AQA GCSE Physics 4.6

The Electromagnetic Spectrum

Radio to gamma — properties, uses and hazards of each region. All electromagnetic waves travel at 3×10⁸ m/s in a vacuum.

📡 State the order of regions of the electromagnetic spectrum from radio waves to gamma rays, including their relative wavelengths and frequencies

⚡ Recall and apply the wave equation: v = fλ, using c = 3×10⁸ m/s for all EM waves in a vacuum

🔬 Describe the properties, uses and hazards of each region of the electromagnetic spectrum

☢️ Explain how the hazard posed by EM radiation relates to its frequency and energy

📻 Give examples of how different regions of the EM spectrum are produced and detected

🌡️ Describe how the human body emits infrared radiation and the role of the atmosphere in absorbing EM waves

🌊 What is the Electromagnetic Spectrum?

Electromagnetic (EM) waves are transverse waves that transfer energy from a source to an absorber. Unlike sound waves, they do not require a medium and can travel through a vacuum. All EM waves travel at the same speed in a vacuum:

c = 3 × 10⁸ m/s (the speed of light)

The electromagnetic spectrum is the continuous family of all EM waves, ordered by wavelength or frequency. As frequency increases, wavelength decreases (and vice versa), because they are linked by the wave equation:

v = f × λ
v = wave speed (m/s) | f = frequency (Hz) | λ = wavelength (m)

For EM waves in a vacuum, v = c = 3 × 10⁸ m/s, so:

c = f × λ ⟹ f = c ÷ λ ⟹ λ = c ÷ f

The spectrum is divided into seven named regions. From longest wavelength (lowest frequency) to shortest wavelength (highest frequency):

Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma ray
Mnemonic: Raging Martians Invaded Venus Using X-ray Guns

Region	Approx. Wavelength	Approx. Frequency
Radio	> 0.1 m	< 3 × 10⁹ Hz
Microwave	1 mm – 0.1 m	3×10⁹ – 3×10¹¹ Hz
Infrared	700 nm – 1 mm	3×10¹¹ – 4×10¹⁴ Hz
Visible	400 nm – 700 nm	4×10¹⁴ – 7×10¹⁴ Hz
Ultraviolet	10 nm – 400 nm	7×10¹⁴ – 3×10¹⁶ Hz
X-ray	0.01 nm – 10 nm	3×10¹⁶ – 3×10¹⁹ Hz
Gamma ray	< 0.01 nm	> 3×10¹⁹ Hz

📡 Radio Waves and Microwaves

Radio Waves: EM waves with wavelengths greater than about 0.1 m, produced by oscillating electrical charges in an antenna.

Uses of Radio Waves:

Broadcasting: AM and FM radio, television signals are transmitted as radio waves. Long-wave radio can travel thousands of kilometres by diffracting around the curvature of the Earth.
Satellite communications: Signals are sent to satellites in orbit and beamed back to receivers on Earth.
Radar: Radio waves are reflected off objects to detect position and speed of aircraft and ships.

Hazards of Radio Waves: At low intensities, radio waves are not considered harmful. At very high intensities, they can cause heating of body tissues, but everyday exposure poses negligible risk.

Microwaves: EM waves with wavelengths between about 1 mm and 0.1 m. Produced by specialised electronic devices such as magnetrons.

Uses of Microwaves:

Microwave ovens: Microwaves are absorbed by water molecules in food, causing them to vibrate and heat the food from within. The specific frequency used (around 2.45 GHz) is chosen because it is strongly absorbed by water.
Satellite communication and mobile phone networks: Microwaves pass easily through the atmosphere and are used to carry phone signals and data to/from satellites.
Speed cameras: Doppler shift of reflected microwaves is used to calculate vehicle speed.

Hazards of Microwaves: Internal heating of body tissue — they can penetrate below the skin surface. Safety standards limit exposure from devices like mobile phones.

🌡️ Infrared, Visible Light and Ultraviolet

Infrared (IR): EM radiation with wavelengths from about 700 nm to 1 mm. All objects above absolute zero emit infrared radiation; hotter objects emit more and at shorter wavelengths.

Uses of Infrared: Thermal imaging cameras (night vision), TV remote controls, optical fibre communications, toasters and grills, physiotherapy treatments, and infrared astronomy. The atmosphere absorbs some IR, which contributes to the greenhouse effect.

Hazards of Infrared: Skin burns and eye damage with excessive exposure; overheating of the body.

Visible Light: The narrow band of EM radiation (400–700 nm) that the human eye can detect. Violet has the shortest wavelength; red has the longest.

Uses of Visible Light: Human vision, photography, optical fibres (for communications), lasers (surgery, cutting, bar-code scanners), and illumination. The visible spectrum seen in a rainbow goes: violet, blue, green, yellow, orange, red.

Hazards of Visible Light: Very intense visible light (e.g. lasers) can damage the retina. Generally, visible light poses little hazard at normal intensities.

Ultraviolet (UV): EM radiation with wavelengths from about 10 nm to 400 nm, just beyond visible violet. Produced by the Sun and UV lamps.

Uses of Ultraviolet: Sterilising medical equipment and water supplies (UV kills bacteria), detecting forged bank notes (security inks fluoresce under UV), sun beds, and treating some skin conditions (phototherapy). The ozone layer in the atmosphere absorbs much of the Sun's UV, protecting life on Earth.

Hazards of Ultraviolet: UV can damage DNA, increasing the risk of skin cancer and eye cataracts. It also causes sunburn and premature skin ageing. UV is ionising at shorter wavelengths — it can remove electrons from atoms, breaking chemical bonds in biological molecules.

☢️ X-rays and Gamma Rays

X-rays: High-frequency EM waves (wavelengths 0.01–10 nm) produced when fast-moving electrons are rapidly decelerated by a metal target (e.g. tungsten) in an X-ray tube.

Uses of X-rays:

Medical imaging: X-rays pass through soft tissue but are absorbed by denser materials like bone or metal. A photographic plate or digital detector behind the patient records a shadow image. CT (computed tomography) scans use rotating X-ray beams to build 3D images.
Security scanning: Airport baggage scanners use X-rays to image contents of luggage.
Radiotherapy: Focused X-rays can destroy cancer cells in tumours.
Industrial quality control: Checking for cracks or defects inside metal components.

Hazards of X-rays: X-rays are ionising radiation — they can damage or kill cells and cause mutations in DNA, leading to cancer. Medical staff use lead shielding and limit exposure time. Patients are given only the minimum necessary dose.

Gamma Rays (γ): The highest-frequency, shortest-wavelength EM waves, emitted from the nuclei of unstable (radioactive) atoms during nuclear decay.

Uses of Gamma Rays:

Medical diagnosis: Gamma-emitting tracers (e.g. technetium-99m) injected into the body allow gamma cameras to image organs and detect tumours.
Radiotherapy: The gamma knife focuses beams of gamma rays precisely onto cancerous tumours, destroying them while minimising damage to surrounding tissue.
Sterilisation: Gamma rays are used to sterilise medical equipment and food (irradiation).

Hazards of Gamma Rays: Gamma rays are highly penetrating ionising radiation — they can pass through the whole body, ionising cells and damaging DNA. This can lead to radiation sickness, increased cancer risk, or death at very high doses. Lead and thick concrete are needed for shielding.

Key relationship: As frequency increases across the EM spectrum, each photon carries more energy (E = hf). This is why gamma rays are far more dangerous than radio waves — each gamma photon carries enough energy to ionise atoms and break chemical bonds in DNA.

🔗 Key Equations and Symbol Table

The single most important equation for this topic is the wave equation applied to EM waves:

c = f × λ
c = speed of light in vacuum = 3 × 10⁸ m/s
f = frequency (Hz, hertz)
λ = wavelength (m, metres)

You may also encounter the photon energy equation at Higher tier:

E = h × f
E = photon energy (J, joules)
h = Planck's constant = 6.63 × 10⁻³⁴ J s
f = frequency (Hz)

Symbol	Quantity	SI Unit
c	Speed of light in vacuum	m/s
f	Frequency	Hz (hertz)
λ	Wavelength	m (metres)
E	Photon energy	J (joules)
h	Planck's constant	J s
T	Period (time for one wave)	s (seconds)

Useful unit conversions:
1 nm = 1 × 10⁻⁹ m | 1 GHz = 1 × 10⁹ Hz | 1 MHz = 1 × 10⁶ Hz | 1 mm = 1 × 10⁻³ m

Example 1: A radio station broadcasts at a frequency of 98.4 MHz. Calculate the wavelength of the radio waves it transmits. Give your answer in metres.

1 Write down the known values:
f = 98.4 MHz = 98.4 × 10⁶ Hz = 9.84 × 10⁷ Hz
c = 3 × 10⁸ m/s

2 Select and rearrange the equation:
c = f × λ ⟹ λ = c ÷ f

3 Substitute values:
λ = (3 × 10⁸) ÷ (9.84 × 10⁷)
λ = 3.049... m

4 Round to appropriate significant figures:
λ ≈ 3.05 m (3 s.f.)

λ = 3.05 m | This confirms the wave is in the radio wave region of the spectrum (wavelength > 0.1 m).

Example 2: Visible green light has a wavelength of 520 nm. Calculate the frequency of this green light.

1 Convert wavelength to metres:
λ = 520 nm = 520 × 10⁻⁹ m = 5.20 × 10⁻⁷ m
c = 3 × 10⁸ m/s

2 Rearrange the wave equation:
c = f × λ ⟹ f = c ÷ λ

3 Substitute values:
f = (3 × 10⁸) ÷ (5.20 × 10⁻⁷)
f = 5.769... × 10¹⁴ Hz

4 Round and state units:
f ≈ 5.77 × 10¹⁴ Hz (3 s.f.)

f = 5.77 × 10¹⁴ Hz | This lies in the visible light range (4–7 × 10¹⁴ Hz). ✓

Example 3: An X-ray has a frequency of 3.0 × 10¹⁸ Hz. Calculate (a) its wavelength and (b) the energy of one photon. (h = 6.63 × 10⁻³⁴ J s)

1 Part (a) — Find the wavelength:
c = 3 × 10⁸ m/s | f = 3.0 × 10¹⁸ Hz
λ = c ÷ f = (3 × 10⁸) ÷ (3.0 × 10¹⁸)

2 Calculate wavelength:
λ = 1.0 × 10⁻¹⁰ m = 0.1 nm
This is well within the X-ray range (0.01–10 nm). ✓

3 Part (b) — Find the photon energy:
E = h × f
E = (6.63 × 10⁻³⁴) × (3.0 × 10¹⁸)

4 Calculate energy:
E = 1.989 × 10⁻¹⁵ J ≈ 1.99 × 10⁻¹⁵ J (3 s.f.)

(a) λ = 1.0 × 10⁻¹⁰ m | (b) E = 1.99 × 10⁻¹⁵ J | Compare to a radio wave photon (f ~ 10⁸ Hz): E ~ 10⁻²⁶ J — X-ray photons carry ~10¹⁰ times more energy!

Example 4: A microwave oven operates at a frequency of 2.45 GHz. (a) Calculate the wavelength of these microwaves. (b) Explain why microwaves are used to heat food rather than radio waves.

1 Convert frequency to Hz:
f = 2.45 GHz = 2.45 × 10⁹ Hz
c = 3 × 10⁸ m/s

2 Calculate wavelength:
λ = c ÷ f = (3 × 10⁸) ÷ (2.45 × 10⁹)
λ = 0.1224... m ≈ 0.122 m (12.2 cm)

3 Part (b) — Explanation:
The frequency of 2.45 GHz corresponds to the natural resonant frequency at which water molecules absorb microwave energy efficiently. When water molecules absorb this radiation, they vibrate more, increasing the internal (thermal) energy of the food.

4 Why not radio waves?
Radio waves have much lower frequencies and much longer wavelengths. They are not efficiently absorbed by water molecules, so they do not transfer energy to food effectively. The energy per photon (E = hf) is also much lower for radio waves.

(a) λ ≈ 0.122 m | (b) Microwaves at 2.45 GHz are strongly absorbed by water molecules in food, efficiently converting EM energy into thermal energy. Radio waves are not absorbed by water and so cannot heat food.

Question 1: Which of the following correctly orders regions of the EM spectrum from longest wavelength to shortest wavelength?

Question 2: A gamma ray has a frequency of 5.0 × 10²⁰ Hz. What is its wavelength?

Question 3: Calculate the frequency of UV light with a wavelength of 200 nm. Give your answer in standard form (Hz).

Hint: Convert nm to m first. c = 3 × 10⁸ m/s. Enter your answer as e.g. 1.5e15

Question 4: Which statement about X-rays and gamma rays is correct?

Question 5: A mobile phone transmits a signal at a wavelength of 0.150 m. Calculate the frequency of this signal in GHz. (Enter your answer in GHz, e.g. 2.00)

Challenge 1 [6 marks]: The Hubble Space Telescope detects ultraviolet light from a distant galaxy at a frequency of 1.50 × 10¹⁵ Hz.

(a) Show that the wavelength of this UV light is 200 nm. [2 marks]

(b) Calculate the energy of one photon of this UV radiation. (h = 6.63 × 10⁻³⁴ J s) [2 marks]

(c) Explain why UV radiation from the Sun can be more hazardous to human health than infrared radiation of the same intensity. [2 marks]

Challenge 2 [5 marks]: A hospital X-ray machine produces X-rays with a wavelength of 2.5 × 10⁻¹⁰ m.

(a) Calculate the frequency of these X-rays. [2 marks]

(b) State two precautions taken in hospitals to reduce the risk to patients and staff from X-ray exposure, and explain the physics behind each precaution. [3 marks]

Challenge 3 [6 marks]: Radio astronomers detect a signal from space at a wavelength of 21 cm (the hydrogen line).

(a) Calculate the frequency of this signal. [2 marks]

(b) Another signal is detected at a frequency of 4.6 × 10⁸ Hz. Calculate its wavelength and identify which region of the EM spectrum it belongs to. [3 marks]

(c) Explain why all EM waves travel at the same speed in a vacuum, even though they have very different wavelengths and frequencies. [1 mark]

Challenge 4 — Extended Response [4 marks]: Evaluate the risks and benefits of using gamma radiation in medicine. You should refer to both diagnostic uses and therapeutic uses, and explain the physics underlying the hazards.