In November 1895, a German physicist named Wilhelm Röntgen was experimenting with a cathode ray tube. He noticed something strange: a screen coated with barium platinocyanide was glowing, even though it was far from the tube and shielded from visible light. Something invisible was travelling through the air and causing the screen to fluoresce. He did not know what it was, so he called it "X-radiation" — X for unknown.
Within weeks, Röntgen had taken the first X-ray image of a human body — his wife's hand, showing the bones inside. The world was astonished. For the first time, doctors could see inside a living body without surgery. X-rays have since become one of the most important tools in medicine, industry, and science. In this chapter, we are going to explore what X-rays are, how they are produced, how they behave, and how they are used. We will also learn about their dangers and how to use them safely. Let us begin.
I once asked a class, "What would you do if you discovered a new kind of ray that could see through things?" A student said, "I would tell everyone!" I said, "That is exactly what Röntgen did. He published his findings freely, and within months, doctors around the world were using X-rays to help patients. He won the first Nobel Prize in Physics in 1901. Science advances fastest when discoveries are shared.By the end of this chapter, you should be able to:
X-rays are a form of electromagnetic radiation with very short wavelengths, typically in the range of 10⁻⁸ m to 10⁻¹¹ m. They have high frequencies and high energies, which makes them highly penetrating.
Think of X-rays as light that is much more energetic than the visible light you see. They are invisible to the eye but can pass through soft body tissue, wood, and thin metal. They are absorbed by denser materials like bone and lead.
| Property | Value |
|---|---|
| Wavelength range | 10⁻⁸ m to 10⁻¹¹ m |
| Frequency range | 3 × 10¹⁶ Hz to 3 × 10¹⁹ Hz |
| Speed in vacuum | 3 × 10⁸ m/s |
| Type of wave | Transverse electromagnetic wave |
| Medium needed? | No |
X-rays are produced when high-energy electrons strike a metal target. The electrons lose kinetic energy, and some of that energy is converted into X-ray photons.
The X-ray tube:
How X-rays are produced:
| Part of X-ray Tube | Function |
|---|---|
| Filament (cathode) | Emits electrons by thermionic emission |
| Target (anode) | Produces X-rays when struck by electrons |
| High-voltage supply | Accelerates the electrons |
| Vacuum | Allows electrons to travel freely |
| Lead shielding | Absorbs stray X-rays |
| Cooling system | Removes heat from the anode |
X-rays have several important properties:
| Property | Evidence or Application |
|---|---|
| Travel in straight lines | Sharp shadows in X-ray images |
| Highly penetrating | Pass through soft tissue but not bone |
| Not deflected by fields | No charge — unlike cathode rays |
| Cause fluorescence | Used in X-ray screens |
| Affect photographic film | Used to record X-ray images |
| Ionise gases | Used in Geiger counters |
| Damage living cells | Requires safety precautions |
| Diffracted by crystals | Used in X-ray crystallography |
When X-rays are produced, they have a range of wavelengths. The spectrum of X-rays consists of two parts: the continuous spectrum and the characteristic spectrum.
Continuous spectrum:
Minimum wavelength: λ_min = h × c / (e × V)
λ_min = minimum wavelength (m), h = Planck's constant (6.63 × 10⁻³⁴ J s), c = speed of light (3 × 10⁸ m/s), e = electron charge (1.6 × 10⁻¹⁹ C), V = accelerating voltage (V)
Characteristic spectrum:
| Feature | Continuous Spectrum | Characteristic Spectrum |
|---|---|---|
| Origin | Deceleration of electrons | Electron transitions in atoms |
| Shape | Continuous curve | Sharp peaks |
| Depends on target? | No | Yes |
| Depends on voltage? | Yes (λ_min) | Yes (intensity) |
X-rays have wavelengths comparable to the spacing between atoms in a crystal. When X-rays pass through a crystal, they are diffracted by the regular arrangement of atoms, producing a diffraction pattern.
Bragg's Law: The condition for constructive interference of X-rays diffracted by a crystal.
Bragg's Law: n × λ = 2 × d × sin θ
n = order of diffraction (integer), λ = wavelength of X-rays (m), d = spacing between atomic planes (m), θ = angle of incidence (degrees)
How it works:
| Application | How It Uses Bragg's Law |
|---|---|
| X-ray crystallography | Determines the arrangement of atoms in crystals |
| DNA structure | Rosalind Franklin used X-ray diffraction to reveal DNA's double helix |
| Protein structure | Used to determine the structure of proteins |
| Materials science | Studies the structure of metals and alloys |
In 1913, Henry Moseley discovered that the frequency of characteristic X-rays is related to the atomic number of the target element. This is known as Moseley's Law.
Moseley's Law: √f = a × (Z − b)
f = frequency of characteristic X-ray (Hz), Z = atomic number, a and b = constants
Significance of Moseley's Law:
| Field | Application | How It Works |
|---|---|---|
| Medicine | Radiography | X-rays pass through soft tissue but are absorbed by bone |
| Medicine | CT scans | Multiple X-ray images combine to form 3D images |
| Medicine | Radiotherapy | High-energy X-rays destroy cancer cells |
| Dentistry | Dental X-rays | Detect cavities and problems in teeth |
| Security | Airport scanners | X-rays reveal the contents of luggage |
| Industry | Non-destructive testing | Detect cracks and flaws in metal structures |
| Science | X-ray crystallography | Determine the structure of crystals and molecules |
| Astronomy | X-ray telescopes | Observe black holes and hot gases in space |
X-rays are ionising radiation. This means they have enough energy to remove electrons from atoms, which can damage living cells and DNA.
Dangers of X-rays:
Safety precautions:
| Precaution | Purpose |
|---|---|
| Lead apron | Protects the body from scattered X-rays |
| Lead screen | Protects the operator |
| Dosimeter | Monitors radiation exposure |
| Distance | Reduces exposure (inverse square law) |
| Time limit | Reduces total exposure |
X-rays and cathode rays are often confused because both are produced in vacuum tubes. But they are very different.
| Feature | Cathode Rays | X-Rays |
|---|---|---|
| Nature | Streams of electrons (particles) | Electromagnetic waves |
| Charge | Negative | No charge |
| Deflected by electric field? | Yes | No |
| Deflected by magnetic field? | Yes | No |
| Speed | Less than speed of light | Speed of light |
| Penetrating power | Low | High |
| Production | Emitted from heated cathode | Produced when electrons hit a target |
Think of cathode rays as a stream of bullets and X-rays as flashes of light. The bullets are particles; the flashes are waves. Both can be produced in the same tube, but they behave very differently.
The distinction between cathode rays and X-rays is important. Cathode rays are electrons — charged particles that can be deflected by fields. X-rays are electromagnetic waves — no charge, no deflection. When cathode rays hit a metal target, some of their energy is converted into X-rays. This is how X-ray tubes work.The design of an X-ray tube involves several practical considerations:
| Design Feature | Purpose |
|---|---|
| Tungsten target | High X-ray production, high melting point |
| Rotating anode | Spreads heat over a larger area |
| Oil cooling | Removes heat |
| Beryllium window | Allows X-rays to exit |
| Lead shielding | Protects operator |
X-ray crystallography is a technique that uses X-ray diffraction to determine the atomic structure of crystals.
How it works:
Applications:
Think of X-ray crystallography as a way of "seeing" atoms. The X-rays diffract around the atoms, and the pattern they form reveals the atomic arrangement. It is like shining a light through a lace curtain — the pattern of shadows tells you about the weave.
X-ray crystallography is one of the most powerful techniques in science. It has revealed the structure of thousands of molecules, including DNA, proteins, and viruses. It has led to new drugs, new materials, and a deeper understanding of the building blocks of life. Physics at its most beautiful.Minimum wavelength of X-rays: λ_min = h × c / (e × V)
h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s, e = 1.6 × 10⁻¹⁹ C, V = accelerating voltage (V)
Photon energy: E = h × f = h × c / λ
Bragg's Law: n × λ = 2 × d × sin θ
Moseley's Law: √f = a × (Z − b)
Speed of X-rays in vacuum: c = 3 × 10⁸ m/s
Wavelength range of X-rays: 10⁻⁸ m to 10⁻¹¹ m
Question: An X-ray tube operates at an accelerating voltage of 50 000 V. Calculate the minimum wavelength of the X-rays produced. Use h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s, e = 1.6 × 10⁻¹⁹ C.
Answer:
Formula: λ_min = h × c / (e × V)
Substitution: λ_min = (6.63 × 10⁻³⁴ × 3 × 10⁸) / (1.6 × 10⁻¹⁹ × 50 000)
λ_min = (1.989 × 10⁻²⁵) / (8 × 10⁻¹⁵)
Answer: λ_min = 2.49 × 10⁻¹¹ m
Units check: J s × m/s / (C × V) = m. The answer is in metres. Does 2.49 × 10⁻¹¹ m make sense? Yes, this is a typical X-ray wavelength. Notice that the minimum wavelength depends only on the accelerating voltage.Question: An X-ray photon has a wavelength of 1.5 × 10⁻¹⁰ m. Calculate its energy. Use h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s.
Answer:
Formula: E = h × c / λ
Substitution: E = (6.63 × 10⁻³⁴ × 3 × 10⁸) / (1.5 × 10⁻¹⁰)
E = (1.989 × 10⁻²⁵) / (1.5 × 10⁻¹⁰)
Answer: E = 1.326 × 10⁻¹⁵ J
Units check: J s × m/s / m = J. The answer is in joules. X-ray photons have much more energy than visible light photons, which is why they can ionise atoms and damage living cells.Question: X-rays of wavelength 0.2 nm are diffracted by a crystal with atomic planes spaced 0.1 nm apart. Calculate the angle of the first-order diffraction maximum.
Answer:
Formula: n × λ = 2 × d × sin θ
For first order, n = 1.
Substitution: 1 × 0.2 nm = 2 × 0.1 nm × sin θ
sin θ = 0.2 / 0.2 = 1
θ = sin⁻¹(1) = 90°
Answer: The angle is 90°. (Note: This is a special case where the wavelength is twice the spacing. In practice, the angle would be smaller.)
Units check: the answer is in degrees. Notice that the wavelength must be comparable to the atomic spacing for diffraction to occur. This is why X-rays, with their very short wavelengths, are ideal for studying crystal structures.Question: The characteristic X-ray frequency for an element with atomic number Z = 30 is 1.2 × 10¹⁸ Hz. Estimate the frequency for an element with Z = 40. Use Moseley's Law: √f = a(Z − b), and assume b = 1.
Answer:
For Z = 30: √f₁ = a(30 − 1) = 29a
For Z = 40: √f₂ = a(40 − 1) = 39a
Ratio: √f₂ / √f₁ = 39 / 29 = 1.345
f₂ / f₁ = (1.345)² = 1.808
f₂ = 1.808 × 1.2 × 10¹⁸ = 2.17 × 10¹⁸ Hz
Answer: The frequency is approximately 2.17 × 10¹⁸ Hz.
Units check: the answer is in Hz. Notice that higher atomic number gives higher frequency. This is because the inner-shell electrons are more tightly bound in heavier atoms, so the energy transitions are larger.Question: Compare the energy of an X-ray photon (λ = 10⁻¹⁰ m) with a visible light photon (λ = 5 × 10⁻⁷ m). Use h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s.
Answer:
X-ray: E = hc/λ = (6.63 × 10⁻³⁴ × 3 × 10⁸) / (10⁻¹⁰) = 1.989 × 10⁻¹⁵ J
Visible: E = hc/λ = (6.63 × 10⁻³⁴ × 3 × 10⁸) / (5 × 10⁻⁷) = 3.978 × 10⁻¹⁹ J
Ratio: 1.989 × 10⁻¹⁵ / 3.978 × 10⁻¹⁹ = 5 000
Answer: The X-ray photon has about 5 000 times more energy than the visible photon.
Units check: the answers are in joules. This huge difference in energy explains why X-rays can ionise atoms and damage living cells, while visible light is generally harmless. It is all about the energy of the photon.Graphs help us understand X-ray spectra and their properties.
X-ray spectrum (intensity vs wavelength): The X-ray spectrum has two parts: a continuous curve with sharp peaks on top.
Effect of changing target material: The continuous spectrum remains the same, but the positions of the characteristic peaks change. Each element has its own unique set of peaks.
Moseley's Law graph: If you plot √f on the vertical axis and Z on the horizontal axis, you get a straight line. The gradient is a, and the intercept on the Z-axis is b.
Bragg's Law graph: If you plot n on the vertical axis and sin θ on the horizontal axis, you get a straight line through the origin. The gradient is 2d/λ.
These graphs help us visualise the relationships in X-ray physics. They turn equations into pictures.
Think of a graph as a map of a relationship. The shape tells you how one quantity changes with another.
Note: Direct experiments with X-rays require specialised equipment and strict safety precautions. This practical is usually done as a demonstration or simulation.
Apparatus (for demonstration): An X-ray diffraction apparatus, a crystal sample, and a detector or photographic film.
Method:
Calculation: If the first-order diffraction maximum occurs at θ = 15° with λ = 0.15 nm, then d = λ / (2 sin θ) = 0.15 / (2 × 0.259) = 0.29 nm.
Precautions:
Likely source of error: Misalignment of the crystal can cause errors in the diffraction angles. Carefully align the crystal before starting.
X-ray diffraction is a beautiful experiment, but it requires strict safety precautions. The diffraction pattern reveals the atomic structure of the crystal — a window into the invisible world of atoms. It is a powerful demonstration of the wave nature of X-rays.X-rays are a form of electromagnetic radiation with very short wavelengths, typically 10⁻⁸ m to 10⁻¹¹ m.
X-rays are produced when high-energy electrons strike a metal target. The electrons lose kinetic energy, and some of it is converted into X-ray photons.
They travel in straight lines; they are highly penetrating; they are not deflected by electric or magnetic fields; they cause fluorescence; they ionise gases; they can damage living cells.
The continuous spectrum is a smooth curve produced by deceleration of electrons. The characteristic spectrum consists of sharp peaks produced by electron transitions in the target atoms.
nλ = 2d sin θ, where n is the order of diffraction, λ is the wavelength, d is the spacing between atomic planes, and θ is the angle of incidence.
λ_min = hc/(eV) = (6.63 × 10⁻³⁴ × 3 × 10⁸) / (1.6 × 10⁻¹⁹ × 100 000) = 1.24 × 10⁻¹¹ m.
Medical imaging (radiographs, CT scans); industrial inspection; security scanning; X-ray crystallography.
Dangers: cell damage, cancer risk. Precautions: lead shielding, limit exposure time.
(a) What are X-rays? [2]
(b) Describe how X-rays are produced in an X-ray tube. [5]
(c) State three properties of X-rays. [3]
(a) X-rays are electromagnetic waves with very short wavelengths (10⁻⁸ to 10⁻¹¹ m). (2 marks.)
(b) Electrons are emitted from a heated filament (thermionic emission). A high voltage accelerates them toward a metal target. When they strike the target, they lose kinetic energy, and some is converted into X-rays. (5 marks.)
(c) They travel in straight lines; they are highly penetrating; they are not deflected by electric or magnetic fields. (3 marks.)
(a) Explain the difference between the continuous and characteristic X-ray spectra. [5]
(b) An X-ray tube operates at 60 000 V. Calculate the minimum wavelength of the X-rays produced. Use h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s, e = 1.6 × 10⁻¹⁹ C. [4]
(c) State two safety precautions when using X-rays. [2]
(a) Continuous spectrum: produced by deceleration of electrons, smooth curve, depends only on voltage. Characteristic spectrum: produced by electron transitions, sharp peaks, depends on target material. (5 marks.)
(b) λ_min = hc/(eV) = (6.63 × 10⁻³⁴ × 3 × 10⁸) / (1.6 × 10⁻¹⁹ × 60 000) = 2.07 × 10⁻¹¹ m. (4 marks.)
(c) Use lead shielding; limit exposure time; keep distance from source. (2 marks.)
(a) State Bragg's Law and explain its significance. [4]
(b) X-rays of wavelength 0.1 nm are diffracted by a crystal with atomic planes spaced 0.2 nm apart. Calculate the angle of the first-order diffraction maximum. [4]
(c) Describe one application of X-ray diffraction. [2]
(a) nλ = 2d sin θ. It describes the condition for constructive interference of X-rays diffracted by a crystal. It is used to determine atomic structure. (4 marks.)
(b) n = 1: 1 × 0.1 = 2 × 0.2 × sin θ → sin θ = 0.1/0.4 = 0.25 → θ = 14.5°. (4 marks.)
(c) Determining the structure of DNA; analysing protein structures; studying metals and alloys. (2 marks.)
Explain why X-rays are not deflected by electric or magnetic fields, while cathode rays are.
X-rays are electromagnetic waves — they have no charge, so they do not experience a force in electric or magnetic fields. Cathode rays are streams of electrons — they are negatively charged, so they experience a force in both electric and magnetic fields. This is a fundamental difference between waves and charged particles.
Explain why the minimum wavelength of X-rays depends only on the accelerating voltage, not on the target material.
The minimum wavelength corresponds to the maximum energy photon that can be produced, which occurs when an electron converts all its kinetic energy into a single X-ray photon. The electron's kinetic energy is determined solely by the accelerating voltage (eV). The target material affects the characteristic spectrum but not the maximum energy of the continuous spectrum. So λ_min = hc/(eV) depends only on V.
Explain why X-rays are used in medicine despite their dangers.
X-rays provide a unique way to see inside the human body without surgery. They can detect broken bones, tumours, and other conditions that would otherwise be invisible. The benefits of accurate diagnosis and treatment far outweigh the small risks when X-rays are used properly with appropriate safety precautions. The dose used in a single X-ray is very low, and the risk is carefully managed.
X-rays are the invisible light that reveals the hidden — from the bones inside our bodies to the atoms inside crystals — and in their discovery, Röntgen opened a window into both the human body and the structure of matter itself.
