S4.10.7 Chapter 7

The electromagnetic spectrum

In empty space, a radio wave and a gamma ray leave a star at the same moment. Which reaches the Earth first?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

A The gamma rays, because their frequency is higher.
You picked A. Read on. At the end, the chapter comes back to your guess.
B The radio waves, because their wavelength is longer.
You picked B. Read on. At the end, the chapter comes back to your guess.
C The radio waves, because they carry less energy.
You picked C. Read on. At the end, the chapter comes back to your guess.
D They arrive together.
You picked D. Read on. At the end, the chapter comes back to your guess.

By the end you can

List electromagnetic waves in order of wavelength and frequency
Give a use of each kind of electromagnetic wave

Light is not the only kind of wave that crosses empty space. Radio waves, the heat from a fire, and the X-rays at a hospital are all waves of the same family. They are electromagnetic waves.

An electromagnetic wave is a pattern of electric and magnetic fields that changes in step and moves through space. It is a transverse wave. It needs no medium, so it crosses a vacuum, and it carries energy.

All electromagnetic waves travel at the same speed in a vacuum: 3 × 10⁸ m/s, which is 300 000 km/s. Radio waves, light and gamma rays all travel at this speed. In air the speed is almost the same. In glass and water it is lower.

Every electromagnetic wave goes at the same speed in a vacuum.

What makes the waves differ is their frequency and wavelength. They are linked by the wave equation. For electromagnetic waves in a vacuum we write c for the speed: c = fλ. So the longer the wavelength, the lower the frequency.

The whole family is the electromagnetic spectrum. It has seven main kinds. In order of falling wavelength and rising frequency they are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays.

The electromagnetic spectrum. The edges are not sharp, and different books put them a little differently. Some books count microwaves as the short end of radio. X-rays and gamma rays overlap.

The wavelengths run from kilometres to far smaller than an atom. A nanometre, nm, is 10⁻⁹ m, a billionth of a metre. The frequencies run in the opposite order, from a few kilohertz to more than 10¹⁹ Hz. Visible light is only a thin slice.

One megahertz, MHz, is 1 000 000 Hz, which is 10⁶ Hz. FM radio stations are often near 100 MHz. Mobile phones and Wi-Fi use frequencies from several hundred to several thousand megahertz.

Worked example

An FM radio station broadcasts at 100 MHz. Find the wavelength of its waves.

Change the frequency to hertz: 100 MHz = 100 × 10⁶ = 1 × 10⁸ Hz.
Rearrange c = fλ to λ = c ÷ f.
λ = 3 × 10⁸ ÷ (1 × 10⁸) = 3 m.

Answer: 3 m

Worked example

Blue green light has a wavelength of 500 nm. Find its frequency. Use 1 nm = 10⁻⁹ m.

Change the wavelength to metres: 500 nm = 500 × 10⁻⁹ = 5 × 10⁻⁷ m.
Rearrange c = fλ to f = c ÷ λ.
f = 3 × 10⁸ ÷ (5 × 10⁻⁷) = 0.6 × 10¹⁵ Hz.
In standard form, f = 6 × 10¹⁴ Hz.

Answer: 6 × 10¹⁴ Hz

Now go through the seven kinds, starting at the long wave end. Each has uses that come from how it passes through things and how things absorb it.

Radio waves have the longest wavelengths. They carry radio and television, signals to aircraft and ships, and the signals between spacecraft and Earth. Some stars and galaxies also send them out, and radio telescopes collect them.

Microwaves are shorter. A microwave oven uses them because water in food absorbs them and heats up. Mobile phones, satellites, Wi-Fi and radar use them too. The oven is shielded so that the microwaves stay inside.

Infrared waves are given out by every warm object. Heaters, toasters and your own body give them out. A television remote control sends a code in infrared. Cameras that sense infrared make pictures of heat, and they work in the dark.

Visible light is the only part we see. It lets us see, and it is used in lamps, cameras, lasers and optical fibres. Its wavelengths run from about 700 nm for red light to about 400 nm for violet light.

Typical wavelengths of the colours, rounded. The colours blend into each other, and indigo lies between blue and violet.

Ultraviolet is a little shorter than violet light, and our eyes cannot see it. It is used to sterilise water and surfaces, and to show security marks on notes and cards. Lamps that make some materials glow use it. Sunlight contains it.

X-rays pass through soft parts of the body and are blocked more by bone. Doctors and dentists use them to take pictures of bones and teeth. Airports use them to look inside bags.

Gamma rays have the shortest wavelengths and are very penetrating. They are used to kill cancer cells, to sterilise medical equipment, and to follow a tracer through the body. They come from the nuclei of atoms.

A use for each kind of electromagnetic wave. The next chapter looks at calls and at health.

X-rays and gamma rays overlap in wavelength. They differ in where they come from. X-rays come from fast moving electrons, and gamma rays from the nuclei of atoms. For the same wavelength they behave in the same way.

Not to scale. A gamma ray wave is far shorter than a radio wave. Both go at the same speed.

Try it

Feel infrared from a warm mug

You need: a mug of hot water, hot from a kettle but not boiling, poured by an adult, a card or a book, your hand.

Be safe: Use water that is hot but not boiling, and let an adult pour it. Stand the mug where it cannot be knocked over, and keep your hand to the side, never over the steam.

Stand the mug on a table. Hold the back of your hand beside the mug, a few centimetres from the side, at the height of the mug. Do not touch it.
Notice the warmth on your hand.
Slide the card in between your hand and the mug. Notice what happens to the warmth.
Take the card away, and notice the warmth come back.

What you will see: The warmth you feel at the side of the mug comes mostly from infrared. Warm air rises, so it does not reach your hand at the side. The card is opaque to infrared, so it stops it.

If you cannot try it, this is what happens.

Try it

See a remote control with a phone camera

You need: a television remote control or similar remote, a phone with a camera, in a dim room.

Be safe: The light from a remote control is weak and safe. Never look at the Sun, a laser or a very bright lamp through a camera or in any other way.

Point the end of the remote at your eye from a metre away and press a button. Look for a light.
Now look at the end of the remote through the phone camera screen, and press a button again.
Try the front camera and the back camera.

What you will see: To your eye there is nothing to see, because the remote sends infrared. Many phone cameras can see infrared, and show a flickering light. Some cameras filter it out, so yours may show nothing.

If you cannot try it, this is what happens.

A wrong idea many people have

Gamma rays travel faster than radio waves, because they have more energy.

Why it feels right: In daily life, things with more energy often go faster, and gamma rays sound like the most powerful waves.

The test that breaks it: A burst of gamma rays from a far galaxy can also give a flash of light. Both travel for billions of years, yet the flash can arrive within seconds of the gamma rays. If gamma rays were faster, they would arrive long before the light.

What is true: Every electromagnetic wave travels at 3 × 10⁸ m/s in a vacuum. The energy of a gamma ray goes with its frequency, not its speed.

A wrong idea many people have

Radio waves are sound waves.

Why it feels right: We hear a radio, so it seems that the radio waves must be sound that travels through the air.

The test that breaks it: Sound cannot cross a vacuum, but radio waves cross space to reach spacecraft far from the Earth. Radio waves are electromagnetic. The radio set turns them back into sound.

What is true: Radio waves are electromagnetic waves, like light. They are transverse and need no medium. The loudspeaker makes the sound.

A wrong idea many people have

A wave with a longer wavelength has a higher frequency.

Why it feels right: Both are measures of how big the wave is, and big things can seem to go together.

The test that breaks it: Use c = fλ with c fixed. A radio wave of 3 m has f = 3 × 10⁸ ÷ 3 = 1 × 10⁸ Hz. A wave of 1 m has f = 3 × 10⁸ Hz. The shorter wave has the higher frequency.

What is true: For electromagnetic waves in a vacuum, f and λ go opposite ways. A longer wavelength means a lower frequency.

Key words

electromagnetic waves: transverse waves of electric and magnetic fields. They need no medium and go at 3 × 10⁸ m/s in a vacuum.
electromagnetic spectrum: the family of electromagnetic waves, in order of wavelength.
radio waves: the longest wavelength electromagnetic waves.
microwaves: electromagnetic waves a little shorter than radio waves, used in ovens, phones and Wi-Fi.
infrared: electromagnetic waves given out by warm things, just longer than red light.
ultraviolet: electromagnetic waves just shorter than violet light.
X-rays: short wavelength electromagnetic waves that pass through soft parts of the body.
gamma rays: the shortest wavelength electromagnetic waves. They come from the nuclei of atoms.

Back to your guess

The answer is D: They arrive together.

All electromagnetic waves travel at the same speed in a vacuum, about 3 × 10⁸ m/s. Radio waves and gamma rays differ in frequency and wavelength, not in speed. They arrive together.

Keep it

Copy this into your exercise book.

Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma: wavelength falls, frequency rises. All go at 3 × 10⁸ m/s in a vacuum. c = fλ.

Draw: Seven boxes in a row in order, with an arrow under them labelled frequency rises and one above labelled wavelength falls.