CK-12-Chemistry Intermediate

http://www.ck12.org Chapter 5. Electrons in Atoms

on the type of wave, wavelengths are often measured in meters, centimeters, or nanometers (1 m = 10^9 nm). The
frequency, represented by the Greek letter nu (ν),is the number of waves that pass a certain point in a specified
amount of time.Typically, frequency is measured in units of cycles per second or waves per second. One wave per
second is also called a Hertz (Hz), which can be expressed in SI base units as a reciprocal second (s−^1 ).

Pictured above (Figure5.2) is the important relationship between the wavelength and frequency of a wave. The top
wave clearly has a shorter wavelength than the second wave. If you picture yourself at a stationary point watching
these waves pass by, more waves of the first kind would pass by in a given amount of time. Thus the frequency of
the first waves is greater than that of the second waves. Wavelength and frequency are therefore inversely related.
As the wavelength of a wave increases, its frequency decreases. The equation that relates the two is:

c=λν

The variablecis the speed at which the wave is traveling. In the case of electromagnetic radiation,cis equal to the
speed of light. If the value used for the speed of light has units of m/s, the wavelength must be in meters and the
frequency must be in Hertz.

Returning to the figure above (Figure5.1), you can see how the electromagnetic spectrum displays a wide variation
in wavelength and frequency. Radio waves can have wavelengths that are hundreds of meters long, while the
wavelength of gamma rays are on the order of 10−^12 m. The corresponding frequencies range from 10^6 to 10^21
Hz. Visible light can be split into different colors with the use of a prism (Figure5.3), yielding the visible spectrum
of light. Red light has the longest wavelength and the lowest frequency, while violet light has the shortest wavelength
and the highest frequency. Overall, visible light ranges in wavelength from about 400 –700 nm and has frequencies
in the range of 10^14 Hz.

FIGURE 5.3

A small beam of white light is refracted

(bent) as it passes through a glass prism.

The shorter the wavelength of light, the

greater the refraction, so white light is

separated into its various components ac-

cording to their wavelengths (colors).

Sample Problem 5.1: Wavelength and Frequency

The color orange within the visible light spectrum has a wavelength of about 620 nm. What is the frequency of
orange light?

Step 1: List the known quantities and plan the problem.

Known

• wavelength (λ) = 620 nm


• speed of light (c) = 3.00× 108 m/s


• conversion factor 1 m = 10^9 nm

Unknown

• Frequency (ν)