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Electromagnetic (EM) waves are transverse waves consisting of oscillating electric and magnetic fields, perpendicular to each other and to the direction of propagation. They require no medium and all travel at the speed of light in a vacuum: c = 3.00 × 10⁸ m s⁻¹.
Spec mapping: This lesson sits under AQA 7408 section 3.3.1 and covers the regions of the electromagnetic spectrum, their characteristic wavelength and frequency ranges, typical sources, principal uses, and the biological hazards that scale with photon energy E = hf. Candidates are expected to know the order of the seven named regions and to perform calculations of frequency, wavelength and photon energy across the spectrum. (Refer to the official AQA specification document for exact wording.)
Synoptic links:
- Section 3.2.2 (quantum phenomena): photon energy E = hf is the bridge between this lesson's classical-wave description of EM radiation and the photon model used in the photoelectric effect and atomic line spectra.
- Section 3.8 (nuclear physics): gamma emission from radioactive decay is the highest-energy region of the EM spectrum; understanding its photon energy explains why it is the most penetrating and most ionising.
- Section 3.3.2 (refraction, diffraction, interference): every region of the EM spectrum exhibits these wave phenomena, with the magnitude of the effect scaling with wavelength — diffraction is significant for radio waves at apertures of metres but negligible for visible light at the same apertures.
All electromagnetic waves share the following properties:
The electromagnetic spectrum is a continuous range of wavelengths and frequencies. We divide it into named regions for convenience, but there are no sharp boundaries between them.
The following table summarises the approximate wavelength range, frequency range, and key properties of each region. Wavelength decreases and frequency increases from top to bottom.
| Region | Wavelength Range | Frequency Range | Typical Source |
|---|---|---|---|
| Radio waves | > 0.1 m | < 3 × 10⁹ Hz | Oscillating charges in aerials/antennae |
| Microwaves | 1 mm – 0.1 m | 3 × 10⁹ – 3 × 10¹¹ Hz | Magnetrons, klystrons |
| Infrared (IR) | 700 nm – 1 mm | 3 × 10¹¹ – 4.3 × 10¹⁴ Hz | Hot objects, heaters |
| Visible light | 400 nm – 700 nm | 4.3 × 10¹⁴ – 7.5 × 10¹⁴ Hz | Very hot objects, LEDs, lasers |
| Ultraviolet (UV) | 10 nm – 400 nm | 7.5 × 10¹⁴ – 3 × 10¹⁶ Hz | The Sun, UV lamps, very hot stars |
| X-rays | 0.01 nm – 10 nm | 3 × 10¹⁶ – 3 × 10¹⁹ Hz | Decelerating electrons hitting a metal target |
| Gamma rays (γ) | < 0.01 nm | > 3 × 10¹⁹ Hz | Radioactive decay of unstable nuclei |
Exam Tip: You must know the order of the EM spectrum and typical wavelength/frequency ranges. A common mnemonic is: Running Mice In Valleys Use X-tra Grass.
Within the visible spectrum, wavelengths range from approximately:
| Colour | Approximate Wavelength |
|---|---|
| Red | 620 – 700 nm |
| Orange | 590 – 620 nm |
| Yellow | 570 – 590 nm |
| Green | 495 – 570 nm |
| Blue | 450 – 495 nm |
| Violet | 380 – 450 nm |
Higher-frequency EM radiation carries more energy per photon (E = hf) and is generally more hazardous to biological tissue.
| Region | Key Hazards |
|---|---|
| Microwaves | Internal heating of body tissue (especially water-rich organs like eyes) |
| Infrared | Skin burns, eye damage (cataracts with prolonged exposure) |
| Ultraviolet | Skin cancer (melanoma), sunburn, eye damage (photokeratitis), premature ageing |
| X-rays | Cell damage, mutations, increased cancer risk (ionising radiation) |
| Gamma rays | Severe cell damage, radiation sickness, cancer, genetic mutations (strongly ionising) |
Exam Tip: When describing hazards, always state the specific biological effect (e.g., "causes mutations in DNA leading to cancer"), not just "it is dangerous."
All objects above absolute zero emit electromagnetic radiation. The dominant wavelength emitted depends on the temperature of the object:
When EM radiation is absorbed by matter, its energy is transferred to the atoms or molecules of the absorbing material. This can cause:
Worked Example 1 — Calculate the frequency of green light with wavelength 550 nm.
λ = 550 nm = 550 × 10⁻⁹ m = 5.50 × 10⁻⁷ m
f = c/λ = (3.00 × 10⁸)/(5.50 × 10⁻⁷) = 5.45 × 10¹⁴ Hz
Worked Example 2 — A microwave oven operates at 2.45 GHz. Calculate the wavelength of the microwaves.
f = 2.45 GHz = 2.45 × 10⁹ Hz
λ = c/f = (3.00 × 10⁸)/(2.45 × 10⁹) = 0.122 m = 12.2 cm
Worked Example 3 — An X-ray has a wavelength of 0.050 nm. Calculate its frequency and the energy of one photon.
λ = 0.050 nm = 5.0 × 10⁻¹¹ m
f = c/λ = (3.00 × 10⁸)/(5.0 × 10⁻¹¹) = 6.0 × 10¹⁸ Hz
Energy per photon: E = hf = (6.63 × 10⁻³⁴) × (6.0 × 10¹⁸) = 4.0 × 10⁻¹⁵ J
Converting to eV: E = (4.0 × 10⁻¹⁵)/(1.60 × 10⁻¹⁹) = 2.5 × 10⁴ eV = 25 keV
This is a typical energy for diagnostic X-rays.
Worked Example 4 — A radio transmitter broadcasts at 200 kHz. What is the wavelength?
f = 200 kHz = 2.00 × 10⁵ Hz
λ = c/f = (3.00 × 10⁸)/(2.00 × 10⁵) = 1500 m = 1.50 km
This is a long-wave radio wavelength — these waves can diffract around hills and buildings due to their very large wavelength.
Exam Tip: When comparing EM waves, remember that all travel at the same speed in a vacuum. A higher frequency always means a shorter wavelength, and vice versa. The product fλ is always c.
The speed of light in a vacuum, c ≈ 2.998 × 10⁸ m s⁻¹, is one of the foundational constants of physics. Historically it was measured by Ole Rømer (1676, by timing Jupiter's moon Io), Fizeau (1849, with a toothed wheel and distant mirror), Foucault (1850, with a rotating mirror), and Michelson (1926, refined to 0.001% precision). The modern value is defined exactly as c = 299 792 458 m s⁻¹ — the metre itself is now defined in terms of c and the second (the SI base unit definition since 1983). This means that no experiment can ever measure c with non-zero uncertainty in the SI system; instead, experiments measure the metre against a standardised time interval.
Three reasons elevate c beyond a mere kinematic parameter:
In a medium other than vacuum, the phase velocity of light is v = c/n where n is the refractive index. This is not a slowing-down of individual photons; rather, the wave inside the medium is a superposition of the original incoming wave and the wavelets re-radiated by polarised electrons in the medium, and the resulting net wave has a phase velocity less than c.
Speed in glass: v = distance / time = 2.50 / (12.4 × 10⁻⁹) = 2.016 × 10⁸ m s⁻¹
Refractive index: n = c/v = (3.00 × 10⁸) / (2.016 × 10⁸) = 1.49
This is typical of crown glass.
Time = distance / c = (1.50 × 10¹¹) / (3.00 × 10⁸) = 500 s = 8 minutes 20 seconds
The Sun's photosphere has an effective temperature of approximately 5800 K. Using Wien's displacement law λ_peak T = 2.898 × 10⁻³ m K (just outside the A-Level spec but useful here):
λ_peak = 2.898 × 10⁻³ / 5800 = 500 nm — green light, in the centre of the visible spectrum.
This is no coincidence: human vision evolved to exploit the wavelength range where solar radiation is most intense.
When a source of EM radiation moves relative to an observer, the observed frequency shifts. For source speed v_source much less than c, the frequency shift is approximately:
Δf/f ≈ v_source/c (for motion directly toward or away from the observer)
This is the basis for measuring the radial velocities of stars and galaxies. Edwin Hubble's 1929 observation that distant galaxies are systematically redshifted — with greater redshift at greater distance — established the expansion of the universe and led to the Big Bang model.
Δλ/λ ≈ v/c, with Δλ = 656.5 − 656.3 = 0.20 nm
v = c × Δλ/λ = (3.00 × 10⁸) × (0.20 / 656.3) = 91 km s⁻¹, moving away (redshift).
For comparison, the Andromeda galaxy is moving toward us at about 110 km s⁻¹ (blueshift) and will collide with the Milky Way in ~4 billion years.
The most striking observational confirmation of the Big Bang is the cosmic microwave background (CMB) — a nearly uniform background of microwave radiation at a characteristic blackbody temperature of 2.725 K, peaking at λ ≈ 1.06 mm. The CMB is the redshifted remnant of the radiation released when the universe became transparent to photons, approximately 380,000 years after the Big Bang. Its existence was predicted by Gamow, Alpher and Herman in 1948 and accidentally detected by Penzias and Wilson in 1964 (Nobel Prize 1978).
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