The Electromagnetic Spectrum

One phenomenon, seven regions

Tune a radio to an FM station and music reaches you through nothing but empty space. Stand outside in the dark and warmth from the sun still finds you. Undergo an X-ray and the image forms without the beam touching you. In each case, energy has arrived as an oscillating electric and magnetic field, a self-propagating electromagnetic wave requiring no medium, travelling at exactly $c = 3.00 \times 10^8$ m/s. All electromagnetic waves share three fundamental properties: they are transverse waves, they travel at the speed of light in vacuum, and they do not require a medium.

The electromagnetic spectrum is traditionally divided into seven regions, ordered by increasing frequency (and decreasing wavelength):

Radio waves ($\lambda \sim 10^3$ m): Used for communication, AM/FM radio, television and mobile phones. Their photons are non-ionising; sufficiently intense radiofrequency fields can still deposit energy and heat tissue.

Microwaves ($\lambda \sim 10^{-2}$ m): Used in microwave ovens (heating water molecules), radar, and Wi-Fi. Can cause heating of tissue.

Infrared ($\lambda \sim 10^{-5}$ m): Felt as heat. Used in remote controls, thermal imaging, and night vision. Can cause burns at high intensity.

Visible light ($\lambda \sim 400$–$700$ nm): The only region our eyes can detect. Red has the longest wavelength ($\approx 700$ nm); violet the shortest ($\approx 400$ nm).

Ultraviolet ($\lambda \sim 10^{-8}$ m): Causes sunburn and skin damage. Used in sterilisation and forensics. Can damage DNA.

X-rays ($\lambda \sim 10^{-10}$ m): Pass through soft tissue but are absorbed by bone. Used in medical imaging and airport security. Ionising, dangerous in high doses.

Gamma rays ($\lambda \sim 10^{-12}$ m): Highest energy, produced by nuclear decay and cosmic events. Used in cancer treatment (radiotherapy). Highly ionising and dangerous.

The electromagnetic spectrum has seven regions ordered by increasing frequency: radio, microwave, infrared, visible, UV, X-ray, gamma. All EM waves are transverse and travel at $c = 3.00 \times 10^8$ m/s in vacuum, no medium required. Higher frequency means shorter wavelength and greater photon energy ($E = hf$).

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The universal constant that connects wavelength and frequency

We just saw that the EM spectrum spans seven regions all travelling at $c$. That raises a question: how do frequency and wavelength relate mathematically, and what determines a photon's energy? This card answers it → the wave equation $c = f\lambda$ and the photon energy formula $E = hf$.

All electromagnetic waves in vacuum obey the fundamental wave equation $c = f\lambda$, where $c = 3.00 \times 10^8$ m/s is the speed of light in vacuum, $f$ is frequency in hertz (Hz), and $\lambda$ is wavelength in metres (m). Since $c$ is constant, wavelength and frequency are inversely proportional: high frequency means short wavelength, and vice versa.

Each photon of electromagnetic radiation carries energy:

These equations reveal why gamma radiation can ionise atoms whereas radiofrequency radiation cannot: a gamma photon carries $\sim10^{15}$ times more energy than a radio photon. Biological risk also depends on absorbed dose and exposure conditions; non-ionising radiation can still cause heating at sufficient intensity.

When EM waves enter a medium such as glass or water, they slow down. The speed in a medium is $v = c/n$, where $n$ is the refractive index. The frequency stays the same, but the wavelength decreases: $\lambda_{\text{medium}} = \lambda_{\text{vacuum}}/n$.

For all EM waves: $c = f\lambda$ (speed = frequency × wavelength, $c = 3.00 \times 10^8$ m/s). Photon energy $E = hf = hc/\lambda$ where $h = 6.63 \times 10^{-34}$ J·s. In a medium, speed decreases to $v = c/n$, wavelength decreases, but frequency remains unchanged.

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From wavelength to energy across the spectrum

We just saw that $E = hf$ links frequency to photon energy. That raises a question: how do you apply this to concrete calculations involving wavelengths in different units or energies in electronvolts? This card answers it → a step-by-step approach to photon calculations across the spectrum.

Photon calculation method: convert $\lambda$ to metres → $f = c/\lambda$ → $E = hf$ in joules → divide by $1.60 \times 10^{-19}$ for eV. Reverse: eV to J → $f = E/h$ → $\lambda = c/f$. Power emitted ÷ energy per photon = photons per second.

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Why photon energy determines safety, not wave speed

We just saw how to calculate photon energy from wavelength or frequency. That raises a question: since all EM waves travel at $c$, why do some harm living tissue while others do not? This card answers it → it is photon energy $E = hf$, not speed, that determines ionisation and biological effects.

Because all EM waves travel at the same speed, it might seem they should all have the same effect on matter. The key difference is photon energy, $E = hf$. High-frequency photons carry enough energy to ionise atoms (strip electrons away), damaging molecules including DNA. Low-frequency photons deposit only tiny amounts of energy, too little to cause ionisation.

Key biological effects to know:

• UV: Damages DNA, causing sunburn and increasing skin cancer risk. Some UV is beneficial (vitamin D synthesis).
• X-rays: Penetrate soft tissue; absorbed by dense bone. Ionising, dose must be carefully managed in medical imaging.
• Gamma rays: Penetrate almost everything; produced in nuclear reactions. Used in cancer radiotherapy, targeted to tumour cells.
• Infrared: Causes heating (molecular vibrations), not ionisation. Prolonged exposure can burn skin.
• Radio/microwave: These photons are non-ionising. At sufficient intensity the fields can deposit energy and heat tissue; microwave ovens heat food through dielectric absorption.

Ionisation depends on photon energy $E = hf$, not wave speed. X-rays and gamma rays are ionising; sufficiently short-wavelength ultraviolet can also ionise, while the UV boundary is not rigid. Radio, microwave, infrared and visible photons are non-ionising but can still cause harm through heating or photochemical effects depending on dose. Medical uses include X-ray imaging, gamma radiotherapy and UV sterilisation.

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How theory predicted that light is an electromagnetic wave

James Clerk Maxwell unified electricity and magnetism into one theory and showed, from that theory alone, that light is an electromagnetic wave.

In the 1860s, James Clerk Maxwell unified electricity and magnetism into a single theory of electromagnetism (Maxwell's equations). His equations predicted that a changing electric field produces a changing magnetic field, and vice versa, so the two propagate together as a self-sustaining electromagnetic wave through a vacuum, with no medium required.

Maxwell calculated the speed of these waves as $c = 1/\sqrt{\varepsilon_0\mu_0} \approx 3\times10^8$ m/s, determined only by the electric permittivity ($\varepsilon_0$) and magnetic permeability ($\mu_0$) of the vacuum. This matched the measured speed of light, leading to the conclusion that light is an electromagnetic wave.

Maxwell's work therefore unified optics with electricity and magnetism. His prediction was confirmed experimentally about 20 years later by Heinrich Hertz, who generated and detected radio waves travelling at the speed of light.

Copy the highlighted points (Maxwell's prediction of EM waves and $c = 1/\sqrt{\varepsilon_0\mu_0}$) into your book.