Electromagnetic Waves • Topic 3 of 3

The Electromagnetic Spectrum

The electromagnetic spectrum is the complete range of electromagnetic waves, ordered by wavelength (or equivalently frequency), from long-wavelength radio waves to ultra-short gamma rays. Every part of the spectrum is the same kind of wave — they all travel at $c$ in vacuum and obey $c=f\lambda$ — and they differ only in wavelength and frequency. As wavelength shrinks, frequency rises and so does the energy of each photon ($E=hf$), which is why X-rays and gamma rays are far more penetrating and dangerous than radio waves.

The relation $c=f\lambda$ ties the whole spectrum together: a higher frequency always means a shorter wavelength. There are no sharp boundaries between the bands; they overlap and are named by how they are produced and used. Going from the longest to the shortest wavelength:

  • Radio waves ($\lambda>0.1\ \text{m}$, $f<10^{9}\ \text{Hz}$): produced by oscillating currents in antennas (accelerating charges in conductors). Used for radio and television broadcasting, and in mobile and satellite communication. AM/FM radio and TV signals are radio waves.
  • Microwaves ($\lambda\sim1\ \text{mm}$ to $0.1\ \text{m}$, $f\sim10^{9}$–$10^{11}\ \text{Hz}$): produced by special vacuum tubes such as klystrons and magnetrons. Used in RADAR, satellite and mobile communication, and in microwave ovens (they make water molecules in food vibrate).
  • Infrared (IR) ($\lambda\sim700\ \text{nm}$ to $1\ \text{mm}$): produced by hot bodies and vibrating molecules. We feel it as heat. Used in night-vision devices, TV remote controls, physiotherapy, and weather and Earth-observation satellites. IR is sometimes called heat radiation.
  • Visible light ($\lambda\sim400$–$700\ \text{nm}$): the only part our eyes can detect, produced by atoms and molecules during electron transitions and by hot objects. It runs from violet (shortest) to red (longest) and lets us see the world.
  • Ultraviolet (UV) ($\lambda\sim10$–$400\ \text{nm}$): produced by very hot bodies such as the Sun and by special UV lamps. It causes sunburn and is used to sterilise surgical instruments and water. The ozone layer absorbs most solar UV, protecting life.
  • X-rays ($\lambda\sim0.01$–$10\ \text{nm}$): produced when high-speed electrons are suddenly stopped by a metal target. They penetrate soft tissue and are used in medical imaging and in studying crystal structure (X-ray diffraction).
  • Gamma rays ($\lambda<0.01\ \text{nm}$, highest frequency): emitted by radioactive nuclei and in nuclear reactions. They are the most penetrating and energetic, used to treat cancer (radiotherapy) and to sterilise medical equipment.

A memory aid. In order of increasing frequency (decreasing wavelength): Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma. A common mnemonic is Roman Men Invented Very Unusual X-ray Guns. All these waves share the same speed $c$ in vacuum — only their wavelengths and frequencies (and hence photon energies and uses) differ.

Electromagnetic spectrum from radio to gamma raysRadioMicroInfraredVisibleUVX-rayGammalong lambdashort lambdalow fhigh fall travel at c in vacuum; c = f lambda
1
Worked Example
A microwave oven operates at a frequency of $2.45\ \text{GHz}$. Find the wavelength of the microwaves. ($c=3\times10^{8}\ \text{m/s}$.)
Solution
  1. Step 1: Use $\lambda=\frac{c}{f}$.
  2. Step 2: $\lambda=\frac{3\times10^{8}}{2.45\times10^{9}}$.
  3. Step 3: Compute: $\lambda\approx0.122\ \text{m}=12.2\ \text{cm}$.

Answer: $\lambda\approx12.2\ \text{cm}$.

2
Worked Example
Green light has a wavelength of $550\ \text{nm}$. Find its frequency. ($c=3\times10^{8}\ \text{m/s}$.)
Solution
  1. Step 1: Use $f=\frac{c}{\lambda}$ with $\lambda=550\times10^{-9}\ \text{m}$.
  2. Step 2: $f=\frac{3\times10^{8}}{550\times10^{-9}}$.
  3. Step 3: Compute: $f\approx5.45\times10^{14}\ \text{Hz}$.

Answer: $f\approx5.45\times10^{14}\ \text{Hz}$.

3
Worked Example
An X-ray has a frequency of $3\times10^{18}\ \text{Hz}$. Find its wavelength. ($c=3\times10^{8}\ \text{m/s}$.)
Solution
  1. Step 1: Use $\lambda=\frac{c}{f}$.
  2. Step 2: $\lambda=\frac{3\times10^{8}}{3\times10^{18}}$.
  3. Step 3: Compute: $\lambda=1\times10^{-10}\ \text{m}=0.1\ \text{nm}$.

Answer: $\lambda=0.1\ \text{nm}$ (typical X-ray wavelength).

4
Worked Example
Arrange the following in order of increasing frequency: visible light, radio waves, X-rays, infrared.
Solution
  1. Step 1: Recall the spectrum order by increasing frequency: radio, microwave, infrared, visible, UV, X-ray, gamma.
  2. Step 2: Pick out the four given bands in that order.
  3. Step 3: Radio < infrared < visible < X-rays.

Answer: Radio waves < Infrared < Visible light < X-rays.

5
Worked Example
An FM radio station broadcasts at $98\ \text{MHz}$. Find the wavelength. ($c=3\times10^{8}\ \text{m/s}$.)
Solution
  1. Step 1: Use $\lambda=\frac{c}{f}$ with $f=98\times10^{6}\ \text{Hz}$.
  2. Step 2: $\lambda=\frac{3\times10^{8}}{98\times10^{6}}$.
  3. Step 3: Compute: $\lambda\approx3.06\ \text{m}$.

Answer: $\lambda\approx3.06\ \text{m}$.

6
Worked Example
Which part of the EM spectrum is produced when high-speed electrons strike a metal target, and name one of its uses?
Solution
  1. Step 1: When fast electrons are suddenly decelerated by a metal target, high-energy short-wavelength radiation is emitted.
  2. Step 2: This radiation lies in the X-ray band ($\lambda\sim0.01$–$10\ \text{nm}$).
  3. Step 3: X-rays are used in medical imaging (bone radiographs) and in X-ray diffraction to study crystals.

Answer: X-rays; used in medical imaging (and crystal-structure analysis).

Key Points

  • The EM spectrum, in order of increasing frequency (decreasing wavelength), is: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
  • All EM waves travel at $c$ in vacuum and obey $c=f\lambda$; higher frequency means shorter wavelength and higher photon energy ($E=hf$).
  • Sources: radio — oscillating antenna currents; microwave — klystron/magnetron; IR — hot bodies; visible & UV — atoms and hot bodies; X-rays — fast electrons hitting metal; gamma — radioactive nuclei.
  • Key uses: radio/TV & communication; RADAR & microwave ovens; night vision & remotes (IR); vision (visible); sterilisation (UV); imaging & diffraction (X-ray); cancer therapy & sterilisation (gamma).
  • The bands overlap and have no sharp boundaries; they are classified by how they are produced and used.
Tap an option to check your answer0 / 4
Q1.Which of these has the longest wavelength?
Explanation: Radio waves have the longest wavelength (and lowest frequency) of the listed bands.
Q2.The waves used in a microwave oven and in RADAR are:
Explanation: Microwaves ($\lambda\sim1\ \text{mm}$ to $0.1\ \text{m}$) are used in RADAR, satellite communication and microwave ovens.
Q3.Radiation produced by radioactive nuclei and used to treat cancer is:
Explanation: Gamma rays come from nuclei, are the most energetic and penetrating, and are used in radiotherapy and sterilisation.
Q4.All electromagnetic waves in vacuum have the same:
Explanation: Every EM wave travels at $c=3\times10^{8}\ \text{m/s}$ in vacuum; only wavelength, frequency and photon energy differ.