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Light’s dual nature
To explain the photoelectric effect, Albert Einstein proposed in 1905 that light has a
dual nature. A beam of light has wavelike and particlelike properties. It can be thought
of, or modeled, as a beam of bundles of energy called photons. A
photon
is a massless
particle that carries a quantum of energy. Extending Planck’s idea of quantized energy,
Einstein calculated that a photon’s energy depends on its frequency.
Energy of a Photon
E
photon
=
h
ν
E
photon
represents energy.
h
is Planck’s constant.
ν
represents frequency.
The energy of a photon is given by the product of Planck’s constant and the frequency.
Einstein also proposed that the energy of a photon must have a certain threshold value
to cause the ejection of a photoelectron from the surface of the metal. Thus, even small
numbers of photons with energy above the threshold value will cause the photoelectric
effect. Einstein won the Nobel Prize in Physics in 1921 for this work.
ADDITIONAL PRACTICE
EXAMPLE
Problem 2
CALCULATE THE ENERGY OF A PHOTON
Every object gets its color by reflecting a certain
portion of incident light. The color is determined by the wavelength of the reflected photons, thus
by their energy. What is the energy of a photon from the violet portion of the Sun’s light if it has a
frequency of 7.230
×
10
14
s
-
1
?
1 ANALYZE THE PROBLEM
Known
Unknown
ν =
7.230
×
10
14
s
-
1
E
photon
=
? J
h
=
6.626
×
10
-
34
J ⋅ s
2
SOLVE FOR THE UNKNOWN
E
photon
=
h
ν
State the equation for the energy of a photon.
E
photon
= (
6.626
×
10
-
34
J⋅ s)(7.230
×
10
14
s
-
1
)
Substitute
h
=
6.626
×
10
-
34
J⋅s and
ν =
7.230
×
10
14
s
-
1
.
E
photon
=
4.791
×
10
-
19
J
Multiply and divide numbers and units.
3
EVALUATE THE ANSWER
As expected, the energy of a single photon of light is extremely small. The unit is joules, an
energy unit, and there are four significant figures.
PRACTICE
Problems
5.
Calculate the energy possessed by a single photon of each of the following types of
electromagnetic radiation.
a.
6.32
×
10
20
s
-
1
b.
9.50
×
10
13
Hz
c.
1.05
×
10
16
s
-
1
6.
The blue color in some fireworks occurs when copper(l) chloride is heated to approximately
1500 K and emits blue light of wavelength 4.50
×
10
2
nm. How much energy does one photon of
this light carry?
7. CHALLENGE
The microwaves used to heat food have a wavelength of 0.125 m. What is the
energy of one photon of the microwave radiation?
Lesson 1 • Light and Quantized Energy
113