One wave, many names
Every electromagnetic wave travels through vacuum at \(c = 3\times10^8\,\text{m/s}\). One wave differs from another only in its frequency \(f\), and so in its wavelength \(\lambda = c/f\). Arranged by frequency, the waves form the electromagnetic spectrum. It runs from radio waves kilometres long to gamma rays far smaller than an atom.
The spectrum is divided into seven bands. In order of rising frequency, and so of falling wavelength, they are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. The edges between the bands are conventions, not sharp lines, and neighbouring bands overlap. The table uses the edges of the NCERT textbook.
Visible light is a sliver of the spectrum in the figure above. It spans less than one power of ten, while the whole strip spans seventeen. The eye is blind to everything else. Each band needs its own detector: an antenna for radio, the skin for infrared, a photographic plate for X-rays.
(a) Find the frequency of microwaves of wavelength \(3\,\text{cm}\). Find the wavelength of FM radio at \(100\,\text{MHz}\), and the frequency of X-rays of wavelength \(1\,\text{nm}\). (b) To which band does each wavelength belong: \(500\,\text{nm}\), \(1\,\text{mm}\), \(10\,\text{pm}\), \(300\,\text{m}\)?
(a) \(f = c/\lambda = 3\times10^8/0.03 = 10^{10}\,\text{Hz}\). Then \(\lambda = c/f = 3\times10^8/10^8 = 3\,\text{m}\). Then \(f = 3\times10^8/10^{-9} = 3\times10^{17}\,\text{Hz}\).
(b) \(500\,\text{nm}\) is visible, green light. \(1\,\text{mm}\) is a microwave, on the border with the far infrared. \(10\,\text{pm}\) is a hard X-ray or a gamma ray; the two bands overlap there. \(300\,\text{m}\) is a radio wave of the medium-wave band.
Values used: \(c = 3\times10^8\,\text{m/s}\).
Across the spectrum the energy of each photon grows with the frequency. The chapter Photons and the Photoelectric Effect shows that light arrives in packets of energy \(hf\). So gamma rays carry the most energy in each packet, and radio waves the least. That is why gamma rays and X-rays can break molecules apart, while radio waves pass through us harmlessly.
Put these bands in order of rising frequency, lowest first.
A microwave oven works at \(2.45\,\text{GHz}\). What is the wavelength of its waves, in centimetres?
Which band has photons of the highest energy?
Where each band comes from, and what it does
Every band is made by accelerated charges, but the charges differ. Radio waves come from currents in antennas. Infrared and visible light come from the jiggling atoms of hot bodies and from electrons changing orbits. X-rays come from fast electrons stopped suddenly in metal. Gamma rays come from inside nuclei. The higher the frequency, the smaller and faster the moving charge must be.
A microwave oven works at \(2.45\,\text{GHz}\), a wavelength of \(12\,\text{cm}\). That is just past the NCERT edge of \(0.1\,\text{m}\), yet everyone calls it a microwave, which shows that the edges are only conventions. The water molecules in food turn to follow the field and heat the food. The water purifier in many Indian kitchens passes the water under an ultraviolet lamp to kill germs. The Bhabhatron, a cancer therapy machine built by BARC in Mumbai, uses the gamma rays of cobalt-60.
The atmosphere lets only some bands through. Visible light and most radio waves reach the ground. The ozone layer absorbs most of the Sun's ultraviolet, and the air absorbs X-rays and gamma rays from space. So X-ray and gamma-ray telescopes must fly above the atmosphere, on satellites such as India's AstroSat.
Which of these pairs of a band and its source are right?
In 1895, in Kolkata, Jagadish Chandra Bose made electromagnetic waves only a few millimetres long, far shorter than Hertz's. At a public demonstration his waves passed through walls and through a person's body to ring a distant bell. He built horn antennas, lenses and prisms for them, and a detector of crystal, which was among the first semiconductor devices. Microwave engineers still use his horn antenna.
Three ways across the country
High in the atmosphere, from about \(60\) to several hundred kilometres up, sunlight knocks electrons out of the air molecules. This layer of charged particles is the ionosphere. It turns back radio waves below about \(30\,\text{MHz}\) and lets higher frequencies pass through. That one fact decides how each kind of radio signal travels.
All India Radio's medium-wave stations broadcast between about \(530\) and \(1600\,\text{kHz}\). Their waves are \(190\) to \(570\,\text{m}\) long. By day they creep along the ground; by night they also bounce off the ionosphere and reach far away. Short waves, from about \(3\) to \(30\,\text{MHz}\), bounce between the ionosphere and the ground. In that way they cross oceans.
FM radio uses about \(88\) to \(108\,\text{MHz}\). Doordarshan's old transmitters used bands between about \(50\) and \(230\,\text{MHz}\). Mobile phones use frequencies of about \(900\) and \(1800\,\text{MHz}\) and higher. These waves pass through the ionosphere and are lost to space, so they must travel in a straight line of sight. That is why Doordarshan built tall towers, and why a mobile tower stands every few kilometres.
Satellites and spacecraft need waves that do pass the ionosphere. ISRO's ground station at Byalalu speaks to its spacecraft in the S-band, near \(2\,\text{GHz}\), and the X-band, near \(8\,\text{GHz}\). These are microwaves, \(15\) and \(3.75\,\text{cm}\) long.
A mobile phone works at \(900\,\text{MHz}\). What is the wavelength of its waves, in centimetres?
A station in Delhi is heard at night in a town \(1500\,\text{km}\) away, far beyond the horizon. Which kind of wave is it most likely using?
- Thinking different bands travel at different speeds in vacuum.Every electromagnetic wave travels at \(c\) in vacuum; only \(f\) and \(\lambda\) differ.
- Treating band edges as sharp.The edges are conventions; X-rays and gamma rays overlap, and so do microwaves and radio waves.
- Expecting high-frequency radio to bounce off the ionosphere.Only waves below about \(30\,\text{MHz}\) are turned back; FM, television, phones and microwaves pass through.