CDS Physics · Modern Physics

Photons and X-rays

Light as photons with energy and momentum, atoms that absorb and give out exact frequencies (the atomic clock), and what X-rays are, what they do and what they are used for.

All Modern Physics notes

Why this matters

Seven CDS questions from 2016 (II) to 2026 (II), five of them MODERATE. Five are about X-rays, and three of those ask the same thing: whether an electric or a magnetic field can bend an X-ray beam (2020 (I), 2025 (II) and 2026 (I)). The other two ask for a photon's energy from its momentum and how an atomic clock works.

Concept 1 of 2: Photons: energy, momentum and atomic energy levels

Light comes in small packets called photons. A photon has no rest mass, but it carries energy and momentum. The higher its frequency (the shorter its wavelength), the more energy it carries, so a blue photon has more energy than a red one. An atom can only sit at certain energy levels, so it takes in or gives out photons of exact frequencies only. An atomic clock counts the waves of one such frequency.

Definition

The rules:

Photon energy $E = h\nu = \dfrac{hc}{\lambda}$ , with $h = 6.63 \times 10^{-34}$ J s. A handy form: $E\,(\text{eV}) = \dfrac{1240}{\lambda\,(\text{nm})}$ .
A photon has zero rest mass and momentum $p = \dfrac{E}{c} = \dfrac{h}{\lambda}$ . So a photon of momentum $x$ MeV/ $c$ has energy $x$ MeV.
Shorter wavelength, higher frequency, more energy: radio < visible < X-rays < gamma rays.
An atom jumping between two energy levels gives out or takes in a photon with $h\nu$ equal to the gap.
Atomic clock: counts the exact resonant frequency of an atom, usually caesium-133 (or rubidium). Since 1967 the second has been defined as 9,192,631,770 cycles of the caesium-133 radiation.

Photon energy and momentum

E = h\nu = \dfrac{hc}{\lambda} \qquad p = \dfrac{E}{c} = \dfrac{h}{\lambda} \qquad E\,(\text{eV}) = \dfrac{1240}{\lambda\,(\text{nm})}

hPlanck's constant, 6.63 × 10⁻³⁴ J s
νfrequency of the light
λwavelength
pmomentum of the photon

Worked example

Green light has a wavelength of 500 nm. Find the energy of one photon in electron-volts and in joules, and its momentum in eV/c.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2016 · CDS (II) 2016 — General Knowledge · Q38Moderate

Example 1 · Modern Physics · Photons and X-rays

The energy of a photon, whose momentum is

10\ \text{MeV}/c

, where

c

is the speed of light, is given by

For a photon, energy is momentum times c

A photon has no rest mass, so

\tfrac{1}{2}mv^{2}

does not apply. Use

E = pc

: a momentum in MeV/

c

gives the same number in MeV.

Shorter wavelength means more energy

E = hc/\lambda

: halving the wavelength doubles the energy. X-rays and gamma rays carry far more energy per photon than visible light.

Drill 1 more on photons: energy, momentum and atomic energy levels

Concept 2 of 2: X-rays: what they are and what they do

X-rays are light of a very short wavelength, made when fast electrons slam into a metal target. They carry no charge, so electric and magnetic fields cannot bend them. They pass through flesh but are stopped by bone and metal, which is why a bone shows up on an X-ray picture and why metal objects spoil it.

Definition

What to know:

Found by Wilhelm Röntgen in 1895. Made when fast electrons strike a heavy metal target.
Electromagnetic waves of wavelength about 0.01 to 10 nm, far shorter than visible light (400 to 700 nm).
No charge, so neither an electric nor a magnetic field deflects them.
Pass through soft tissue; bone and metal (dense, heavy atoms) absorb them strongly.
Uses: medical pictures and CT scans, checking welds and castings for hidden cracks, finding the arrangement of atoms in crystals (X-ray diffraction, since their wavelength is close to the gap between atoms), airport baggage checks.
They are ionising and can harm cells, so staff stand behind lead screens.

Property or use	Fact
Nature	Electromagnetic waves with no charge
Electric and magnetic fields	Do not deflect X-raysQ Asked in 2020 (I), 2025 (II) and 2026 (I): neither an electric nor a magnetic field bends X-rays.
Wavelength	About 0.01 to 10 nm, much shorter than visible light
Penetration	Pass through flesh; stopped by bone and metal
Metal objects during a scan	Block or reflect the beam, leaving a bright or dark patch that hides the body partQ CDS 2026 (II): metal is removed because it spoils the image.
Welds, castings and crystals	Show hidden cracks; reveal how atoms are arrangedQ CDS 2024 (II): checking welded joints and studying crystals are both uses.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2026 · CDS (I) 2026 — General Knowledge · Q15Moderate

Example 2 · Modern Physics · Photons and X-rays

An X-ray beam can be deflected by :

No charge, no bending

X-rays are electromagnetic waves, not charged particles. A field bends a beam of electrons, but neither an electric nor a magnetic field bends X-rays.

Metal is removed to save the picture

Metal blocks X-rays and leaves a patch on the image that hides the body part. It does not melt, spark or get changed by the X-rays.

Drill 4 more on x-rays: what they are and what they do

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Photons: energy, momentum and atomic energy levels
Photon energy and momentum
$E = h\nu = \dfrac{hc}{\lambda} \qquad p = \dfrac{E}{c} = \dfrac{h}{\lambda} \qquad E\,(\text{eV}) = \dfrac{1240}{\lambda\,(\text{nm})}$

Reference tables (1)

X-rays: what they are and what they do6 rows

Property or use	Fact
Nature	Electromagnetic waves with no charge
Electric and magnetic fields	Do not deflect X-raysQ Asked in 2020 (I), 2025 (II) and 2026 (I): neither an electric nor a magnetic field bends X-rays.
Wavelength	About 0.01 to 10 nm, much shorter than visible light
Penetration	Pass through flesh; stopped by bone and metal
Metal objects during a scan	Block or reflect the beam, leaving a bright or dark patch that hides the body partQ CDS 2026 (II): metal is removed because it spoils the image.
Welds, castings and crystals	Show hidden cracks; reveal how atoms are arrangedQ CDS 2024 (II): checking welded joints and studying crystals are both uses.

Watch out for (4)

For a photon, energy is momentum times c
→ Photons: energy, momentum and atomic energy levels
Shorter wavelength means more energy
→ Photons: energy, momentum and atomic energy levels
No charge, no bending
→ X-rays: what they are and what they do
Metal is removed to save the picture
→ X-rays: what they are and what they do

Test yourself on a real paper

Sit a past CDS paper, timed and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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