The Foundations of Chemistry

EXAMPLE 5-4 Wavelength of Light

Light near the middle of the ultraviolet region of the electromagnetic radiation spectrum has

a frequency of 2.73 1016 s
^1. Yellow light near the middle of the visible region of the spec-

trum has a frequency of 5.26 1014 s
^1. Calculate the wavelength that corresponds to each of

these two frequencies of light.

Plan

Wavelength and frequency are inversely proportional to each other,     c. We solve this rela-

tionship for and calculate the wavelengths.

Solution

(ultraviolet light)1.10 10 
^8 m (1.10 102 Å)

(yellow light) 5.70 10 
^7 m (5.70 103 Å)

You should now work Exercise 38.

We have described light in terms of wave behavior. Under certain conditions, it is also

possible to describe light as composed of particles,or photons.According to the ideas

presented by Max Planck (1858–1947) in 1900, each photon of light has a particular

amount (a quantum) of energy. The amount of energy possessed by a photon depends on

the frequency of the light. The energy of a photon of light is given by Planck’s equation

Eh or E

h



c



where his Planck’s constant, 6.6260755 10 
^34 J s, and is the frequency of the light.

Thus, energy is directly proportional to frequency. Planck’s equation is used in Example

5-5 to show that a photon of ultraviolet light has more energy than a photon of yellow light.

EXAMPLE 5-5 Energy of Light

In Example 5-4 we calculated the wavelengths of ultraviolet light of frequency 2.73 1016 s
^1

and of yellow light of frequency 5.26 1014 s
^1. Calculate the energy, in joules, of an indi-

vidual photon of each. Compare these photons by calculating the ratio of their energies.

Plan

We use each frequency to calculate the photon energy from the relationship Eh. Then we

calculate the required ratio.

Solution

(ultraviolet light)Eh (6.626 10 
^34 J s)(2.73 1016 s
^1 ) 1.81 10 
^17 J

(yellow light) Eh (6.626 10 
^34 J s)(5.26 1014 s
^1 ) 3.49 10 
^19 J

(You can check these answers by calculating the energies directly from the wavelengths, using

the equation Ehc/.)

Now, we compare the energies of these two photons.

3.00 108 m s
^1



5.26 1014 s
^1

c



3.00 108 m s
^1



2.73 1016 s
^1

c



196 CHAPTER 5: The Structure of Atoms