Electron, thermionic emission & photoelectric effect

Learning goals

What students should be able to explain, calculate and investigate after completing The Electron, Thermionic Emission and Photoelectric Effect.

Goals marked Higher Level are required only for Higher Level students; the remaining goals are for all students.

• Describe evidence for the existence and properties of the electron.
• Explain thermionic emission and describe cathode rays.
• Predict the deflection of an electron beam in electric and magnetic fields.
• Explain the photoelectric effect and why it supports the particle model of light.
• Higher Level: Use Einstein's photoelectric equation to solve problems.
• Describe how X-rays are produced by braking radiation and characteristic X-ray emission in a metal target.

Key definitions

Precise terms, symbols and SI units used in The Electron, Thermionic Emission and Photoelectric Effect.

The Electron and Thermionic Emission

Experiments (such as those with cathode ray tubes) provided evidence that cathode rays consist of streams of identical, negatively charged particles.

The electron carries the smallest (indivisible) quantity of electric charge found in nature, e = 1.602 × 10⁻¹⁹ C. Thermionic emission is the process by which heating a metal cathode gives its free electrons enough kinetic energy to escape the metal's surface entirely, producing a supply of free electrons that can then be accelerated and directed as a beam (e.g. in an electron gun).

Deflection of Electron Beams

A beam of electrons carries charge, so it experiences a force (and is deflected) in electric and magnetic fields, just as any other charged particle would.

In a uniform electric field (e.g. between two charged parallel plates), the beam curves towards the positive plate, following a path similar to horizontal projectile motion (constant velocity in the original direction, constant acceleration towards the positive plate). In a uniform magnetic field, the force on the moving electrons is always perpendicular to their velocity (F = qvB), so the beam follows a curved (circular) path rather than a parabola, and its speed stays constant (the magnetic force does no work, since it never has a component along the direction of motion).

• For a charge moving at angle θ to a magnetic field, the force magnitude is F = |q|vB sin θ. The shorter form F = |q|vB applies only when the motion is perpendicular to the field.

The Photoelectric Effect

When light shines on certain metal surfaces, electrons can be emitted — but only if the light's frequency is at or above a threshold frequency specific to that metal.

This could not be explained by the wave theory of light (which predicts that sufficiently intense light of any frequency should eventually transfer enough energy to eject electrons, given enough time) — it was explained by Einstein using the particle model of light: light arrives in discrete photons, each with energy E = hf, and each photoelectron is emitted by absorbing a single photon in one interaction. If a photon's energy exceeds the work function (the minimum energy needed to free an electron from that surface), the excess energy becomes the electron's kinetic energy: this is the principle of conservation of energy underlying Einstein's photoelectric equation.

Einstein’s photoelectric law applies conservation of energy to one photon and one emitted electron. The photon supplies energy hf. The metal uses the work function Φ to release the electron, and any remaining energy becomes the electron’s maximum kinetic energy.

• h is Planck’s constant, 6.63 × 10⁻³⁴ J s.
• f is the frequency of the incident light, measured in hertz (Hz).
• Φ is the work function: the minimum energy needed to release an electron, measured in joules (J).
• E_k(max) is the maximum kinetic energy of an emitted electron, measured in joules (J).
• m is the electron mass, measured in kilograms (kg), and v_max is the maximum electron speed, measured in m s⁻¹.
• f₀ is the threshold frequency, measured in hertz (Hz), and is defined by hf₀ = Φ.

Frequency and intensity: Increasing frequency above threshold increases the maximum kinetic energy. At a fixed frequency above threshold, increasing intensity supplies more photons each second, so more electrons are emitted and the photoelectric current increases. It does not increase the maximum kinetic energy when the frequency is unchanged.

Photocells

A photocell uses the photoelectric effect: light above the threshold frequency ejects electrons from a photosensitive surface and produces an electrical response.

If photon energy is below the relevant threshold, increasing intensity alone cannot release photoelectrons. Above threshold, greater intensity supplies more photons per second and can increase the photoelectric current.

• A photocell converts incident light into an electrical response.
• The response depends on photon energy and the number of photons arriving per second.
• Photocells are used in light sensors, automatic controls and measurement devices.

X-Ray Production

X-rays are produced in an X-ray tube. Electrons are released from a heated cathode by thermionic emission and accelerated through a large potential difference towards a metal target (anode). When the fast electrons strike the target and are rapidly decelerated, some of their kinetic energy is converted into X-ray photons.

The accelerated electrons gain kinetic energy from the electric field. When they strike the metal target, they lose energy. Most of this energy becomes heat, but some is emitted as X-rays.

• A low-voltage heater supply heats the filament at the cathode. The heated cathode releases electrons by thermionic emission.
• A large potential difference makes the cathode negative and the metal target positive. The electric field accelerates electrons from the cathode towards the target (anode).
• The tube is evacuated so the electrons can travel to the target without repeatedly colliding with gas particles.
• When the fast electrons strike the target, they are rapidly decelerated. Some of their kinetic energy is converted into X-ray photons, but most becomes heat. A high-melting-point target such as tungsten and effective cooling are therefore needed.
• Increasing the accelerating voltage increases the maximum X-ray photon energy and penetrating ability. If an electron gains energy eV, the maximum photon energy is E_max = eV and the minimum wavelength is λ_min = hc/(eV).
• Increasing the filament heating mainly increases the number of emitted electrons and therefore the X-ray intensity.
• Shielding and controlled exposure are essential because X-rays are ionising radiation.

1. Braking radiation (bremsstrahlung): Fast electrons are rapidly decelerated as they pass close to nuclei in the target. The loss of kinetic energy is emitted as X-ray photons.

2. Characteristic X-rays: A fast incoming electron can remove an inner-shell electron from an atom in the target. An electron from a higher energy level then falls into the vacancy, and the energy difference is emitted as an X-ray photon.

Diagrams and formulae

Concise revision diagrams and formulae for The Electron, Thermionic Emission and Photoelectric Effect.

• Electron beam deflection: in a uniform electric field the beam follows a curved (parabolic) path towards the positive plate; in a uniform magnetic field the force is always perpendicular to the velocity, giving a circular path.
• Einstein’s photoelectric law (recap): hf = Φ + E_k(max). Frequency controls the maximum kinetic energy; at fixed frequency above threshold, intensity controls the emission rate and photoelectric current.
• X-ray tube: thermionically emitted electrons accelerate through a large potential difference towards the metal target (anode). Their rapid deceleration produces X-rays, while most of their energy becomes heat.

Electron beam deflection: in a uniform electric field the beam follows a curved (parabolic) path towards the positive plate; in a uniform magnetic field the force is always perpendicular to the velocity, giving a circular path.

The photoelectric effect: an incoming photon of energy hf is absorbed by an electron at the metal surface; if hf exceeds the work function Φ, the electron is ejected with the remaining energy as kinetic energy.

X-ray tube: thermionically emitted electrons accelerate through a large potential difference towards the metal target (anode). Their rapid deceleration produces X-rays, while most of their energy becomes heat.

• Key relationships
• Electron charge: e = 1.602 × 10⁻¹⁹ C Photon energy: E = hf (h = 6.63 × 10⁻³⁴ J s) Work function: Φ = hf₀ Einstein's photoelectric equation: hf = Φ + Eₖ(max) where Eₖ(max) = ½mv²max Force on a charge in a magnetic field: F = qvB

Worked Example

A step-by-step calculation applying the central relationships in The Electron, Thermionic Emission and Photoelectric Effect.

Light of frequency 7.5 × 10¹⁴ Hz shines on a metal with work function 3.5 × 10⁻¹⁹ J. Calculate the maximum kinetic energy of an emitted photoelectron. (h = 6.63 × 10⁻³⁴ J s.)

• E (photon) = hf = 6.63 × 10⁻³⁴ × 7.5 × 10¹⁴ = 4.97 × 10⁻¹⁹ J
• E = Φ + ½mv²max → ½mv²max = E − Φ = 4.97 × 10⁻¹⁹ − 3.5 × 10⁻¹⁹ = 1.47 × 10⁻¹⁹ J

Practical / Investigation

Experimental planning, measurement and evaluation for The Electron, Thermionic Emission and Photoelectric Effect.

Investigation: Verifying the photoelectric effect using secondary data

• Task: using provided or sourced secondary data (e.g. a table or graph of maximum kinetic energy against frequency for a given metal), verify that a photocell only produces a current above a threshold frequency, and that maximum photoelectron kinetic energy increases linearly with frequency above threshold, consistent with E = Φ + ½mv²max.
• Data-analysis skill: plotting maximum kinetic energy (y-axis) against frequency (x-axis) for light above the threshold frequency gives a straight line; the slope equals Planck's constant h, and the negative y-intercept relates to the work function Φ.
• Evaluate real-life applications: relate the photoelectric effect to devices such as photocells in automatic lighting, and light sensors in cameras.

• Clean a zinc plate attached to an electroscope and charge it negatively. Shine ultraviolet light directly on the zinc: the leaf collapses as emitted electrons leave the plate.
• Repeat with ordinary glass between the UV source and zinc. The discharge is greatly reduced because ordinary glass absorbs much of the relevant ultraviolet radiation.
• With the zinc plate positively charged, UV does not produce the same collapse because emitted electrons are attracted back and electron loss would make the plate more positive.
• Use an enclosed school UV source, avoid eye/skin exposure, and treat this as a qualitative demonstration rather than a measurement of Planck’s constant.

• Use maximum kinetic energy data for several frequencies above threshold, all for the same photosurface.
• Do not treat light intensity as the variable controlling maximum electron energy; intensity mainly affects photocurrent when f exceeds threshold.

Quick-Check Questions

Short retrieval questions covering the essential ideas in The Electron, Thermionic Emission and Photoelectric Effect.

1. What is thermionic emission?

2. Why can't the wave theory of light explain the threshold-frequency behaviour of the photoelectric effect?

3. State Einstein's photoelectric equation and the meaning of each term.

4. Describe the shape of the path of an electron beam moving through a uniform magnetic field.

5. How are X-rays produced in an X-ray tube?

Common mistakes and exam tips

Common misconceptions and exam-technique checks for The Electron, Thermionic Emission and Photoelectric Effect.

• Avoid: Thinking sufficiently intense light below threshold frequency eventually ejects electrons. Correct idea: Below threshold frequency, no photoelectrons are emitted regardless of intensity.
• Avoid: Saying intensity determines the maximum kinetic energy of photoelectrons. Correct idea: Above threshold, frequency determines maximum kinetic energy; intensity mainly affects the emission rate for fixed frequency.
• Avoid: Drawing magnetic deflection of a perpendicular electron beam as a parabola. Correct idea: A uniform magnetic field perpendicular to the velocity produces circular motion; a uniform electric field can produce a parabolic path.

• Separate the effects of frequency and irradiance/intensity in photoelectric-effect answers.
• Check that hf ≥ Φ before calculating photoelectron kinetic energy.
• Identify the field type before predicting an electron-beam path.

Exam-style questions

Five exam-style questions with worked answers on The Electron, Thermionic Emission and Photoelectric Effect.

Higher Level — Required Content

Required Higher Level content for this topic.

• φ is the work function: the minimum energy needed to remove an electron from the surface.
• At the threshold frequency, emitted electrons have zero maximum kinetic energy, so φ = hf₀.
• Increasing frequency above threshold increases maximum kinetic energy; increasing intensity mainly increases the number emitted.

End-of-unit revision

Formulae, definitions, experiments and mixed revision questions for The Electron, Thermionic Emission and Photoelectric Effect.

Try without notes: state Einstein's photoelectric equation and explain why intensity alone cannot cause emission below the threshold frequency.

• e = 1.602 × 10⁻¹⁹ C
• E = hf
• Φ = hf₀
• E = Φ + ½mv²max
• F = qvB (force on a moving charge in a magnetic field)

• Thermionic emission
• Threshold frequency
• Work function
• Photoelectric effect

• Electron beam deflection in electric (parabolic) and magnetic (circular) fields
• Photoelectric effect: photon absorbed, electron ejected
• X-ray tube structure

• Verifying the photoelectric effect using secondary data (kinetic energy vs frequency graph)

• Thinking intensity (not frequency) determines whether photoelectric emission occurs
• Describing magnetic deflection as parabolic instead of circular
• Confusing thermionic emission with the photoelectric effect

1. A photon has energy 4 × 10⁻¹⁹ J. Calculate its frequency. (h = 6.63 × 10⁻³⁴ J s.)

2. Explain why increasing the intensity of light above the threshold frequency increases the photocell current, but does not increase the maximum kinetic energy of individual photoelectrons.

3. A metal has a work function of 2.5 × 10⁻¹⁹ J. Light of frequency 6 × 10¹⁴ Hz shines on it. Calculate the maximum kinetic energy of an emitted electron.

4. Explain the two main ways in which X-rays are produced when fast electrons strike the metal target.

1. f = E/h = (4×10⁻¹⁹) ÷ (6.63×10⁻³⁴) ≈ 6.03 × 10¹⁴ Hz.

2. Increasing intensity means more photons arrive per second, so more individual photon-electron interactions occur, ejecting more photoelectrons per second (more current); but each photon still carries the same energy hf, so the maximum kinetic energy of any single ejected electron is unchanged.

3. E = hf = 6.63×10⁻³⁴ × 6×10¹⁴ = 3.98×10⁻¹⁹ J. ½mv²max = E − Φ = 3.98×10⁻¹⁹ − 2.5×10⁻¹⁹ = 1.48×10⁻¹⁹ J.

4. Braking radiation is produced when fast electrons are decelerated near target nuclei and lose kinetic energy as X-ray photons. Characteristic X-rays are produced when an incoming electron removes an inner-shell electron and an electron from a higher energy level falls into the vacancy, emitting the energy difference as an X-ray photon.

The table below shows which equations from this unit appear in the official State Examinations Commission Formulae and Tables book, and where.