Light Source: The fall rate of the gold leaf remains unchanged, but the maximum kinetic energy of emitted electrons increases with frequency.

• Filament Light Source: Causes no change in the gold leaf’s position, as its frequency is below the required threshold.

• Positively Charged Plate: No change because emitted electrons are attracted back to the plate; electrons cannot escape unless they are on the metal surface.

• Emission of Photoelectrons: Occurs instantaneously when the photon energy equals the work function of the metal.

Explaining the Observations

• Closer UV Light Source: Increases intensity, resulting in faster photoelectron emission.

• Higher Frequency Light Source: Affects maximum kinetic energy without altering the emission rate.

• Filament Light Source: Inadequate frequency means no emission irrespective of intensity.

• Positively Charged Plate: Electrons remain bound unless emitted directly.

• Instant Emission of Photoelectrons: A single photon interacts with a single electron, triggering immediate release if energy conditions are met.

Interaction Between a Photon & Surface Electron

• Each surface electron interacts with a single photon, demonstrating the quantised nature of light.

• The number of photoelectrons emitted is equal to the number of incident photons.

• Increasing the intensity of electromagnetic radiation raises the number of photons per area, thus increasing the number of emitted photoelectrons.

The Photoelectric Equation

Due to energy conservation, the energy of an incident photon is equal to the sum of:

1. The work function (Φ)

2. The maximum kinetic energy of the photoelectron (KE max)

Energy within a photon: E = hf This energy is required to release the electron from the material (the work function) with the remaining energy given as kinetic energy to the emitted photoelectron:

The Photoelectric Equation:

E = hf = Φ + ½ mv²(max) Where:

• h: Planck's constant (J s)

• f: Frequency of incident radiation (Hz)

• Φ: Work function of the material (J)

• ½ mv²(max): KE(max) = maximum kinetic energy of the photoelectrons (J)

Key Points

• If incident photons lack sufficient energy (frequency) to overcome the work function (Φ), no electrons will be emitted.

• For hf₀ = Φ, photoelectric emission barely occurs at the threshold frequency (f₀).

• KE(max) depends only on the frequency of the incident photon, not on the intensity of radiation.

• Most emitted photoelectrons will have kinetic energies less than KE(max).

Graphical Representation of Work Function

The photoelectric equation can be rearranged into the straight line equation: y = mx + c Comparing it to: KE(max) = hf - Φ

• The work function (Φ) is the y-intercept.

• The threshold frequency (f₀) is the x-intercept.

• The gradient equals Planck's constant (h).

• No electrons are emitted below the threshold frequency (f₀).

Threshold Frequency & Wavelength

The threshold frequency is defined as:

• The minimum frequency of incident electromagnetic radiation required to remove a photoelectron from the surface of a metal.

The threshold wavelength, related to threshold frequency by the wave equation, is defined as:

• The longest wavelength of incident electromagnetic radiation that would remove a photoelectron from the surface of a metal.

Threshold frequency and wavelength are properties of a material and vary from metal to metal.

Work Function

The work function Φ, or threshold energy, of a material, is defined as:

• The minimum energy required to release a photoelectron from the surface of a metal.

Consider the electrons in a metal as trapped inside an ‘energy well’ where the energy between the surface and the top of the well is equal to the work function Φ. A single electron absorbs one photon. Therefore, an electron can only escape from the surface of the metal if it absorbs a photon which has an energy equal to Φ or higher.

Different metals have different threshold frequencies and hence different work functions. Using the well analogy:

• A more tightly bound electron requires more energy to reach the top of the well.

• A less tightly bound electron requires less energy to reach the top of the well.

Alkali metals, such as sodium and potassium, have threshold frequencies in the visible light region because the attractive forces between the surface electrons and positive metal ions are relatively weak. Transition metals, such as zinc and iron, have threshold frequencies in the ultraviolet region because the attractive forces between the surface electrons and positive metal ions are much stronger.

Examiner Tip

A useful analogy for threshold frequency is a fairground coconut shy:

• One person is throwing table tennis balls at the coconuts, and another person has a pistol. No matter how many of the table tennis balls are thrown at the coconut it will still stay firmly in place – this represents the low-frequency quanta.

• However, a single shot from the pistol will knock off the coconut immediately – this represents the high-frequency quanta.

The Maximum Kinetic Energy of Photoelectrons & Intensity

The maximum kinetic energy of the photoelectrons is independent of the intensity of the incident radiation. This is because each electron can only absorb one photon. Kinetic energy is only dependent on the frequency of the incident radiation. Intensity is a measure of the number of photons incident on the surface of the metal. Therefore, increasing the number of photons striking the metal will not increase the kinetic energy of the electrons; it will increase the number of photoelectrons emitted.

Rate of Emission of Photoelectrons

The photoelectric current is the rate of emission of photoelectrons emitted per second. The photoelectric current is proportional to the intensity of the radiation incident on the surface of the metal because intensity is proportional to the number of photons striking the metal per second. Since each photoelectron absorbs a single photon, the photoelectric current must be proportional to the intensity of the incident radiation.

**Kinetic energy of photoelectrons is independent of intensity, whereas the photoelectric current is proportional to intensity and independent of frequency.