State the approximate wavelength (or frequency) ranges for the principal regions of the electromagnetic (EM) spectrum, from radio waves to γ‑rays, and explain the relevance of these ranges to other parts of the syllabus (progressive waves, photons, polarisation, and applications).
Units reminder
• Wavelength λ: metres (m) – or nanometres (nm) for convenience (1 nm = 10⁻⁹ m).
• Frequency ν: hertz (Hz).
• Photon energy E: electron‑volts (eV) – 1 eV = 1.602 × 10⁻¹⁹ J.
• Speed of light in vacuum c = 3.00 × 10⁸ m s⁻¹ (exact by definition).
• Planck’s constant h = 6.626 × 10⁻³⁴ J s.
Fundamental relationships
All EM radiation travels at the speed of light in vacuum: c = λ ν ≈ 3.00 × 10⁸ m s⁻¹.
Photon energy is linked to frequency (or wavelength) by E = h ν = h c / λ.
The limits given below are the conventional boundaries used throughout the Cambridge syllabus (they are approximate and regions overlap slightly).
Ionising vs non‑ionising radiation
Radiation is classified according to the energy of an individual photon:
Non‑ionising radiation: photon energy < ≈ 10 eV. Insufficient to remove tightly bound electrons from atoms. Includes radio, microwaves, infrared, visible light, and most of the ultraviolet (UVA, UVB).
Ionising radiation: photon energy ≥ ≈ 10 eV. Capable of ionising atoms or molecules, which can damage biological tissue. Includes the higher‑energy UV (UVC), X‑rays, and γ‑rays.
Wavelength, frequency and photon‑energy ranges (free space)
Region
λ (metres)
λ (nanometres)
ν (hertz)
Typical photon energy
Radio waves
1.0 × 10³ → 1.0 × 10⁻¹ m
1.0 × 10¹² → 1.0 × 10⁸ nm
3.0 × 10⁵ → 3.0 × 10⁹ Hz
1.0 × 10⁻⁹ → 1.0 × 10⁻⁵ eV
Microwaves
1.0 × 10⁻¹ → 1.0 × 10⁻³ m
1.0 × 10⁸ → 1.0 × 10⁶ nm
3.0 × 10⁹ → 3.0 × 10¹¹ Hz
1.0 × 10⁻⁵ → 1.0 × 10⁻³ eV
Infrared (IR)
1.0 × 10⁻³ → 7.0 × 10⁻⁷ m
1.0 × 10⁶ → 7.0 × 10² nm
3.0 × 10¹¹ → 4.3 × 10¹⁴ Hz
1.0 × 10⁻³ → 1.8 eV
Visible light
7.0 × 10⁻⁷ → 4.0 × 10⁻⁷ m
7.0 × 10² → 4.0 × 10² nm
4.3 × 10¹⁴ → 7.5 × 10¹⁴ Hz
1.8 → 3.1 eV
Ultraviolet (UV)
4.0 × 10⁻⁸ → 4.0 × 10⁻⁷ m
4.0 × 10¹ → 4.0 × 10² nm
7.5 × 10¹⁴ → 7.5 × 10¹⁵ Hz
3 → 30 eV
X‑rays
1.0 × 10⁻⁸ → 1.0 × 10⁻¹¹ m
1.0 × 10¹ → 1.0 × 10⁻² nm
3.0 × 10¹⁶ → 3.0 × 10¹⁹ Hz
30 → 300 keV (3.0 × 10⁴ → 3.0 × 10⁵ eV)
γ‑rays
< 1.0 × 10⁻¹¹ m
< 1.0 × 10⁻² nm
> 3.0 × 10¹⁹ Hz
> 300 keV (often MeV–GeV range)
Key concepts to remember
c = λ ν holds for every region; a shorter wavelength always means a higher frequency and a higher photon energy.
From radio waves to γ‑rays the wavelength decreases by more than 20 orders of magnitude, while the frequency (and energy) increases by the same factor.
All EM waves are transverse; the electric‑field vector is perpendicular to the direction of propagation. This underpins the phenomenon of polarisation (Syllabus 7.5).
Ionising radiation (≥ 10 eV) can remove electrons from atoms, making it hazardous and requiring shielding; non‑ionising radiation cannot.
Typical applications (linking the spectrum to other syllabus topics):
Radio waves – broadcasting, mobile communications (relates to modulation and antennas).
Microwaves – cooking ovens, radar (connects to Doppler shift in astrophysics).
Infrared – thermal imaging, fibre‑optic data transmission (ties to black‑body radiation).
Visible – human vision, colour filters (relevant for photometry).
Ultraviolet – sterilisation, fluorescence (used in chemistry/biology).
X‑rays – medical imaging, crystallography (bridges to matter‑wave interaction).
γ‑rays – nuclear medicine, radiation therapy, astrophysical sources (connects to radioactive decay and particle physics).
Cross‑references to other A‑Level topics
Progressive waves (7.1 – 7.3): the same wave‑equation formalism (v = f λ) that defines the spectrum also describes sound, water waves and mechanical vibrations.
Photons (9.1): photon energy E = h f = h c / λ is derived directly from the table above.
Polarisation (7.5): recognising EM waves as transverse explains linear, circular and elliptical polarisation.
Quantum physics (9.2 – 9.4): ionising radiation (X‑rays, γ‑rays) is used in experiments illustrating the photoelectric effect and Compton scattering.
Suggested diagram
Logarithmic plot of the electromagnetic spectrum (wavelength on the horizontal axis, frequency on the vertical axis). Each region is shaded, conventional boundaries are marked, and representative applications are labelled (e.g., “radio broadcast”, “microwave oven”, “IR camera”, “visible colours”, “UV steriliser”, “X‑ray scanner”, “γ‑ray therapy”).
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