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# 2. The Electromagnetic Spectrum

• • Wendell Potter and David Webb et al.
• Physics at UC Davis

# Frequency of Electromagnetic Waves

Our explanation for electromagnetic waves (an oscillating electric field creates an oscillating magnetic field, which in turn creates an oscillating electric field, and on and on...), suggests a way for creating electromagnetic waves. Taking charges (the source of electric fields) and oscillating them up and down should get the whole process started! The frequency with which charges oscillate up and down sets the frequency of the electromagnetic waves produced, like similar to how the frequency of the wave on a string is set by a person at the end of the string, oscillating it. For electromagnetic waves, like all the other waves we have dealt with, the frequency is determined by the source.

## Different Kinds of Light Occur at Different Frequencies

This seems a little odd, however. Most of us have been zapped by a sweater we were wearing at some point in our lives, due to the build-up of charge on it. By swaying backwards and forwards we were making those charges oscillate, but we did not seem to suddenly create light! In Physics 7A we learned that atoms at temperatures higher than absolute zero oscillated, and these atoms are made up of electrons and protons yet most objects do not appear to glow in the dark. In fact, it seems if light is the oscillation of charge it should be very difficult to find darkness at all!

In fact we do give off electromagnetic radiation as we sway back and forth, and objects in dark rooms do glow. The light created in these circumstances is not visible light. For visible light the charges have to be oscillating back-and-forth around 1014 times per second! For objects at room temperature (around 300K) the oscillating atoms give off electromagnetic light at roughly 1013 Hz. This light is called infrared, because its frequency is closest to red in visible light. While people cannot see this light, some animals can and we can make cameras that can detect this light. For example night-vision goggle operate by detecting infrared light. If we want an object to give off a significant amount of visible light, we must make its atoms vibrate faster. As we learned in 7A, one way to do this is to increase the temperature. A wood fire, for example, burns at around 1500 Kelvin. While most of the light is let off in the infrared, enough is let off in the visible that the flames can be seen. The night sky that we see is full of electromagnetic radiation with a frequency of $$3 \times 10^{11} \text{ Hz}$$ which we cannot see directly. Just like infrared light, we have devices that can detect this light, and studying it gives us further insights into the origin of the universe.

## Low-Frequency, Long-Wavelength Light

Different frequencies of electromagnetic waves can be used for very different purposes. At the lowest frequencies, or at the longest wavelengths (because $$\lambda = v_{wave}/f$$), we have radio waves. This is a broad range of frequencies lower than roughly $$10^9 \text{ Hz}$$. Most of our television and radio programs are broadcast at this frequency. At higher frequencies, there are microwaves, which are used in RADAR and microwave ovens. Above $$10^{11} \text{ Hz}$$ we have the infrared, which is the light given off most strongly by objects in the temperature between 3 K and 5000 K. The “narrow” range between $$4 \times 10^{14} \text{ Hz}$$ and $$7.5 \times 10^{14} \text{ Hz}$$ corresponds the spectrum of visible light. In this range, different frequencies correspond to different colors of light that we can see.

## High-Frequency, Short-Wavelength Light

At even higher frequencies we find ultraviolet light (UV). This region covers frequencies from $$8.6 \times 10^{14}$$ to $$3.75 \times 10^{16} \text{ Hz}$$ and is further broken down into the categories UVA, UVB, UVC, Far UV, and Extreme UV. UV light can be damaging to the skin (UV light given off by the sun is the cause of sunburns). The risk of damage increases with the frequency of the UV light. The sun emits radiation in the UVA, UVB, and UVC sub-bands, however almost all of the UVB and UVC radiation from the sun is absorbed in the Earth’s ozone layer in the upper atmosphere.

The use of the term X-ray varies a little. Some people take the definition of an x-ray as the manner in which the light is produced, such as an atomic transition. Others take "x-ray" to describe a frequency range, like our previous definitions (this latter set tend to be astronomers talking about “x-ray telescopes”). The definition is actually fairly irrelevant, except where extra clarity is needed. Whichever definition we use, it is accepted that x-rays have very high frequencies (greater than $$3.75 \times 10^{16} \text{ Hz}$$) and are energetic enough to pass through tissue. Hence we use x-ray machines to image the bones.

Gamma rays are produced in nuclear transitions, and refer to frequencies higher than 1022 Hz. Because of the quantized nature of light, when discussing gamma rays it's usually more convenient to talk about individual photons than to talk about a continuous wave. For this reason the term "gamma particles" is sometimes used interchangeably with "gamma rays."

## The Full Spectrum

Because different types of light occur along a range of frequencies, we can ascribe each type of light to a section on what's called the electromagnetic spectrum. A diagram of the spectrum is displayed below, with the frequencies appropriately labeled. It's worth noting that the partitions between different types of light are based on how people experience light. We could section off the spectrum into any arbitrary pieces if we wanted to.

## Useful Approximations

Table 1 gives typical approximations for the order of magnitudes of wavelengths from each part of the spectrum. Because wavelength depends on medium, note that he wavelengths presented here are only valid in a vacuum.

Table 1: Order of magnitudes of Spectral Regions
Piece of the Spectrum Typical Wavelength Size in Vacuum
Shortwave Radio $$\lambda \sim$$ Buildings
AM Radio, FM Radio, TV Broadcast $$\lambda \sim$$ People
Microwaves $$\lambda \sim$$ Insects
Infrared $$\lambda \sim$$ Fleas
Visible $$\lambda \sim$$ Cells
Ultraviolet $$\lambda \sim$$ Molecules
X-rays $$\lambda \sim$$ Atoms
$$\gamma$$-rays $$\lambda \sim$$ Atomic Nuclei

Table 2 below gives the frequencies and wavelengths of different sections of the visible light spectrum (different colors). The wavelengths presented here are only correct in vacuum, but the frequencies are correct in any medium (because frequency is set by the source of the light).

Table 2:
Color $$\lambda$$ range (nm) $$\lambda$$ midpoint (nm) Frequency (1014 ​​​​​​​Hz)
Red 620-750 700 4.3
Orange 590-620 600 5.0
Yellow 570-590 580 5.1
Green 495-570 540 5.5
Blue 450-495 470 6.4
Violet 380-450 400 7.5

## Fire and Chemistry

We remarked that a typical wood fire has a temperature around 1500 K. Emitted frequencies of light at this temperature peak in the infrared range, with some light emitted in the red visible range as well. At low temperature, objects that give off light because of thermal energy (e.g. hot metal) glow a dull red. As the temperature increases, the peak of emitted frequencies becomes higher, and some blue light starts to appear. The dull red becomes an orange as higher frequencies become emitted, and eventually the orange becomes white, which contains many frequencies. The range of frequencies emitted also increases as the temperature goes up, so the light always contains some amount of red in it.. We do not observe objects so hot that only glow blue – there is always some contamination from the lower (red) part of the spectrum.

When you study chemistry, you will observe that burning different metals (e.g. in a Bunsen burner) produces different colors of flames. If you have not seen this in chemistry you have probably seen it in a fireworks show – various chemicals in the fireworks give off different colors when they oxidize. This seems to contradict our previous statement that hotter objects glow at different frequencies, but retain red in their emitted light. However, the light we mentioned here is not really thermal light. Thermal light is due to the random motion of charges and the equipartition of energy. The light given off by fireworks is different colors because oxidizing pure substances gives off light whose frequency is determined by the energy levels available to electrons in the metal. The effect is quantum mechanical, not thermal. We discuss this effect more when we talk about photons and the energy spectrum available to a system.