Learning Objectives
By the end of this module, you will be able to:
- Describe light with its frequency and wavelength.
- Describe light as a particle of energy.
Our last “picture” of the atom consisted of a nucleus containing protons and neutrons (constituting most of the atom’s mass), surrounded by a sea of electrons. The limitations of this model are that it doesn’t show how the electrons are arranged or how they move. It turns out that this electronic structure is the primary factor controlling how an atom behaves.
To get a more complete view of the atom, we need more experimental evidence and interpretation. One of the main ways to investigate electrons in atoms is to use light with two techniques; 1) by shining a light on the atoms and seeing what happens to the light (absorption spectroscopy), and 2) by heating the atoms and seeing what kind of light is given off (emission spectroscopy). Clearly, we will need to start with an understanding of the nature of light. We will then move on to describe and interpret experiments with light that give us our understanding of what electrons in atoms are doing. Finally, we see how the properties of electrons are related to the way the atoms behave.
What we know as light is more properly called electromagnetic radiation. We know from experiments that light acts as a wave. As such, it can be described as having a frequency and a wavelength.
The wavelength of light is the distance between corresponding points in two adjacent light cycles. Wavelength is typically represented by λ, the lowercase Greek letter lambda, and has units of length (meters, centimeters, etc.). Figure 1 shows how wavelength is defined.
The frequency of light is the number of cycles of light that pass a given point in one second. Frequency is represented by ν, the lowercase Greek letter nu, and has units of per second, written as s−1 and sometimes called a hertz (Hz). The amplitude (a) corresponds to the magnitude of the wave’s displacement and so, in Figure 2, this corresponds to one-half the height between the peaks and troughs. The amplitude is related to the intensity of the wave, which for light is the brightness, and for sound is the loudness.
Light acts as a wave and can be described by a wavelength λ and a frequency ν.
One property of waves is that their speed is equal to their wavelength times their frequency. That means we have
speed = λν
m/s = m x s-1
For light, however, speed is actually a universal constant when light is traveling through a vacuum (or, to a very good approximation, air). The measured speed of light (c) in a vacuum is 2.9979 × 108 m/s, or about 3.00 × 108 m/s. Thus, we have
c = λν
m/s = m x s-1
Because the speed of light is a constant, the wavelength and the frequency of light are related to each other: as one increases, the other decreases and vice versa. We can use this equation to calculate what one property of light has to be when given the other property.
Light also behaves like a package of energy. It turns out that for light, the energy of the “package” of energy is proportional to its frequency. (For most waves, energy is proportional to wave amplitude, or the height of the wave.) The mathematical equation that relates the energy (E) of light to its frequency is
E = hν
where ν is the frequency of the light, and h is a constant called Planck’s constant. Its value is 6.626 × 10−34 J·s — a very small number that is another fundamental constant of our universe, like the speed of light. The units on Planck’s constant may look unusual, but these units are required so that the algebra works out.
Because a light wave behaves like a little particle of energy, light waves have a particle-type name: the photon. It is not uncommon to hear light described as photons.
Wavelengths, frequencies, and energies of light span a wide range; the entire range of possible values for light is called the electromagnetic spectrum. We are mostly familiar with visible light, which is light having a wavelength range between about 400 nm and 700 nm. Light can have much longer and much shorter wavelengths than this, with corresponding variations in frequency and energy. Figure 3 “The Electromagnetic Spectrum” shows the entire electromagnetic spectrum and how certain regions of the spectrum are labelled. You may already be familiar with some of these regions; they are all light—with different frequencies, wavelengths, and energies.
Technology and the Electromagnetic Spectrum
Figure 4 shows the electromagnetic spectrum, the range of all types of electromagnetic radiation. Each of the various colors of visible light has specific frequencies and wavelengths associated with them, and you can see that visible light makes up only a small portion of the electromagnetic spectrum.
Because the technologies developed to work in various parts of the electromagnetic spectrum are different, for reasons of convenience and historical legacies, different units are typically used for different parts of the spectrum. For example, radio waves are usually specified as frequencies (typically in units of MHz), while the visible region is usually specified in wavelengths (typically in units of nm or angstroms).
Wireless Communication
Many valuable technologies operate in the radio (3 kHz-300 GHz) frequency region of the electromagnetic spectrum (Figure 5).
At the low frequency (low energy, long wavelength) end of this region are AM (amplitude modulation) radio signals (540-2830 kHz) that can travel long distances. FM (frequency modulation) radio signals are used at higher frequencies (87.5-108.0 MHz). In AM radio, the information is transmitted by varying the amplitude of the wave (Figure 6). In FM radio, by contrast, the amplitude is constant and the instantaneous frequency varies.
Other technologies also operate in the radio-wave portion of the electromagnetic spectrum. For example, 4G cellular telephone signals are approximately 880 MHz, while Global Positioning System (GPS) signals operate at 1.228 and 1.575 GHz, local area wireless technology (Wi-Fi) networks operate at 2.4 to 5 GHz, and highway toll sensors operate at 5.8 GHz. The frequencies associated with these applications are convenient because such waves tend not to be absorbed much by common building materials.
Key Concepts and Summary
Key Equations
c = λν
[latex]E = h\nu = \frac{hc}{\lambda}[/latex], where h = 6.626 × 10−34 J·s
Glossary
amplitude: extent of the displacement caused by a wave (for sinusoidal waves, it is one-half the difference from the peak height to the trough depth, and the intensity is proportional to the square of the amplitude)
continuous spectrum: electromagnetic radiation given off in an unbroken series of wavelengths (e.g., white light from the sun)
electromagnetic radiation: energy transmitted by waves that have an electric-field component and a magnetic-field component
electromagnetic spectrum: range of energies that electromagnetic radiation can comprise, including radio, microwaves, infrared, visible, ultraviolet, X-rays, and gamma rays; since electromagnetic radiation energy is proportional to the frequency and inversely proportional to the wavelength, the spectrum can also be specified by ranges of frequencies or wavelengths
frequency (ν): number of wave cycles (peaks or troughs) that pass a specified point in space per unit time
hertz (Hz): the unit of frequency, which is the number of cycles per second, s−1
intensity: property of wave-propagated energy related to the amplitude of the wave, such as brightness of light or loudness of sound
photon: smallest possible packet of electromagnetic radiation, a particle of light
wave: oscillation that can transport energy from one point to another in space
wavelength (λ): distance between two consecutive peaks or troughs in a wave