Sources, detectors and uses

The same question for every band

For each part of the spectrum we ask four questions. How is the wave made? How do we detect it? What is it used for? What does it do to us? The answers explain why the bands were found one by one, over a hundred years.

Radio waves

• Source. Charges accelerated to and fro in an antenna, driven by an oscillating circuit.
• Detector. A second antenna and a circuit tuned to the frequency, as in a radio receiver.
• Uses. Radio and television broadcasts, mobile phones, wireless networks.
• Effect. Harmless at ordinary power.

Microwaves

• Source. Electron tubes such as the klystron and the magnetron, and the Gunn diode, which make waves of a few gigahertz and above.
• Detector. Point-contact diodes and a horn that gathers the wave.
• Uses. Radar, satellite links, long-distance telephone links, and the microwave oven. Radar finds the distance of a target from the time of an echo, $d = ct/2$. The change of frequency of the echo (the Doppler shift) gives the speed of the target, as in a police speed gun.
• Effect. Water molecules absorb microwaves and the water warms up. This is how an oven cooks. NCERT says that the frequency is chosen to match a resonance of water. In fact water absorbs over a wide range of frequencies, and $2.45$ GHz is a band that engineers may use. At this frequency the waves go a few centimetres into food. Metal reflects microwaves, so an oven has a metal box and a metal mesh in the door.

Infrared

• Source. Every body above absolute zero sends out infrared, because its atoms and molecules vibrate. A warmer body sends out more of it.
• Detector. Thermopiles and bolometers, which warm up and change a reading. Special photographic films. Semiconductor detectors in night-vision and thermal cameras.
• Uses. Heat lamps, remote controls (an infrared LED), thermal cameras, physiotherapy, and drying paint.
• Effect. It warms what absorbs it. It is called "heat radiation" because most thermal radiation is in this band and water absorbs it well. But waves of every band carry energy.

Visible light

• Source. Electrons in atoms and molecules jump between energy levels. Very hot bodies, such as the Sun and a lamp filament, also glow.
• Detector. The eye, photographic film, photocells and the sensor of a camera.
• Uses. Sight, photography, photosynthesis, optical fibres.

Ultraviolet

• Source. Atoms and molecules in electric discharges, mercury lamps, welding arcs, and very hot bodies such as the Sun.
• Detector. Photocells and photographic film, and materials that glow when ultraviolet falls on them (fluorescence).
• Uses. Sterilising water and surgical tools, checking banknotes, eye surgery with a laser, making vitamin D in the skin.
• Effect. Too much of it burns the skin and harms the eyes. The ozone layer takes in most of the harmful part.

X-rays

• Source. An X-ray tube. Electrons are speeded up by a high voltage $V$ and hit a metal target. Two kinds of X-rays come out. A smooth range comes from the electrons slowing down. Sharp lines come from atoms of the target whose inner electrons were knocked out. The electron cannot give a photon more than its own energy $eV$, so there is a shortest wavelength:

• Detector. Photographic film, fluorescent screens, Geiger counters and semiconductor detectors.
• Uses. Medical pictures of bones, CT scans, airport security, and the study of crystals.
• Effect. They ionise atoms and can damage cells, so doses must be small.

Gamma rays

• Source. Nuclei, in radioactive decay and in nuclear reactions.
• Detector. Geiger counters, scintillation counters and ionisation chambers.
• Uses. Treating cancer, sterilising food and medical supplies, and finding flaws in metal.
• Effect. Like X-rays, they can damage cells.

Hot bodies and Wien's law

Every hot body sends out a continuous spread of wavelengths. The strongest part is at the wavelength given by Wien's displacement law:

Double the temperature and the peak moves to half the wavelength.

Set the temperature to $2900$ K. The peak is beyond the red end of the visible band. So a lamp filament sends out most of its power as infrared. Raise the temperature and watch the peak move into the visible band.

A worked example. Find where a lamp filament at $2900$ K, the Sun at $5772$ K and the Earth at $288$ K shine most strongly.

1. The filament. $\lambda_{peak} = \dfrac{2.898 \times 10^{-3}\ \text{m K}}{2900\ \text{K}} = 999$ nm. This is infrared, since it is above $700$ nm.
2. The Sun. $\lambda_{peak} = \dfrac{2.898 \times 10^{-3}\ \text{m K}}{5772\ \text{K}} = 502$ nm. This is in the middle of the visible band. Our eyes match the light of our star.
3. The Earth. $\lambda_{peak} = \dfrac{2.898 \times 10^{-3}\ \text{m K}}{288\ \text{K}} = 10.1\ \mu\text{m}$. This is infrared.

The shortest X-ray. An X-ray tube works at $40$ kV. The electrons have an energy of $40$ keV, so $\lambda_{\min} = \dfrac{1240\ \text{eV nm}}{40000\ \text{eV}} = 31.0$ pm. A higher voltage gives a shorter wavelength, and a harder X-ray.

Other books. A-Level and IB give Wien's law in the same form. They also use $b = 2.90 \times 10^{-3}$ m K.

Practise with new numbers

Try it in Python

The program uses Wien's law for six hot bodies, from the Earth's surface to a hot blue star. It prints the wavelength of the peak and its band.

Common mistakes

• Calling infrared "heat" and thinking other waves carry none. Every band carries energy. Infrared is only the band that most warm bodies send out and that water absorbs best.
• Mixing up the two parts of an X-ray spectrum. The smooth part and its sharp shortest wavelength depend on the voltage. The sharp lines depend on the target metal.
• Using the wrong half of the echo path. A radar echo goes there and back, so $d = ct/2$.
• Thinking a bright star is hot. Wien's law ties the colour to the temperature, not the brightness.

Remember these

• Radio: accelerated charges. Microwave: tubes. Infrared: hot bodies. Visible and UV: electrons in atoms. X-rays: fast electrons stopped in metal. Gamma: nuclei.
• Wien's law: $\lambda_{peak}T = 2.898 \times 10^{-3}$ m K.
• X-ray tube: $\lambda_{\min} = hc/eV$.
• Radar: $d = ct/2$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Which band of the spectrum is sent out by every warm body, and which is made by an X-ray tube's slowed electrons?

2. A body at $4000$ K shines most strongly at what wavelength?

3. An X-ray tube works at $25$ kV. What is the shortest wavelength of its X-rays?

4. Why does an oven with a metal box and a mesh door not let microwaves out into the kitchen?

References

• OpenStax, University Physics Volume 2, Chapter 16 (Electromagnetic Waves): the electromagnetic spectrum.
• NCERT Physics Class 12, Chapter 8 (Electromagnetic Waves): the table of sources, detectors and uses.
• OpenStax, University Physics Volume 3, the chapter on Atomic Structure: atomic spectra and X-rays.