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# 10.8 Properties of Electromagnetic Radiation

Static Electricity: Contact with the slide has left her hair positively charged so that the individual hairs repel one another. The hair may also be attracted to the negatively charged slide surface. Click here for original source URL.

The magnetic field of a bar magnet revealed by iron filings on paper. Click here for original source URL.

The nature of electromagnetic radiation can be confusing. On the one hand, it acts like a stream of particles carrying energy from one place to another. On the other hand, it acts a stream of waves by displaying the properties of diffraction and interference. If electromagnetic radiation acts like a wave, what is doing the waving? In physics, the word field describes something that extends through space, having a magnitude or value at every point. Fields can exert influence on a distant object. For example, because of their "field" properties, magnets can attract or repel each other without any apparent connection; static electricity too exerts an attraction across space. The gravity "field" holds the Earth in its orbit around the Sun across the vacuum of space.

Luckily, we can use simple mathematics to describe the properties of electromagnetic radiation without worrying about whether we should visualize it as a wave or as a particle. In terms of waves, electromagnetic radiation is described by its wavelength. The velocity, or speed, of all electromagnetic waves including light is about 300,000 kilometers per second, written as the symbol c.

The velocity is the product of the wavelength and the frequency. Equivalently, there is an inverse relationship between the wavelength and the frequency of the wave. In equation form

wavelength x frequency = c

We can look at some examples. Red light has a wavelength of 7 x 10-7 meters, hundreds of times smaller than the thickness of a human hair. Expressed in meters per second, the speed of light is 3 x 108. So the frequency of a red light wave is c / wavelength = 3 x 108 / 7 x 10-7 = 4 x 1014 cycles per second (or Hertz). This is an extremely rapid wave or oscillation!

Diagram of the Electromagnetic Spectrum. Click here for original source URL.

Your favorite radio station might have a frequency of 400 MHz, which is 4 x 108Hertz. These radio waves have a wavelength of c / frequency = 3 x 108 / 4 x 108 = 0.75 meters. This is a wave big enough for you to easily imagine (but not see, because your eyes cannot detect radio waves). Since there is a simple relationship between wavelength and frequency, you can specify an electromagnetic wave by either quantity. Radio engineers tend to characterize waves by their frequency (radio stations are listed in units of cycles per second or Hertz). Optical astronomers, on the other hand, tend to refer to waves by their wavelength.

In the particle description of radiation, it is the properties of photons that are important. The energy of a photon is proportional to the frequency of the radiation. Higher frequencies or shorter wavelengths carry more energy than lower frequencies or longer wavelengths. It makes sense that shorter waves carry more energy than long waves. We know that it is the ultraviolet radiation from the Sun that can damage our skin with sunburn, and the highest energy gamma rays can cause even more tissue and cellular damage. On the other hand, the air is full of low energy radio waves, which apparently do us no harm! In equation form

energy = h x frequency

Max Planck. Click here for original source URL.

If the frequency is given in units of cycles per second or Hertz, the energy comes out in units of Joules. The number h is Planck's constant, named after a German physicist who was one of the first winners of the Nobel Prize in physics. Its value is 6.63 x 10-34 Joule seconds, a fantastically small number!

Light and all other forms of electromagnetic radiation come in tiny bundles of energy called photons. This minimum unit of radiation or energy is called a quantum (plural: quanta) and it refers to a fundamental "graininess" in the physical world. Just as all matter is made up of indivisible particles in the atom, such as electrons, so radiation is also made up of indivisible units of energy called quanta. The discovery that light is distributed in discrete, or quantized units, was one of the major discoveries in physics in the last century.

How small is the quantum of energy? Let's look at a single photon of white light. It has a wavelength of 5 x 10-7 meters, so it has a frequency of c / wavelength = 3 x 108 / 5 x 10-7 = 6 x 1014 Hertz. The energy is therefore 6 x 1014 x 6.6 x 10-34 = 4 x 10-19 Joules. The energy of a single visible photon is tiny indeed, as indicated by the extremely small value of Planck's constant. For example, using the fact that a Watt of power is one Joule of energy per second, a 100 Watt light bulb emits 100 / 4 x 10-19 = 2.5 x 1020 photons per second. This is a rate of 250 billion billion photons per second! In other words, the "graininess" of light and matter is so fine that we cannot see it in the everyday world.