The electromagnetic spectrum — an overview — Physics

Before this

This leads to

Properties and uses of each EM wave type
The photoelectric effect · coming soon
The postulates of special relativity · coming soon

Seven names for one thing

Right now, without any equipment, you are detecting several kinds of wave. Your eyes detect light. The warmth of sunshine on your skin is your body detecting infrared. If a phone is near you, its antenna is detecting radio waves, and the phone is sending some back.

Light, infrared and radio sound like three different things. They are used in different ways, and they are detected in different ways. Add microwaves, ultraviolet, X-rays and gamma rays, and you have seven names that feel like seven different subjects.

They are one thing. All seven are the same kind of wave, travelling at the same speed. The only real difference between them is the frequency, and so the wavelength. This lecture shows what that one thing is, why its speed is fixed, and what changes as you move along the family from radio waves to gamma rays.

What an electromagnetic wave is

The waves you have met so far all move through a medium: sound through air, ripples through water, a pulse along a string. An electromagnetic wave is different. It is made of two fields that change together: an electric field and a magnetic field.

A field is a region where a force acts. Near a charged balloon there is an electric field, and near a magnet there is a magnetic field. In an electromagnetic wave, both fields keep changing in strength and direction, many times a second, as the wave passes. A changing electric field creates a magnetic field, and a changing magnetic field creates an electric field. So each field keeps the other going, and the pattern travels on by itself.

An electromagnetic wave. The electric field (solid) and the magnetic field (dashed) oscillate at right angles to each other and to the direction of travel. One wavelength λ is marked from crest to crest.

The figure shows three facts. The two fields are at right angles to each other. Both are at right angles to the direction of travel, so an electromagnetic wave is transverse. And the two fields rise and fall together, in phase.

Because the fields do not need anything to push against, an electromagnetic wave needs no medium. It crosses the empty space between the Sun and the Earth. Sound cannot do that.

This idea came from theory before anyone had made such a wave. In 1865, James Clerk Maxwell worked out from the laws of electricity and magnetism that changing fields should travel as a wave. He calculated the speed from measurements of electric and magnetic forces alone. It came out almost exactly equal to the measured speed of light. Maxwell concluded that light itself is an electromagnetic wave. Starting in 1887, Heinrich Hertz made electromagnetic waves with electric sparks and detected them across his laboratory. They were what we now call radio waves.

One speed for the whole family

In a vacuum, every electromagnetic wave travels at the same speed, the speed of light, written $c$ :

c \approx 3.00 \times 1 0^{8} m/s

The exact value is 299 792 458 m/s. Since 1983, the metre itself has been defined from this number, so it is now exact by definition. For calculations, 3.00 × 10⁸ m/s is close enough.

The wave equation from the wave properties lecture still holds: speed = frequency × wavelength. For an electromagnetic wave in a vacuum, the speed is always $c$ :

The wave equation for electromagnetic waves

$c = f λ$ , with $c \approx 3.00 \times 1 0^{8}$ m/s in a vacuum.

Because $c$ is fixed, frequency and wavelength are inversely proportional: double the frequency and the wavelength halves.

This is the key to the whole spectrum. Since the speed never changes, choosing a frequency fixes the wavelength, and choosing a wavelength fixes the frequency. You only ever need one of them to know where a wave sits in the family.

In a material such as glass or water, light travels more slowly. The refraction lecture used this: the refractive index is $n = c / v$ . In glass, the speed also depends slightly on the frequency, so violet light slows a little more than red. That is why a prism spreads white light into colours. In a vacuum there is no such spreading. Every frequency travels at exactly $c$ .

Predict — a race across space

A distant star explodes. It sends out a flash of gamma rays and a burst of radio waves at the same moment. Both cross empty space towards Earth. Which arrives first? Choose before you read on.

The question: a star sends out gamma rays and radio waves at the same moment, across empty space. Which arrives first? The answer: they arrive together, because every electromagnetic wave travels at $c$ in a vacuum. Higher photon energy does not mean higher speed, and neither does a longer wavelength or a brighter signal.

The most common wrong answer is "the gamma rays, because they have more energy". It feels natural, because faster objects do carry more kinetic energy. But a photon's energy is not energy of motion at different speeds. For electromagnetic waves, energy goes with frequency, and the speed is the same for all.

The spectrum, in order

Arrange all electromagnetic waves by frequency and you get the electromagnetic spectrum. From the lowest frequency (longest wavelength) to the highest frequency (shortest wavelength), the seven families are:

radio · microwaves · infrared · visible light · ultraviolet · X-rays · gamma rays

The electromagnetic spectrum, with approximate wavelength ranges. The scale is logarithmic: each step down the bar makes the wavelength 1000 times shorter. The edges between families are conventions, not sharp lines.

Look at the scale. Each labelled step on the bar makes the wavelength one thousand times shorter. The longest radio waves are kilometres long. The shortest gamma rays are shorter than the width of an atom. Visible light, the only part your eyes can detect, is a tiny slice in the middle, from about 700 nm (red) to about 400 nm (violet).

Do not learn the edges as exact numbers. They are agreements, and books draw them in slightly different places. The X-ray and gamma-ray ranges actually overlap. The real difference between them is where they come from. X-rays are made by fast electrons, and gamma rays by changes inside the nucleus of an atom.

To remember the order, make a sentence whose words start with R, M, I, V, U, X, G, such as "Raging Monkeys In Vans Use X-ray Glasses". A sentence you make up yourself is easier to remember. But the order also follows from one idea: the frequency rises at every step.

Explore — travel along the spectrum

Move the slider to change the wavelength. Watch the frequency and the energy of one photon change with it. Try the four presets, then find the point where photons start to be able to ionise atoms.

Wavelength:

Four points on the spectrum, worked out with $f = c / λ$ and $E = h f$ .

Wave and wavelength	Frequency	One photon
FM radio, 2.86 m	1.05 × 10⁸ Hz	≈ 6.96 × 10⁻²⁶ J
Microwave oven, ≈ 12.2 cm	2.45 × 10⁹ Hz	≈ 1.62 × 10⁻²⁴ J
Green light, 550 nm	≈ 5.45 × 10¹⁴ Hz	≈ 3.62 × 10⁻¹⁹ J
Medical X-ray, 0.1 nm	3.00 × 10¹⁸ Hz	≈ 1.99 × 10⁻¹⁵ J

Only the X-ray photon has more than the 2.18 × 10⁻¹⁸ J needed to ionise a hydrogen atom.

As the wavelength gets shorter by a factor of ten, the frequency gets larger by a factor of ten, and so does the energy of each photon. The next section explains what a photon is, and why that energy matters so much.

A first look at photons

Electromagnetic waves behave like waves when they travel: they reflect, refract, diffract and interfere. But when they are absorbed, the energy arrives in small packets. Each packet is called a photon. The energy of one photon depends only on the frequency:

E = h f

Here $h$ is the Planck constant, $h \approx 6.63 \times 1 0^{- 34}$ J s. The photoelectric effect lecture, later in the course, shows the experiment that forced physicists to accept photons. For now, take the result and see what follows.

Higher frequency means more energy in each photon. This is the reason the two ends of the spectrum behave so differently with living things. To ionise an atom, something must knock an electron out of it. For a hydrogen atom, that takes about 2.18 × 10⁻¹⁸ J. A photon is absorbed whole or not at all, so only a photon with at least that much energy can do it alone.

Radio, microwave, infrared and visible photons have far too little energy. X-ray and gamma-ray photons have far more. Ultraviolet is split: the shortest-wavelength part is ionising, and the rest is not, though it can still damage molecules. So X-rays, gamma rays and the shortest ultraviolet are called ionising radiation. Ionising radiation can break the molecules in living cells, including DNA, which is why it is used with great care.

Stop and think

A powerful radio transmitter sends out 100 000 J of energy every second. A dental X-ray machine delivers far less energy in total. Which one can ionise atoms in your body?

Show the answer

The X-ray machine. What matters for ionising is the energy of one photon, not the total. The transmitter's huge total energy is shared among an enormous number of tiny radio photons, about $1 0^{- 25}$ J each. None of them can knock out an electron, however many there are. Each X-ray photon carries about a thousand times more than a hydrogen atom needs. Brightness tells you how many photons arrive. Frequency tells you what each one can do.

Tuning in: a promise kept

The resonance lecture ended by saying that the electromagnetic spectrum includes the radio waves that every receiver must pick out by resonance. Here is how. Around you, at this moment, hundreds of radio signals pass by, each at its own frequency. The antenna picks up all of them. Inside the receiver, a circuit has a natural frequency that the listener can adjust. Only the signal at that frequency drives the circuit in step, so only that signal builds up a large current. Turning the dial changes the natural frequency, and a different station is selected. In the language of the resonance lecture, the circuit is lightly damped, so its peak is narrow and it is very selective.

Worked examples

Use $c = 3.00 \times 1 0^{8}$ m/s and $h = 6.63 \times 1 0^{- 34}$ J s.

Worked Example 1 — The wavelength of a radio station

A radio station broadcasts at 105 MHz. Find the wavelength of its signal.

Convert the prefix first: 105 MHz = 105 × 10⁶ Hz = 1.05 × 10⁸ Hz. Then rearrange $c = f λ$ :

λ = \frac{c}{f} = \frac{3.00 \times 1 0 ^{8}}{1.05 \times 1 0 ^{8}} \approx 2.86 m

Check: $1.05 \times 1 0^{8} \times 2.86 \approx 3.00 \times 1 0^{8}$ . ✓ FM radio waves are a few metres long.

Worked Example 2 — The frequency of green light

Find the frequency of green light of wavelength 550 nm.

Convert: 550 nm = 550 × 10⁻⁹ m = 5.50 × 10⁻⁷ m.

f = \frac{c}{λ} = \frac{3.00 \times 1 0 ^{8}}{5.50 \times 1 0 ^{- 7}} \approx 5.45 \times 1 0^{14} Hz

The electric field of green light changes direction about 545 million million times every second.

Check: visible frequencies lie between about $4.3 \times 1 0^{14}$ Hz (red) and $7.5 \times 1 0^{14}$ Hz (violet), and $5.45 \times 1 0^{14}$ is in between. ✓

Worked Example 3 — Two photons compared

Compare the energy of an X-ray photon of frequency $3.00 \times 1 0^{18}$ Hz with a radio photon of frequency $1.00 \times 1 0^{8}$ Hz.

E_{X} = h f = 6.63 \times 1 0^{- 34} \times 3.00 \times 1 0^{18} \approx 1.99 \times 1 0^{- 15} J

E_{radio} = 6.63 \times 1 0^{- 34} \times 1.00 \times 1 0^{8} = 6.63 \times 1 0^{- 26} J

The ratio is $1.99 \times 1 0^{- 15} \div 6.63 \times 1 0^{- 26} \approx 3.00 \times 1 0^{10}$ . One X-ray photon carries about thirty thousand million times the energy of one radio photon.

Check: because $E = h f$ , the ratio of energies must equal the ratio of frequencies: $3.00 \times 1 0^{18} \div 1.00 \times 1 0^{8} = 3.00 \times 1 0^{10}$ . ✓

Three traps

Trap 1 — "Higher energy travels faster"

All electromagnetic waves travel at $c$ in a vacuum. Frequency, wavelength and photon energy differ along the spectrum. Speed does not.

Trap 2 — Forgetting to convert the prefix

Most errors in $c = f λ$ come from units, not physics. Change MHz, GHz, nm and pm into Hz and m on their own line before you divide. Then ask whether the answer is sensible: radio waves are metres long, light is hundreds of nanometres.

Trap 3 — Calling all radiation dangerous, or all of it safe

"Radiation" covers the whole spectrum, including the light you read by. The question is whether one photon can ionise. Radio, microwaves, infrared and visible light cannot. X-rays and gamma rays can. Non-ionising waves can still harm you in other ways, for example by heating, but that is a different effect.

Try it yourself

Use $c = 3.00 \times 1 0^{8}$ m/s and $h = 6.63 \times 1 0^{- 34}$ J s. Work each one on paper first. Open a hint only when you are stuck.

Hydrogen gas in space gives out radio waves of frequency 1420 MHz. Radio astronomers use them to map the galaxy. Find their wavelength.

Hint 1
Use $λ = c / f$ .

Hint 2
1420 MHz = 1.42 × 10⁹ Hz.

Full answer
$λ = 3.00 \times 1 0^{8} \div 1.42 \times 1 0^{9} \approx 0.211$ m, about 21 cm. Astronomers call this "the 21 cm line". Check: $1.42 \times 1 0^{9} \times 0.211 \approx 3.00 \times 1 0^{8}$ . ✓
Find the energy of one photon of red light (700 nm) and of violet light (400 nm). How many times more energy does the violet photon carry?

Hint 1
Find each frequency with $f = c / λ$ , then use $E = h f$ .

Hint 2
For the ratio you do not need the energies: $E$ is proportional to $f$ , and $f$ is inversely proportional to $λ$ .

Full answer
Red: $f = 3.00 \times 1 0^{8} \div 7.00 \times 1 0^{- 7} \approx 4.29 \times 1 0^{14}$ Hz, so $E \approx 2.84 \times 1 0^{- 19}$ J. Violet: $f = 7.50 \times 1 0^{14}$ Hz, so $E \approx 4.97 \times 1 0^{- 19}$ J. Ratio: $700 \div 400 = 1.75$ . Check: $2.84 \times 1.75 \approx 4.97$ . ✓
A laser pointer gives out 1.0 mW of red light of wavelength 650 nm. How many photons does it send out each second?

Hint 1
1.0 mW means 1.0 × 10⁻³ J of energy every second.

Hint 2
Find the energy of one photon, then divide the energy per second by it.

Full answer
One photon: $E = h c / λ = 6.63 \times 1 0^{- 34} \times 3.00 \times 1 0^{8} \div 6.50 \times 1 0^{- 7} \approx 3.06 \times 1 0^{- 19}$ J. Number per second: $1.0 \times 1 0^{- 3} \div 3.06 \times 1 0^{- 19} \approx 3.3 \times 1 0^{15}$ . So even a weak beam carries about three thousand million million photons each second, which is why light looks smooth and continuous.
It takes 2.18 × 10⁻¹⁸ J to ionise a hydrogen atom. Find the longest wavelength of light that can do this with one photon. Which part of the spectrum is it in? Explain why a very bright red lamp cannot ionise hydrogen.

Hint 1
Put $E = h f$ and $f = c / λ$ together: $E = h c / λ$ . A longer wavelength means less energy per photon.

Hint 2
Rearrange to $λ = h c / E$ and put in the numbers.

Full answer
$λ = h c / E = 6.63 \times 1 0^{- 34} \times 3.00 \times 1 0^{8} \div 2.18 \times 1 0^{- 18} \approx 9.12 \times 1 0^{- 8}$ m, about 91 nm. That is in the ultraviolet, near its short-wavelength end. Any longer wavelength gives photons with too little energy. A red photon (700 nm, about $2.84 \times 1 0^{- 19}$ J) has less than one-seventh of the energy needed. A brighter lamp sends more red photons, but each one is still too weak, and an atom absorbs one photon at a time. Check: $h c / λ$ with $λ = 9.12 \times 1 0^{- 8}$ m gives back $2.18 \times 1 0^{- 18}$ J. ✓

The bigger idea

Maxwell's result did more than unite seven kinds of wave. His theory gives the speed of light from electric and magnetic constants alone, with no mention of who is measuring it. Experiments later showed that the speed of light really is the same for every observer, however fast they move. Einstein built special relativity on that fact. Note the difference: "every frequency travels at the same speed" is the fact of this lecture, while "every observer measures the same speed" is the fact that changed our ideas of space and time.

The spectrum is also how we learn about the universe. Radio telescopes map cold hydrogen gas. Infrared telescopes see through dust to newborn stars. X-ray and gamma-ray telescopes, above the atmosphere that absorbs those rays, watch the hottest and most violent places we know. Each part of the spectrum shows a different side of the same sky.

Key concepts in this lesson

An electromagnetic wave is a transverse wave of electric and magnetic fields at right angles to each other, and it needs no medium.
Every electromagnetic wave travels at $c \approx 3.00 \times 1 0^{8}$ m/s in a vacuum, so $c = f λ$ and frequency and wavelength are inversely proportional.
In order of increasing frequency, the spectrum is radio, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays, and the edges between them are conventions.
Electromagnetic energy is absorbed in photons, each with energy $E = h f$ , so higher frequency means more energy per photon.
Ionising radiation (X-rays, gamma rays and the shortest ultraviolet) has photons energetic enough to knock electrons out of atoms, and it is the energy per photon, not the brightness, that decides this.