X-Rays and Laser Radiations

Lessons

Senior 6 · Physics

X-Rays and Laser Radiations

4 lessons

Lesson 1 of 4

X-Rays: Nature, Production and Properties

25 min

A glow from across the room

On 8 November 1895 Wilhelm Röntgen was passing electric discharges through an evacuated glass tube covered in black card. A screen coated with a fluorescent salt, lying a metre away, began to glow. No light could escape the card, and cathode rays (electrons) travel only a few centimetres in air, so something new was crossing the room. Röntgen called the unknown radiation "X-rays". Within weeks he had photographed the bones of his wife's hand, and within a year doctors were using X-rays to find bullets and broken bones. In Senior 5 you met cathode rays, thermionic emission and the photon $E = h f$ . This lesson uses them to explain what X-rays are, how they are made and how they behave.

The nature of X-rays

X-rays are electromagnetic waves of very short wavelength, roughly 0.01 nm to 10 nm. Like all electromagnetic radiation they travel at $c = 3.00 \times 10^{8}\,\mathrm{m\,s^{-1}}$ in a vacuum and carry energy in photons of energy

E = hf = \frac{hc}{\lambda}

For $\lambda = 0.01$ to 10 nm this is about 100 keV down to about 100 eV, thousands of times more than a photon of visible light (about 2 eV).

Figure 1.1: X-rays in the electromagnetic spectrum.

The X-ray and gamma-ray ranges overlap. The difference is their origin: X-rays come from fast electrons (being decelerated, or jumping between inner energy levels of atoms), while gamma rays come from nuclei (Unit 5). A 100 keV photon is the same whichever way it was made.

Definition

X-rays are electromagnetic radiation of wavelength about 0.01 nm to 10 nm, produced when high-speed electrons are stopped by matter or when electrons fall into vacancies in the inner shells of atoms. Hard X-rays (short wavelength, high photon energy) are very penetrating; soft X-rays (longer wavelength) are absorbed easily. Example: a photon of wavelength 0.050 nm has energy $\frac{hc}{\lambda} = 24.8\,\mathrm{keV}$ .

Producing X-rays: the X-ray tube

Figure 1.2: A modern X-ray tube (Coolidge type).

Electrons are released from a tungsten filament heated by a low-voltage supply: thermionic emission.
They are accelerated through a high potential difference $V$ , typically 20 kV to 150 kV, in a vacuum (so that they do not collide with gas molecules). Each electron gains kinetic energy $E_{k} = e V$ .
They strike a metal target and are stopped in a few micrometres. A small part of their energy comes out as X-ray photons; the rest heats the target.

Only about 1% of the electrons' energy becomes X-rays in a medical tube, and about 99% becomes heat. So the target is made of tungsten, which has a very high melting point (3422 °C) and a high atomic number (74), which makes X-ray production more efficient. It is set in a copper block that conducts the heat away to oil or cooling fins. In many tubes the target is a disc that rotates, so the electron beam heats a different part of it every instant.

To change	Adjust	Because
the intensity (number of photons per second)	the filament current (tube current)	a hotter filament emits more electrons
the penetrating power ("hardness")	the accelerating voltage	more energetic electrons can produce more energetic photons

A medical X-ray tube with a rotating anode. The cathode (bottom left) faces the tilted edge of the large anode disc, which spins on bearings so that the heat is spread around its rim. Photo: Daniel W. Rickey, CC BY-SA 3.0, via Wikimedia Commons

Worked example 1: electrons in an X-ray tube

Electrons start from rest at the filament and are accelerated through 30 kV. Find (a) their kinetic energy in joules and in keV, (b) their speed, ignoring relativity. ( $e = 1.60 \times 10^{-19}$ C, $m_e = 9.11 \times 10^{-31}$ kg.)

Solution

(a) $E_k = eV = (1.60 \times 10^{-19})(30 \times 10^{3}) = 4.8 \times 10^{-15}\,\mathrm{J} = 30\,\mathrm{keV}$ .

(b) $v = \sqrt{\frac{2E_k}{m_e}} = \sqrt{\frac{2(4.8 \times 10^{-15})}{9.11 \times 10^{-31}}} = 1.03 \times 10^{8}\,\mathrm{m\,s^{-1}}$ , about a third of $c$ .

At this speed relativity matters a little: the true speed is $0.98 \times 10^{8}\,\mathrm{m\,s^{-1}}$ , about 4% lower. In medical tubes at 100 kV and more, the classical formula would be badly wrong.

Worked example 2: where the energy goes

An X-ray tube works at 30 kV with a tube current of 20 mA. (a) How many electrons hit the target each second? (b) What power is delivered to the target? (c) If 1.0% becomes X-rays, how much heat must be removed each second?

Solution

(a) $n = \frac{I}{e} = \frac{20 \times 10^{-3}}{1.60 \times 10^{-19}} = 1.25 \times 10^{17}\,\mathrm{s^{-1}}$ .

(b) $P = IV = (20 \times 10^{-3})(30 \times 10^{3}) = 600\,\mathrm{W}$ .

(c) X-ray power $= 1.0\% \times 600 = 6.0\,\mathrm{W}$ ; heat $= 600 - 6.0 = 594\,\mathrm{W}$ , about the power of a small electric heater, concentrated on a spot a few millimetres across.

Properties of X-rays

They travel in straight lines at the speed of light and are not deflected by electric or magnetic fields, because they carry no charge.
They penetrate matter. Absorption increases steeply with the atomic number and density of the material, and is greater for soft X-rays than for hard ones. Bone (calcium, $Z = 20$ ) absorbs more than soft tissue (mostly H, C, O); lead ( $Z = 82$ ) absorbs strongly.
They ionise gases and can damage living cells.
They make some materials fluoresce (as on Röntgen's screen) and they darken photographic film.
They are diffracted by crystals, because their wavelength is similar to the spacing of atoms.

X-ray diffraction and Bragg's law

In 1913 William Henry Bragg and his son Lawrence treated a crystal as a stack of parallel planes of atoms, a distance $d$ apart. X-rays reflected from neighbouring planes travel paths that differ by $2d\sin\theta$ , where $\theta$ is the angle between the rays and the planes. The reflections reinforce when this path difference is a whole number of wavelengths:

2d\sin\theta = n\lambda, \qquad n = 1, 2, 3, \ldots

Measuring $\theta$ for a crystal of known $d$ gives $\lambda$ ; with a known $\lambda$ it gives the spacing and arrangement of atoms. X-ray diffraction revealed the structure of salt, of proteins and, in Rosalind Franklin's photographs, of DNA.

Worked example 3: diffraction by a salt crystal

X-rays of wavelength 0.0709 nm fall on a crystal of sodium chloride whose planes are 0.282 nm apart. Find the angles $\theta$ of the first-order and second-order reflections.

Solution

$n = 1$ : $\sin\theta = \frac{\lambda}{2d} = \frac{0.0709}{2(0.282)} = 0.126$ , so $\theta = 7.2^\circ$ .

$n = 2$ : $\sin\theta = \frac{2(0.0709)}{2(0.282)} = 0.251$ , so $\theta = 14.6^\circ$ .

The largest possible order needs $\sin\theta \le 1$ : $n \le \frac{2d}{\lambda} = 7.95$ , so there are reflections up to $n = 7$ .

Warning

Safety. X-rays are ionising radiation. X-ray tubes may be operated only by trained people in shielded, licensed rooms (in Rwanda, users of radiation are licensed by RURA). There is no safe school experiment with an X-ray tube: high-voltage discharge tubes can emit X-rays, so never run one above the voltage your teacher sets.

Warning

Common mistakes. (1) Thinking X-rays are particles of matter, like cathode rays: they are electromagnetic waves (photons), and are not deflected by fields. (2) Saying the tube current controls the photon energy: it controls the NUMBER of photons; the voltage controls their maximum energy. (3) Saying most of the electrons' energy becomes X-rays: about 99% becomes heat. (4) In Bragg's law, using the angle to the normal: $\theta$ is measured from the crystal planes.

Tip

Current counts, voltage punches. The tube current sets HOW MANY X-ray photons; the accelerating voltage sets how HARD (energetic and penetrating) they can be.

How X-rays see through your skin, by Ge Wang (TED-Ed). Watch how X-rays are produced in a tube and why bone and tissue absorb them differently.

✦

Practice

State three properties of X-rays that show they are electromagnetic waves and not charged particles.
Find the energy, in keV, of an X-ray photon of wavelength 0.10 nm ( $hc = 1.24 \times 10^{-6}\,\mathrm{eV\,m}$ ).
Explain why the target of an X-ray tube is made of tungsten and mounted in copper.
An X-ray tube operates at 80 kV and 5.0 mA. Find the number of electrons striking the target per second and the power delivered to it.
A radiographer wants (a) a brighter image without changing its contrast, (b) X-rays that penetrate further. What should she change in each case?
X-rays of wavelength 0.154 nm give a first-order Bragg reflection at 15.9° from a crystal. Find the spacing of the crystal planes.
Why is the tube evacuated?
Ishimwe says: "X-rays and gamma rays are different kinds of radiation because X-rays always have lower energy." Evaluate his statement.

Show answersHide answers

Not deflected by electric or magnetic fields; travel at $c$ ; show diffraction by crystals (wave behaviour); cause fluorescence and photoelectric effects like light.
$E = \frac{1.24 \times 10^{-6}}{1.0 \times 10^{-10}} = 1.24 \times 10^{4}\,\mathrm{eV} = 12.4\,\mathrm{keV}$ .
About 99% of the energy becomes heat. Tungsten has a very high melting point and a high atomic number (efficient X-ray production); copper is an excellent conductor of heat, carrying it away to the cooling system.
$n = \frac{5.0 \times 10^{-3}}{1.60 \times 10^{-19}} = 3.1 \times 10^{16}\,\mathrm{s^{-1}}$ ; $P = (5.0 \times 10^{-3})(80 \times 10^{3}) = 400\,\mathrm{W}$ .
(a) Increase the tube (filament) current: more photons of the same spectrum. (b) Increase the accelerating voltage: harder, more penetrating X-rays.
$d = \frac{n\lambda}{2\sin\theta} = \frac{0.154}{2\sin 15.9^\circ} = \frac{0.154}{0.548} = 0.281\,\mathrm{nm}$ .
So that electrons can travel from cathode to anode without colliding with gas molecules and losing energy, and so that the hot filament does not oxidise.
Wrong. The energy ranges overlap; a 100 keV photon is the same whatever its source. The names describe the ORIGIN: X-rays come from electrons (braking or inner-shell transitions), gamma rays from nuclei.

Key points

X-rays: electromagnetic waves of wavelength about 0.01 nm to 10 nm; $E = \frac{hc}{\lambda}$ from about 100 eV to 100 keV.
Tube: thermionic electrons accelerated through $V$ ( $E_{k} = e V$ ) strike a tungsten target; about 1% of the energy becomes X-rays, 99% heat.
Tube current controls intensity; voltage controls hardness.
Properties: uncharged, penetrating (absorption rises with Z), ionising, cause fluorescence, darken film, diffract: $2d\sin\theta = n\lambda$ .

Sources and credits

30.4: X Rays: Atomic Origins and Applications, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Photo: First medical X-ray by Wilhelm Röntgen of his wife Anna Bertha Ludwig's hand by Wilhelm Röntgen, Wikimedia Commons, public domain.
Photo: Rotating anode x-ray tube (labeled).jpg by Daniel W. Rickey, Wikimedia Commons, licensed under CC BY-SA 3.0.
Video: How X-rays see through your skin - Ge Wang, TED-Ed, embedded from YouTube.

The two diagrams, the worked examples and the practice exercises are written by Ganzaa. This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1A glow from across the room

2The nature of X-rays

3Producing X-rays: the X-ray tube

4Properties of X-rays

X-ray diffraction and Bragg's law

A glow from across the room

The nature of X-rays

Producing X-rays: the X-ray tube

Properties of X-rays