The Electromagnetic Spectrum
The electromagnetic (EM) spectrum is the continuous range of all possible frequencies of electromagnetic radiation. These notes cover the properties, order, applications, and hazards of its different parts, which is fundamental for questions on communications, energy transfer, and medical physics.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- All EM waves are transverse, can travel through a vacuum, and move at the speed of light in a vacuum.c = 3 x 108 m/s
- The spectrum is a continuum ordered by wavelength and frequency. As wavelength decreases, frequency and energy increase.
- The order from longest wavelength (lowest frequency) to shortest wavelength (highest frequency) is: Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, Gamma rays.
- The energy carried by an EM wave is directly proportional to its frequency. This means gamma rays are the most energetic and generally the most hazardous.
- When an EM wave enters a different medium (e.g., from air to glass), its speed and wavelength change, but its frequency remains constant.
Diagram
› Why does this happen?
Why can EM waves travel through a vacuum?
Unlike sound waves, which are vibrations of particles and need a medium to travel, EM waves are made of oscillating electric and magnetic fields. A changing electric field creates a magnetic field, and a changing magnetic field creates an electric field. These two fields generate and sustain each other, allowing the wave to propagate through empty space without needing any particles to carry the energy.
Why are high-frequency waves more hazardous?
EM waves deliver energy in discrete packets called photons. The energy of each photon is directly proportional to the wave's frequency. The photons of high-frequency radiation (like UV, X-rays, and gamma rays) carry enough energy to knock electrons out of atoms, a process called ionisation. This ionisation can damage the DNA inside living cells, leading to mutations or cell death. The photons of lower-frequency waves (like radio or microwaves) don't have enough energy to cause ionisation; they mainly just cause atoms and molecules to vibrate, which results in heating.
Why does frequency stay constant when a wave changes medium?
The frequency of a wave is set by its source – it's the number of waves produced each second. When a wave reaches the boundary of a new material, like light hitting glass, the number of waves arriving at the boundary each second must equal the number of waves leaving it. Waves can't just disappear or be created at the boundary. Because the number of waves per second (the frequency) stays the same, but the wave's speed changes in the new material, its wavelength must also change to match. This is because of the wave equation: speed = frequency x wavelength.
Formulae
c = f × lambda To relate the speed of light in a vacuum (c), frequency (f), and wavelength (lambda) of any electromagnetic wave. Remember c is a constant value.
Definitions
- Electromagnetic Wave
- A transverse wave consisting of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of energy propagation. It does not require a medium to travel.
- Ionisation
- The process where an atom or molecule gains or loses an electron, acquiring a net electrical charge. High-frequency EM waves like UV, X-rays, and gamma rays are ionising and can damage living cells.
Worked example
An X-ray has a wavelength of 2.0 x 10-10 m. A radio wave signal has a frequency that is 1.5 x 1010 times smaller than the X-ray's frequency. What is the wavelength of this radio wave? (Use speed of light, c = 3.0 x 108 m/s)
- 1
First, find the frequency of the X-ray using the wave equation:
f = c / lambda - 2 fxray = (3.0 x 108 m/s) / (2.0 x 10-10 m) = 1.5 x 1018 Hz
- 3
Next, calculate the frequency of the radio wave.
It is 1.5 x 1010 times smaller.
- 4 fradio = (1.5 x 1018 Hz) / (1.5 x 1010) = 1.0 x 108 Hz
- 5
Finally, calculate the wavelength of the radio wave using its frequency:
lambda = c / f - 6
lambdaradio = (3.0 x 108 m/s) / (1.0 x 108 Hz) = 3.0 m.
- 7
Alternatively, since frequency and wavelength are inversely proportional, if the frequency is 1.5 x 1010 times smaller, the wavelength must be 1.5 x 1010 times larger.
- 8
lambdaradio = lambdaxray × (1.5 x 1010) = (2.0 x 10-10 m) × (1.5 x 1010) = 3.0 m.
Answer: 3.0 m
Common mistakes
- ×Mixing up the order of the spectrum. Use a mnemonic like 'Rich Men In Vegas Use Xpensive Gadgets' to remember the order of increasing frequency: Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma.
- ×Confusing properties of EM waves and mechanical waves. For instance, assuming EM waves cannot travel in a vacuum, which is a property of sound waves. This is a key `domainconfusion` error.
- ×Forgetting that all EM waves travel at the same speed 'c' in a vacuum, regardless of their frequency. This is a common `missingconstraint` mistake; speed only changes when the medium changes.
- ×Making arithmetic errors with powers of ten in the wave equation. A frequent `offbyfactor` mistake is incorrectly adding/subtracting exponents, e.g., 108 / 10-10 = 10-2 instead of 1018.
No-calculator tips
- ✓Focus on proportions. If a question states wavelength doubles, you know frequency must halve, without needing to calculate the exact values.
- ✓Approximate values to make calculations simpler. For example, if given a frequency of 2.9 x 108 Hz, treat it as 3 x 108 Hz to quickly find the wavelength is approximately 1 m.
- ✓Memorise benchmark wavelengths to quickly identify regions. Visible light is ~500 nm (5 x 10-7 m). A radio wave might be several meters long. X-rays are around the size of an atom (~10-10 m).