5.1 The electromagnetic spectrum — Learn

Prerequisites: Section 4.1, especially transverse waves, wavelength, frequency and the wave equation $v = f\lambda$ ; writing numbers in standard form; the prefixes kilo, mega, giga, micro and nano.

By the end of this section you can: describe the electromagnetic spectrum; list its groups in order of wavelength and frequency; and use the wave equation to find the wavelength or the frequency of any electromagnetic wave.

1. What electromagnetic waves are

An electromagnetic wave is a transverse wave. It is made of a vibrating electric field and a vibrating magnetic field. The two fields vibrate at right angles to each other and at right angles to the direction the wave travels.

An electromagnetic wave carries energy from a source to an absorber. It does not need a medium, so it can travel through a vacuum. This is how energy reaches the Earth from the Sun.

There are seven groups of electromagnetic waves. Together they form the electromagnetic spectrum. The spectrum is continuous, so there are no gaps between the groups.

2. The order of the spectrum

The groups are usually listed from the longest wavelength to the shortest. The same order goes from the lowest frequency to the highest.

Group	Typical wavelength	Typical frequency
Radio waves	longer than 1 m	below 3 × 10⁸ Hz
Microwaves	1 mm to 1 m	3 × 10⁸ Hz to 3 × 10¹¹ Hz
Infrared	700 nm to 1 mm	3 × 10¹¹ Hz to 4 × 10¹⁴ Hz
Visible light	400 nm to 700 nm	4 × 10¹⁴ Hz to 7.5 × 10¹⁴ Hz
Ultraviolet	10 nm to 400 nm	7.5 × 10¹⁴ Hz to 3 × 10¹⁶ Hz
X-rays	0.01 nm to 10 nm	3 × 10¹⁶ Hz to 3 × 10¹⁹ Hz
Gamma rays	shorter than 0.01 nm	above 3 × 10¹⁹ Hz

Every group travels at the same speed in a vacuum. That speed is $c = 3.0 \times 10^8\,\text{m/s}$ . The groups differ in wavelength and in frequency, not in speed.

Because the speed is the same for every group, wavelength and frequency are linked. A wave with a longer wavelength must have a lower frequency. A wave with a shorter wavelength must have a higher frequency.

3. Using the wave equation

The wave equation from Section 4.1 works for every electromagnetic wave:

v = f\lambda

where $v$ is the speed in metres per second, $f$ is the frequency in hertz and $\lambda$ is the wavelength in metres. For electromagnetic waves in a vacuum, $v$ is always $3.0 \times 10^8\,\text{m/s}$ .

Worked example 1. A radio signal has a frequency of 150 MHz. Calculate its wavelength.

\begin{aligned} \lambda &= \frac{c}{f} \\ &= \frac{3.0 \times 10^8}{150 \times 10^6} \\ &= \frac{3.0 \times 10^8}{1.5 \times 10^8} \\ &= 2.0\,\text{m} \end{aligned}

The answer is 2.0 m. A radio wave with this wavelength is a little longer than a person is tall.

Worked example 2. Infrared radiation has a wavelength of 10 μm. Calculate its frequency.

\begin{aligned} f &= \frac{c}{\lambda} \\ &= \frac{3.0 \times 10^8}{10 \times 10^{-6}} \\ &= \frac{3.0 \times 10^8}{1.0 \times 10^{-5}} \\ &= 3.0 \times 10^{13}\,\text{Hz} \end{aligned}

Worked example 3. Green light has a wavelength of 600 nm. Calculate its frequency.

\begin{aligned} f &= \frac{c}{\lambda} \\ &= \frac{3.0 \times 10^8}{600 \times 10^{-9}} \\ &= \frac{3.0 \times 10^8}{6.0 \times 10^{-7}} \\ &= 5.0 \times 10^{14}\,\text{Hz} \end{aligned}

Compare this with Worked example 2. The green light has a much shorter wavelength and a much higher frequency than the infrared radiation.

Worked example 4. An X-ray has a wavelength of $1.0 \times 10^{-10}\,\text{m}$ . Calculate its frequency.

\begin{aligned} f &= \frac{c}{\lambda} \\ &= \frac{3.0 \times 10^8}{1.0 \times 10^{-10}} \\ &= 3.0 \times 10^{18}\,\text{Hz} \end{aligned}

An X-ray has a higher frequency than every other group except gamma rays.

4. Changing the wavelength and the frequency

The figure lets you move along the electromagnetic spectrum.

Predict first. Do not move the slider yet. Write down your answers.

As the frequency increases, does the wavelength get longer or shorter?
Which group has the longest wavelength: radio waves or gamma rays?
Roughly where in the spectrum does visible light sit?

Test. Move the frequency slider from the left to the right. Watch the wavelength and the name of the group. Stop when the name says "visible".

Explain. The speed of every electromagnetic wave is the same. Why does a higher frequency mean a shorter wavelength? Write your answer in two or three sentences.

Watch out. Wavelength and frequency are not the same thing, and they move in opposite directions. When the wavelength goes up, the frequency goes down. Also take care with the prefixes: 150 MHz is $1.5 \times 10^8\,\text{Hz}$ , and 600 nm is $6.0 \times 10^{-7}\,\text{m}$ . Re-check by asking whether your wavelength should be bigger or smaller than a metre.

5. Progress check

Return to the chapter problem. The radio telescope receives a signal with a frequency of 150 MHz. Without a calculator, decide whether the wavelength is closer to 2 cm, 2 m or 200 m. Then work it out with the wave equation.

You should now be able to

describe an electromagnetic wave as a transverse wave that carries energy;
list the seven groups of the spectrum in order of wavelength and frequency;
state that all electromagnetic waves travel at $3.0 \times 10^8\,\text{m/s}$ in a vacuum;
use $v = f\lambda$ to find the wavelength or the frequency of an electromagnetic wave;
explain the link between wavelength and frequency.