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effect. Einstein described the energy in a light wave as quanta The photoelectric effect is explained by considering light
of energy called photons. Each photon has an energy (E) that to be photons with quanta of energy, not a wave of continuous
is related to the frequency (f) of the light through Planck’s energy. This is not the only evidence about the quantum nature

constant (h), or of light, and more will be presented in chapter 8. But, as you
can see, there is a dilemma. The electromagnetic wave theory

E = hf
and the photon theory seem incompatible. Some experiments
equation 7.4 cannot be explained by the wave theory and seem to support
the photon theory. Other experiments are contradictions, pro-
–34
The value of Planck’s constant is 6.63 × 10 J∙s.

viding seemingly equal evidence to reject the photon theory in

This relationship says that higher-frequency light (e.g., blue
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light at 6.50 × 10 Hz) has more energy than lower-frequency support of the wave theory.
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light (e.g., red light at 4.00 × 10 Hz). The energy of such high-

and low-frequency light can be verified by experiment.
The photon theory also explained the photoelectric eff ect. 7.5 THE PRESENT THEORY

According to this theory, light is a stream of moving photons. It
Today, light is considered to have a dual nature, sometimes
is the number of photons in this stream that determines if the
acting as a wave and sometimes acting as a particle. A wave
light is dim or intense. A high-intensity light has many, many
model is useful in explaining how light travels through
photons, and a low-intensity light has only a few photons. At
space and how it exhibits such behaviors as refraction,

any particular fixed frequency, all the photons would have the
interference, and diffraction. A particle model is useful in
same energy, the product of the frequency and Planck’s constant
explaining how light is emitted from and absorbed by mat-
(hf ). When a photon interacts with matter, it is absorbed and
ter, exhibiting such behaviors as blackbody radiation and
gives up all of its energy. In the photoelectric effect, this inter-

the photoelectric effect. Together, both of these models are
action takes place between photons and electrons. When an
part of a single theory of light, a theory that pictures light as
intense light is used, there are more photons to interact with the
having both particle and wave properties. Some properties

electrons, so more electrons are ejected. The energy given up by
are more useful when explaining some observed behaviors,
each photon is a function of the frequency of the light, so at a
and other properties are more useful when explaining other

fixed frequency, the energy of each photon, hf, is the same, and
behaviors.
the acquired kinetic energy of each ejected electron is the same.
Frequency is a property of a wave, and the energy of a
Thus, the photon theory explains the measured experimental

photon is a property of a particle. Both frequency and the
results of the photoelectric eff ect.
energy of a photon are related in equation 7.4, E = hf. It is
thus possible to describe light in terms of a frequency (or
EXAMPLE 7.3 wavelength) or in terms of a quantity of energy. Any part
What is the energy of a photon of red light with a frequency of 4.00 × of the electromagnetic spectrum can thus be described by
14
10 Hz? units of frequency, wavelength, or energy, which are alter-
native means of describing light. The radio radiation parts

of the spectrum are low-frequency, low-energy, and long-
SOLUTION wavelength radiations. Radio radiations have more wave

The relationship between the energy of a photon (E) and its frequency properties and practically no particle properties, since the
(f) is found in equation 7.4. Planck’s constant (h) is given as energy levels are low. Gamma radiation, on the other hand,
–34
6.63 × 10 J∙s. is high-frequency, high-energy, and short-wavelength radia-
tion. Gamma radiation has more particle properties, since
14
f = 4.00 × 10 Hz
the extremely short wavelengths have very high energy lev-
–34
h = 6.63 × 10 J∙s
els. The more familiar part of the spectrum, visible light, is

E = ?
between these two extremes and exhibits both wave and par-
E = hf ticle properties, but it never exhibits both properties at the
14 1 _
–34
= (6.63 × 10 J∙s)( 4.00 × 10 ) same time in the same experiment.

s
1 _ Part of the problem in forming a concept or mental image
14
–34
= (6.63 × 10 )(4.00 × 10 ) J∙s ×

s of the exact nature of light is understanding this nature in terms
–19 J∙s of what is already known. The things you already know about
_

= 2.65 × 10

s
are observed to be particles, or objects, or they are observed to
= 2.65 × 10 –19 J be waves. You can see objects that move through the air, such
as baseballs or footballs, and you can see waves on water or in

a field of grass. There is nothing that acts as a moving object in

EXAMPLE 7.4 some situations but acts as a wave in other situations. Objects
What is the energy of a photon of violet light with a frequency of are objects, and waves are waves, but objects do not become
–19
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7.00 × 10 Hz? (Answer: 4.64 × 10 J) waves, and waves do not become objects. If this dual nature did
exist, it would seem very strange. Imagine, for example, holding
194 CHAPTER 7 Light 7-18