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5.2: The Electromagnetic Spectrum

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  • Learning Objectives

    • Know the difference between wave and particle radiation
    • Understand the relationships of wavelength, frequency, and energy
    • Calculate frequency and wavelength of radiation
    • Know the order of the electromagnetic spectrum (names, not numbers)

    Roentgen, Becquerel and the Curies experimented with radiation. Using machines, Roengten's focused on the production X-rays, which is a wave-type of radiation. Unlike Roengten, Henri Becquerel studied the natural radioactivity of elements. His uranium experiments yielded the production of alpha (particle-type) and gamma (ray-type) radiations. Becquerel's two graduate students, Marie and Pierre Curie, isolated two radioactive elements. Both radium and polonium emit alpha and beta particles upon decay. In this section, wave form radiation will be explored. This type of radiation has an extremely wide range of wavelengths, frequencies, and energies. 

    Properties of Waves

    A wave is a periodic oscillation that transmits energy through space. Anyone who has visited a beach or dropped a stone into a puddle has observed waves traveling through water (Figure \(\PageIndex{1}\)). These waves are produced when wind, a stone, or some other disturbance, such as a passing boat, transfers energy to the water, causing the surface to oscillate up and down as the energy travels outward from its point of origin. As a wave passes a particular point on the surface of the water, anything floating there moves up and down.

    Figure \(\PageIndex{1}\): Characteristics of Light Waves. Light acts as a wave and can be described by a wavelength λ and a frequency ν.

    Waves have characteristic properties (Figure \(\PageIndex{1}\)). Waves are periodic, that is, they repeat regularly in both space and time. The distance between two corresponding points in a wave—between the midpoints of two peaks, for example, or two troughs—is the wavelength (λ), distance between two corresponding points in a wave—between the midpoints of two peaks or two troughs. \(\lambda\) is the lowercase Greek lambda, and \(\nu\) is the lowercase Greek nu. Wavelengths are described by a unit of distance, typically meters. The frequency (ν) is the number of oscillations (i.e., of a wave) that pass a particular point in a given period of time. The unit for frequency is per second (1/s = s−1), which is equivalent to the SI unit of hertz (Hz). Amplitude, or vertical height of a wave, is defined as half the peak-to-trough. As the amplitude of a wave with a given frequency increases, so does its energy.

    In this equation, note how all units cancel. It is important to correlate the symbol with the correct term (\(v\), with the frequency, \(\nu\). In addition, know that wavelength must be converted to meters (SI unit) before being inserted into any frequency/wavelength equation.

    (wavelength)(frequency) = speed

    \[ \lambda \nu =v \label{6.1.1a}\]

    \[ \left ( \dfrac{meters}{\cancel{wave}} \right )\left ( \dfrac{\cancel{wave}}{second} \right )=\dfrac{meters}{second} \label{6.1.1b}\]

    Electromagnetic Radiation

    Energy that is transmitted, or radiated, through space in the form of periodic oscillations of electric and magnetic fields is known as electromagnetic radiation. (Figure \(\PageIndex{2}\)). Some forms of electromagnetic radiation are shown in Figure \(\PageIndex{4}\). In a vacuum, all forms of electromagnetic radiation—whether microwaves, visible light, or gamma rays—travel at the speed of light (c), which is the speed with which all forms of electromagnetic radiation travel in a vacuum, a fundamental physical constant with a value of 2.99792458 × 108 m/s (which is about 3.00 ×108 m/s or 1.86 × 105 mi/s). This is about a million times faster than the speed of sound.


    Figure \(\PageIndex{2}\): The Nature of Electromagnetic Radiation. All forms of electromagnetic radiation consist of perpendicular oscillating electric and magnetic fields.

    Because the various kinds of electromagnetic radiation all have the same speed (c), they differ in only wavelength and frequency. As shown in Figure \(\PageIndex{3}\) and Table \(\PageIndex{1}\), the wavelengths of familiar electromagnetic radiation range from 101 m for radio waves to 10−12 m for gamma rays, which are emitted by nuclear reactions. By replacing \(v\) with \(c\) in Equation \(\ref{6.1.1a}\), we can show that the frequency of electromagnetic radiation is inversely proportional to its wavelength:

    \[ \begin{array}{cc} c=\lambda \nu \\ \nu =\dfrac{c}{\lambda } \end{array} \label{6.1.2} \]

    For example, the frequency of radio waves is about 108 Hz, whereas the frequency of gamma rays is about 1020 Hz. Visible light, which is electromagnetic radiation that can be detected by the human eye, has wavelengths between about 7 × 10−7 m (700 nm, or 4.3 × 1014 Hz) and 4 × 10−7 m (400 nm, or 7.5 × 1014 Hz). Note that when frequency increases, wavelength decreases; c being a constant stays the same. Similarly when frequency decreases, the wavelength increases.

    Please memorize equation 5.2.3 and the speed of light (with units).  In addition, it is important to know which side of the electromagnetic spectrum is deadly.  



    Figure \(\PageIndex{3}\): The Electromagnetic Spectrum. (a) This diagram shows the wavelength and frequency ranges of electromagnetic radiation. The visible portion of the electromagnetic spectrum is the narrow region with wavelengths between about 400 and 700 nm. (b) When white light is passed through a prism, it is split into light of different wavelengths, whose colors correspond to the visible spectrum.


    Table \(\PageIndex{1}\): Common Wavelength Units for Electromagnetic Radiation
    Unit Symbol Wavelength (m) Type of Radiation
    picometer pm 10−12 gamma ray
    nanometer nm 10−9 x-ray
    micrometer μm 10−6 infrared
    millimeter mm 10−3 infrared
    centimeter cm 10−2 microwave
    meter m 100 radio

    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.

    \[ E\; \propto\; \nu \label{6.1.3}\]

    \[ E\; \propto\; \dfrac{1}{\lambda } \label{6.1.4}\]

    Whereas visible light is essentially harmless to our skin, ultraviolet light, with wavelengths of ≤ 400 nm, has enough energy to cause severe damage to our skin in the form of sunburn. Because the ozone layer absorbs sunlight with wavelengths less than 350 nm, it protects us from the damaging effects of highly energetic ultraviolet radiation.

    In this course, we will not do energy calculations.  You should know the relationship between frequency and energy.  Also, you show realize that short wavelength radiation is associated with a high energy.  

    The energy of electromagnetic radiation increases with increasing frequency and decreasing wavelength.

    Example \(\PageIndex{1}\)

    What is the frequency of light if its wavelength is 5.55 × 10−7 m?


    We use the equation that relates the wavelength and frequency of light with its speed. We have

    \[3.00\times 10^{8}m/s=\left ( 5.55\times 10^{-7} m\right )\nu\]

    We divide both sides of the equation by 5.55 × 10−7 m and get

    \[\nu =5.41\times 10^{14}s^{-1}\]

    Note how the m units cancel, leaving s in the denominator. A unit in a denominator is indicated by a −1 power—s−1—and read as “per second.”

    Exercise \(\PageIndex{1}\)

    What is the wavelength (in mm) of light if its frequency is 1.55 × 1010 s−1?


    emag 5.2.1.jpg




    Example \(\PageIndex{2}\)

    Calculate the frequency of radiation if its wavelength is 988 nm.  Where does this radiation appear in the electromagnetic spectrum?


    emag 5.2.2.jpg


    • Light acts like a wave, with a frequency and a wavelength.
    • Frequency and wavelength of light are related by the speed of light, a constant. 
    • The speed of light has units of m/s and all variables must agree with these units.
    • Electromagnetic radiation has a wide spectrum, including gamma rays, X-rays, UV rays, visible light, IR radiation, microwaves, and radio waves.