The electromagnetic spectrum
| English | Chinese | Pinyin |
|---|---|---|
| electromagnetic waves | 电磁波 | diàn cí bō |
| spectrum | 光谱 | guāng pǔ |
| vacuum | 真空 | zhēn kōng |
| microwave | 微波 | wēi bō |
| infrared | 红外线 | hóng wài xiàn |
| ultraviolet | 紫外线 | zǐ wài xiàn |
| gamma | 伽马 | gā mǎ |
All the same family
- Radio, the heat from a fire, sunburn, a hospital X-ray — all are electromagnetic waves 电磁波.
- They differ only in wavelength (and so frequency).
- One family, one spectrum 光谱.
What they share
- All EM waves are transverse.
- In a vacuum 真空 they all travel at the same speed, $c = 3.00 \times 10^{8}\ \dfrac{\text{m}}{\text{s}}$.
The electromagnetic spectrum
Slide across the spectrum
Radio waves, visible light and gamma rays are all the same wave — only the wavelength changes, and with it the frequency, photon energy and everyday use.
All electromagnetic waves are transverse.
Yes — every EM wave is transverse, and all travel at $c$ in a vacuum.
In a vacuum, which EM wave travels the fastest?
In a vacuum every EM wave travels at $c = 3.0 \times 10^{8}\ \dfrac{\text{m}}{\text{s}}$.
The spectrum in order
- From long to short wavelength: radio · microwave 微波 · infrared 红外线 · visible · ultraviolet 紫外线 · X-ray · gamma 伽马.
- As wavelength decreases, frequency increases.
Put these in order of increasing frequency (lowest first).
Frequency rises as wavelength falls: radio (longest) → microwave → visible → X-ray (much shorter).
Wavelengths and the link
- Learn the orders of magnitude: radio $> 10^{-1}\ \text{m}$; microwave $10^{-1}$ to $10^{-3}\ \text{m}$; infrared $10^{-3}$ to $7 \times 10^{-7}\ \text{m}$; visible $400$–$700\ \text{nm}$; ultraviolet $4 \times 10^{-7}$ to $10^{-8}\ \text{m}$; X-rays $10^{-8}$ to $10^{-13}\ \text{m}$; gamma below about $10^{-10}\ \text{m}$.
- Visible light is the narrow band $400$–$700\ \text{nm}$ — violet at the short end, red at the long end.
- Switch between $\lambda$ and $f$ with $c = f\lambda$.
Visible light has wavelengths of roughly:
About $400\ \text{nm}$ (violet) to $700\ \text{nm}$ (red) — a tiny slice of the whole spectrum.
A radio wave has wavelength $3.0\ \text{m}$. What is its frequency, in MHz? (Use $c = 3.0 \times 10^{8}\ \dfrac{\text{m}}{\text{s}}$.)
$f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^{8}}{3.0} = 1.0 \times 10^{8}\ \text{Hz} = 100\ \text{MHz}$.
Naming the region
- Exam questions give a wavelength or a frequency and ask which region. Convert to wavelength if needed, then place it on the ladder.
- Just below $400\ \text{nm}$ is ultraviolet; just above $700\ \text{nm}$ is infrared.
- X-rays and gamma rays overlap in wavelength — they are told apart by where they come from (X-rays from electrons, gamma from nuclei), so either name can be right in the overlap.
Worked example: which region, and what period?
(a) A laser emits waves of wavelength $8.1 \times 10^{-8}\ \text{m}$. (b) A satellite link uses $12\ \text{GHz}$. Name each region and find the period of the satellite waves in picoseconds.
- (a) $8.1 \times 10^{-8}\ \text{m} = 81\ \text{nm}$, which is below $400\ \text{nm}$ but above $10^{-8}\ \text{m}$: ultraviolet. Its frequency is $f = \dfrac{c}{\lambda} = \dfrac{3.00 \times 10^{8}}{8.1 \times 10^{-8}} = 3.7 \times 10^{15}\ \text{Hz}$.
- (b) $\lambda = \dfrac{c}{f} = \dfrac{3.00 \times 10^{8}}{12 \times 10^{9}} = 0.025\ \text{m}$: a few centimetres, so microwave.
- Period: $T = \dfrac{1}{f} = \dfrac{1}{12 \times 10^{9}} = 8.3 \times 10^{-11}\ \text{s} = 83\ \text{ps}$.
- Check: $1\ \text{ps} = 10^{-12}\ \text{s}$, so divide by $10^{-12}$ to convert — an answer of $0.083\ \text{ps}$ means the prefix was applied the wrong way.
An electromagnetic wave has a wavelength of $5.0 \times 10^{-9}\ \text{m}$. Which region of the spectrum is it in?
$5.0 \times 10^{-9}\ \text{m} = 5\ \text{nm}$ — shorter than $10^{-8}\ \text{m}$ (the bottom of the ultraviolet range), so X-rays.
Microwaves in a satellite link have a frequency of $12\ \text{GHz}$. What is their period, in ps?
$T = \dfrac{1}{f} = \dfrac{1}{12 \times 10^{9}} = 8.3 \times 10^{-11}\ \text{s}$, and $1\ \text{ps} = 10^{-12}\ \text{s}$, so $T = 83\ \text{ps}$.
$c = 3.00 \times 10^{8}\ \dfrac{\text{m}}{\text{s}}$ is the speed in a vacuum (air is close enough). In glass or water the wave slows down and its wavelength shortens, but its frequency stays the same — frequency is fixed by the source. And the order of the spectrum by frequency is the reverse of the order by wavelength.
When light passes from air into glass, its speed and wavelength both decrease but its ____ does not change.
Frequency is set by the source. Since $v = f\lambda$, a smaller $v$ with the same $f$ means a smaller $\lambda$.
Recognise them by their uses
- Radio: broadcasting. Microwave: phones, satellite links, ovens. Infrared: remote controls, thermal imaging, heating.
- Visible: seeing, fibre-optic signals. Ultraviolet: fluorescence, sterilising, sunburn.
- X-rays: medical imaging. Gamma: sterilising equipment, treating cancer.
You've got it
- all EM waves are transverse and travel at $c = 3.0 \times 10^{8}\ \dfrac{\text{m}}{\text{s}}$ in a vacuum
- order by wavelength: radio → microwave → IR → visible → UV → X-ray → gamma (frequency runs the other way)
- visible light is $400$–$700\ \text{nm}$; use $c = f\lambda$ and $T = \dfrac{1}{f}$ to name a region