X-ray Production and Energy Spectrum Revision Notes | A Level AQA Physics
Electrons from a heated cathode are accelerated into the anode, producing bremsstrahlung and characteristic X-rays. Free notes and 13 questions answered.
Updated 12 Sept 2026 · Revise Right Team
X-ray Production and Energy Spectrum is part of X-ray imaging (A-level only) in A Level AQA Physics.
8 min
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34
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A Level AQA
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Reviewed by Revise Right
Content review
What this lesson covers
Electrons from a heated cathode are accelerated into the anode, producing bremsstrahlung and characteristic X-rays. Free notes and 13 questions answered.
Explain the physical principles by which X-rays are produced in an X-ray tube
Describe the continuous (bremsstrahlung) and characteristic X-ray spectra and explain the origin of each
Calculate the maximum photon energy and minimum wavelength produced by an X-ray tube for a given accelerating voltage
Compare the features of the continuous and characteristic spectra and explain how tube voltage and target material affect each
Key ideas to keep in view
Use this lesson to stay inside X-ray imaging (A-level only) while connecting the detail back to the wider Medical physics (A-level only) topic.
Bremsstrahlung radiation: Continuous X-ray emission produced when fast-moving electrons decelerate rapidly on interaction with the nuclei of the target anode material, converting kinetic energy into photons across a range of energies.
Characteristic X-rays: Discrete-energy X-ray photons emitted when an inner-shell electron is ejected from a target atom and an outer-shell electron drops down to fill the vacancy, releasing a photon whose energy equals the difference between the two shell energy levels.
Maximum photon energy: The highest possible photon energy in the X-ray spectrum, produced when an electron transfers all of its kinetic energy into a single photon; equal to the work done on the electron by the accelerating voltage: $E_{max} = eV$.
Minimum wavelength: The shortest wavelength present in the X-ray spectrum, corresponding to the maximum photon energy; calculated using $\lambda_{min} = \frac{hc}{eV}$, where $h$ is the Planck constant, $c$ is the speed of light, $e$ is the elementary charge, and $V$ is the accelerating voltage.
Revision notes
Read the core explanations from X-ray Production and Energy Spectrum before testing yourself from memory.
1. How X-rays Are Born: The Big Picture
Picture a beam of electrons, each carrying a precise amount of kinetic energy, fired at a dense metal target at enormous speed. When those electrons slam into the target, their energy has to go somewhere — and a significant fraction of it leaves as X-ray photons. That conversion process, and the spectrum of photon energies it produces, is exactly what this lesson unpacks.
X-ray production sits at the intersection of two ideas you already know well: the work done on a charge by a potential difference, and the photon model of electromagnetic radiation. Bringing those two ideas together gives you a complete picture of the X-ray energy spectrum.
2. Inside the X-ray Tube: Physical Principles
An X-ray tube contains a heated cathode filament and a metal anode target, held under high vacuum. The filament is heated until thermionic emission occurs — electrons boil off the surface. A large potential difference $V$ (the accelerating voltage, typically 20–150 kV in medical imaging) is applied between cathode and anode, accelerating those electrons across the gap.
Each electron gains kinetic energy equal to the work done on it by the electric field. Because the electron carries charge $e$ and is accelerated through potential difference $V$, its kinetic energy on arrival at the anode is $E_k = eV$. This is the energy budget available to produce X-ray photons — and it sets a hard ceiling on the photon energies that can be emitted.
When the high-speed electrons reach the anode, two distinct physical processes produce X-ray photons. The first is a broad, continuous process; the second produces sharp, discrete peaks. Understanding both is essential for interpreting the X-ray energy spectrum.
2a. The Continuous Spectrum: Bremsstrahlung
Most incoming electrons do not stop in a single collision. Instead, each electron passes close to one or more atomic nuclei in the target material and is deflected — decelerated — by the electrostatic (Coulomb) interaction with atomic nuclei. Each deceleration event converts some of the electron's kinetic energy into a single X-ray photon. The German term for this is Bremsstrahlung, meaning 'braking radiation'.
Because each electron undergoes a different degree of deceleration in a different interaction, the photons produced carry a continuous range of energies from near-zero up to a definite maximum. The result is a smooth, continuous spectrum — sometimes called the white radiation or continuous background.
The maximum photon energy in this continuous spectrum corresponds to the rare event where an electron loses all of its kinetic energy in a single interaction, producing one photon of energy $E_{max} = eV$. This sets the short-wavelength cut-off of the spectrum: no photon can have more energy than the electron that produced it.
Because photon energy and wavelength are related by $E = \frac{hc}{\lambda}$, the maximum photon energy corresponds to a minimum wavelength $\lambda_{min}$. Rearranging gives the short-wavelength limit of the spectrum.
2b. The Characteristic Spectrum: Discrete Peaks
Superimposed on the continuous bremsstrahlung background are sharp, narrow peaks at specific photon energies. These are the characteristic X-rays, and they arise from a completely different physical process — one that involves the internal energy-level structure of the target atoms.
When an incoming electron has enough kinetic energy, it can knock an inner-shell electron (for example, a K-shell electron) completely out of a target atom, leaving a vacancy. An electron from a higher energy shell — say the L or M shell — then drops down to fill that vacancy. The energy released in this transition is emitted as a single X-ray photon whose energy equals the difference between the two shell energies: $E_{photon} = E_{upper} - E_{lower}$.
Because atomic energy levels are fixed and unique to each element, the photon energies produced are fixed and unique to the target material. This is why the peaks are called characteristic — they are a fingerprint of the anode element. Change the target material and the peak positions shift; change the voltage and the peak positions stay the same (provided the voltage is still high enough to cause ionisation of the inner shells).
3. The Complete X-ray Energy Spectrum
Putting both processes together gives the full X-ray spectrum: a broad, continuous bremsstrahlung curve with sharp characteristic peaks rising above it at specific energies. The chart below shows the key features you need to be able to describe and explain in an exam.
Notice the sharp cut-off at the high-energy (short-wavelength) end of the continuous spectrum. That cut-off sits at exactly $E_{max} = eV$ — it does not tail off gradually. The curve rises from zero at $E_{max}$, reaches a broad peak at roughly one-third to one-half of $E_{max}$, then falls back towards zero at very low photon energies (very low-energy photons are absorbed within the tube itself before they can exit).
The characteristic peaks sit at fixed positions determined by the target material. They only appear if the accelerating voltage is high enough to ionise the relevant inner shell — below that threshold voltage, the peaks are absent entirely.
Feature
Continuous (Bremsstrahlung)
Characteristic
Origin
Electron deceleration near nuclei
Electron transitions between atomic shells
Energy distribution
Continuous range from ~0 to $E_{max}$
Discrete, fixed energies (sharp peaks)
Depends on target material?
Shape broadly similar for all metals; intensity varies
Yes — peak positions are unique to the element
Depends on accelerating voltage?
Yes — $E_{max}$ and intensity both increase with $V$
Intensity increases with $V$; peak positions unchanged
Threshold condition
None — any voltage produces some bremsstrahlung
Voltage must exceed the shell ionisation energy
4. Calculating Maximum Photon Energy and Minimum Wavelength
Exam questions on this topic almost always ask you to calculate either the maximum photon energy or the minimum wavelength for a given accelerating voltage. The method is straightforward, but unit handling is where marks are lost. Work through the example below carefully — pay particular attention to the unit conversion for voltage.
Worked example: Calculating Maximum Photon Energy and Minimum Wavelength
An X-ray tube operates with an accelerating voltage of 80 kV. Calculate (a) the maximum photon energy and (b) the minimum wavelength of X-rays produced. ($h = 6.63 \times 10^{-34}$ J s, $c = 3.0 \times 10^{8}$ m/s, $e = 1.6 \times 10^{-19}$ C)
$V = 80\text{ kV} = 80 \times 10^{3}\text{ V} = 8.0 \times 10^{4}\text{ V}$ — Always convert kV to V before substituting. This is the most common source of errors in this calculation. [M1]
$E_{max} = 1.6 \times 10^{-19} \times 8.0 \times 10^{4}$ — Multiply the elementary charge by the accelerating voltage in volts. [M1]
$\lambda_{min} = \frac{hc}{E_{max}}$ — Since $E = \frac{hc}{\lambda}$, rearranging gives $\lambda = \frac{hc}{E}$. Use $E_{max}$ to get $\lambda_{min}$. [M1]
$\lambda_{min} = \frac{6.63 \times 10^{-34} \times 3.0 \times 10^{8}}{1.28 \times 10^{-14}}$ — Substitute $h$, $c$, and the $E_{max}$ found in step 3. Keep all values in SI units. [M1]
$\lambda_{min} \approx 1.55 \times 10^{-11}\text{ m} = 0.0155\text{ nm}$ — X-ray wavelengths are typically $10^{-11}$ to $10^{-8}$ m (0.01–10 nm). This value sits at the hard end of the X-ray range, consistent with a high accelerating voltage. Units are metres — correct for wavelength.
Now that you can calculate the key quantities, it is worth stepping back to see how changing the tube's operating conditions reshapes the spectrum as a whole. Examiners frequently ask you to sketch or describe the effect of changing voltage or target material — so build a clear mental model here.
Increasing the accelerating voltage does three things simultaneously: it shifts $\lambda_{min}$ to a shorter value (higher $E_{max}$), it increases the overall intensity of the continuous spectrum (more energetic electrons produce more photons per unit time), and it raises the intensity of the characteristic peaks (more electrons exceed the ionisation threshold). The shape of the continuous curve broadens and the peak shifts upward in energy.
Changing the target material leaves the continuous spectrum shape broadly similar but moves the characteristic peak positions to entirely new energies, because those peaks depend solely on the atomic energy-level structure of the new element. A tungsten anode and a molybdenum anode operated at the same voltage produce the same $\lambda_{min}$ and a similar bremsstrahlung curve, but their characteristic peaks appear at completely different photon energies.
6. Exam Technique and Common Mistakes
Questions on X-ray production tend to follow predictable patterns. The most reliable way to pick up every available mark is to be precise about which process you are describing and to handle units carefully in calculations. The guidance below consolidates the key exam strategies for this topic.
For a 'describe and explain' question worth 4–6 marks, structure your answer by addressing the continuous spectrum and the characteristic spectrum separately. For each, name the process, describe the physical mechanism, and link it to the shape of the spectrum. Examiners award marks for the mechanism, not for restating the observation.
Together, the continuous bremsstrahlung spectrum and the characteristic peaks form the complete X-ray energy spectrum — a direct consequence of the physical principles of electron deceleration and atomic energy-level transitions, both governed by the conservation of energy and the photon model of electromagnetic radiation.
Sources and content standards
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-09-12.
In an X-ray tube, a heated cathode filament releases electrons by thermionic emission, and a potential difference V, typically 20–150 kV, accelerates them to the anode, each gaining kinetic energy eV. In the metal target, electrons decelerated near nuclei produce a continuous spectrum, and electrons that knock out inner-shell electrons produce characteristic X-rays.
What is the wavelength range of X-rays?
X-ray wavelengths are typically 10⁻¹¹ to 10⁻⁸ m, or 0.01–10 nm. A minimum wavelength of about 1.55 × 10⁻¹¹ m, produced by an 80 kV tube, sits at the hard, high-energy end of this range.
What are characteristic X-rays?
Characteristic X-rays are produced when an incoming electron knocks an inner-shell electron, for example from the K-shell, out of a target atom, and an electron from a higher shell drops to fill the vacancy, emitting a photon whose energy equals the difference between the shell energies. They appear as sharp peaks at fixed energies unique to the target element.
What is bremsstrahlung?
Bremsstrahlung, German for 'braking radiation', is the X-ray emission produced when fast electrons are decelerated by the Coulomb interaction with atomic nuclei in the target. Each electron loses a different amount of energy, so the photons have a continuous range of energies from near zero up to a maximum of eV, giving a smooth continuous spectrum.
How does tube voltage affect the X-ray spectrum?
Increasing the accelerating voltage raises the maximum photon energy, eV, so the minimum wavelength becomes shorter; it also increases the intensity of the continuous spectrum and of the characteristic peaks, without moving the peaks. Changing the target material instead shifts the characteristic peaks to new energies, while the continuous curve stays broadly similar.
How do you calculate the minimum wavelength of X-rays from a tube?
The minimum wavelength is λmin = hc/eV, because the maximum photon energy equals eV. For 80 kV, the maximum energy is 1.6 × 10⁻¹⁹ × 8.0 × 10⁴ = 1.28 × 10⁻¹⁴ J, so λmin = 6.63 × 10⁻³⁴ × 3.0 × 10⁸ ÷ 1.28 × 10⁻¹⁴ ≈ 1.55 × 10⁻¹¹ m. The voltage must be converted from kV to V first.
How are electrons released in an X-ray tube?
Electrons are released from the heated cathode filament by thermionic emission: the filament is heated until electrons boil off its surface. A large potential difference, typically 20–150 kV in medical imaging, then accelerates them across the vacuum to the metal anode target.
Why does the X-ray spectrum have a sharp cut-off?
The continuous X-ray spectrum has a sharp cut-off at a maximum photon energy of eV, because no photon can carry more energy than the electron that produced it. The cut-off corresponds to the rare event in which an electron loses all its kinetic energy in a single interaction.
Why don't characteristic peaks move when the voltage changes?
Characteristic peak energies equal the difference between two fixed atomic energy levels of the target element, so they do not depend on the tube voltage. Raising the voltage only increases the intensity of the peaks, provided the voltage is high enough to ionise the inner shells.
What happens to the X-ray spectrum if the target material changes?
Changing the target material moves the characteristic peaks to entirely new energies, because they depend on the atomic energy levels of the element. Tungsten and molybdenum anodes at the same voltage give the same minimum wavelength and a similar bremsstrahlung curve, but different peaks.
When do characteristic X-ray peaks appear?
Characteristic peaks appear only when the accelerating voltage is high enough for incoming electrons to knock an inner-shell electron, such as a K-shell electron, out of a target atom. Under that threshold voltage the peaks are absent, although some bremsstrahlung is produced at any voltage.
Why are very low-energy X-rays missing from the spectrum?
The continuous spectrum falls back towards zero at very low photon energies because those low-energy photons are absorbed within the tube itself before they can exit. The curve rises from the cut-off to a broad peak and then falls at the low-energy end.
Where is the peak of the continuous X-ray spectrum?
The continuous bremsstrahlung spectrum reaches a broad peak at roughly one-third to one-half of the maximum photon energy, eV. Increasing the tube voltage shifts this peak upward in energy and raises the overall intensity of the curve.