Electromagnetic waves and the electromagnetic spectrum
EM waves are transverse waves of electric and magnetic fields. They need no medium and travel at c = 3 × 10⁸ m s⁻¹ in vacuum.
Properties of electromagnetic waves
- They are made by accelerated charges. Maxwell predicted them; Hertz, J. C. Bose and Marconi produced them in experiments.
- They are transverse: the electric field E and the magnetic field B vibrate at right angles to each other and to the direction of travel.
- The field values are linked by E = cB.
- They need no material medium and travel through vacuum at c = 1/√(μ₀ε₀) = 3 × 10⁸ m s⁻¹, the speed of light. So light is an EM wave.
- In a medium they are slower: v = c/√(μᵣεᵣ).
- Their frequency does not change when they pass from one medium to another.
- They carry energy, and the energy of the radiation is E = hν. Their behaviour depends on their frequency, not on how they are made.
The electromagnetic spectrum
All EM waves are the same kind of wave. They differ only in wavelength and frequency, with c = νλ in vacuum. Arranged in order of wavelength, they form the electromagnetic spectrum. The regions have no sharp boundaries, and neighbouring regions overlap. The same wavelength can be made in two ways, but its properties stay the same. Gamma rays have the shortest wavelength and the most energy. Radio waves and the power waves from AC lines have the longest wavelength and the least energy. Visible light, about 400 nm (violet) to 700 nm (red), is only a tiny part of the spectrum. Our eyes are most sensitive to yellow-green light.
The spectrum at a glance (wavelengths are approximate)
| Wave | Wavelength | Produced by | Detected by or used for |
|---|---|---|---|
| Power waves | 5000 km to 6000 km (50 Hz to 60 Hz) | AC power lines | Electric power supply |
| Radio waves | About 0.3 m and longer | Charges accelerated in aerials; LC oscillators | Radio and TV broadcasting, mobile phones |
| Microwaves | 1 mm to 0.3 m | Oscillating currents in special vacuum tubes | Radar for aircraft navigation, microwave ovens, TV and satellite links |
| Infrared | 700 nm to 1 mm | Hot bodies and vibrating molecules | Detected by a thermopile; physiotherapy, infrared photography |
| Visible light | 400 nm to 700 nm | Electrons in atoms jumping to lower energy levels | The eye; seeing and photography |
| Ultraviolet | About 3 nm to 400 nm | The Sun, very hot bodies, special lamps | Killing germs in water, sterilising operation theatres, checking forged documents |
| X-rays | About 4 × 10⁻¹³ m to 4 × 10⁻⁸ m | Fast electrons hitting a metal target such as tungsten | Photographic plates; medical diagnosis, treating some cancers, studying crystals |
| Gamma rays | Shorter than about 10⁻¹⁰ m | Radioactive nuclei such as cobalt-60 and caesium-137; nuclear reactions | Geiger tube or scintillation counter; cancer treatment, finding flaws in metal castings |
How to draw an EM wave and the spectrum chart
- Draw three axes from one point: x upwards, y slanting towards you, and z to the right. Label z direction of travel.
- Draw a sine curve in the vertical x-z plane and label it E.
- Draw a second sine curve in the horizontal y-z plane, with its peaks at the same points along z, and label it B.
- Mark one wavelength λ along the z-axis.
- Spectrum chart: draw a long strip of seven boxes labelled, from left to right, gamma, X-rays, UV, visible, infrared, microwaves, radio. Make the visible box very narrow.
- Draw an arrow pointing right labelled wavelength increases, and one pointing left labelled frequency and energy increase.
Worked example: wavelength, speed and energy
(a) An FM radio station broadcasts at 93.5 MHz. Find the wavelength of its waves. (b) A medium has relative permittivity 4 and relative permeability 1. Find the speed of EM waves in it. (c) Compare the energy of X-rays of wavelength 0.1 nm with ultraviolet of wavelength 300 nm. (c = 3 × 10⁸ m s⁻¹)
- (a) λ = c/ν = 3 × 10⁸ m s⁻¹ ÷ 93.5 × 10⁶ Hz ≈ 3.21 m: radio waves.
- (b) v = c/√(μᵣεᵣ) = 3 × 10⁸ ÷ √(1 × 4) = 3 × 10⁸ ÷ 2 = 1.5 × 10⁸ m s⁻¹.
- (c) E = hc/λ, so E is inversely proportional to λ.
- E(X-ray) ÷ E(UV) = 300 nm ÷ 0.1 nm = 3000.
(a) about 3.21 m; (b) 1.5 × 10⁸ m s⁻¹; (c) the X-rays carry 3000 times more energy
Your mobile phone, the FM radio, the infrared TV remote and the X-ray machine at a hospital all use EM waves of different wavelengths. The ozone layer high in the atmosphere absorbs most of the Sun's harmful ultraviolet before it reaches us.
2 marks: “State four properties of electromagnetic waves.” Transverse; E and B at right angles to each other and to the direction of travel; need no medium; travel at c = 3 × 10⁸ m s⁻¹ in vacuum; produced by accelerated charges; frequency unchanged in a new medium (any four).
2 marks: “Name the EM waves used (a) in radar for aircraft navigation, (b) to kill germs in drinking water. Give one source of each.” (a) Microwaves, made by oscillating currents in special vacuum tubes. (b) Ultraviolet rays, from the Sun or from special UV lamps.
1 marks: “Which gas in the upper atmosphere absorbs most of the Sun's ultraviolet radiation?” Ozone.
Order of increasing wavelength: Good Xylophones Usually Vibrate In My Room: gamma, X-rays, UV, visible, infrared, microwaves, radio.