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PRACTICE
Problems
1.
Objects get their colors from reflecting only certain wavelengths when hit with white light.
Light reflected from a green leaf is found to have a wavelength of 4.90
×
10
-
7
m. What is the
frequency of the light?
2.
When light or longer wavelength electromagnetic radiation is absorbed in matter, it is
generally converted into thermal energy (heat). Shorter wavelength electromagnetic
radiation (ultraviolet, X-rays, gamma rays) can ionize atoms and cause damage to living
cells. X-rays can penetrate body tissues and are widely used
to diagnose and treat disorders of internal body structures.
What is the frequency of an X-ray with a wavelength of
1.15
×
10
-
10
m?
3.
After careful analysis, an electromagnetic wave is found to have
a frequency of 7.8
×
10
6
Hz. What is the speed of the wave?
4. CHALLENGE
While an FM radio station broadcasts at a
frequency of 94.7 MHz, an AM station broadcasts at a frequency
of 820 kHz. What are the wavelengths of the two broadcasts?
Which of the drawings on the right corresponds to the FM
station? To the AM station?
C05_011A
a
b
C05_011A
a
b
EXAMPLE
Problem 1
CALCULATING WAVELENGTH OF AN EM WAVE
Microwaves are used to cook food and
transmit information. What is the wavelength of a microwave that has a frequency of
3.44
×
10
9
Hz?
1
ANALYZE THE PROBLEM
You are given the frequency of a microwave. You also know that because microwaves are part
of the electromagnetic spectrum, their speeds, frequencies, and wavelengths are related by
the formula c
= λν
. The value of c is a known constant. First, solve the equation for wavelength,
then substitute the known values and solve.
Known
Unknown
ν =
3.44
×
10
9
Hz
λ
=
? m
c
=
3.00
×
10
8
m/s
2
SOLVE FOR THE UNKNOWN
Solve the equation relating the speed, frequency, and wavelength of an electromagnetic wave
for wavelength (
λ
).
c
=
λ
ν
State the electromagnetic wave relationship.
λ
=
c/
ν
Solve for
λ
.
λ
=
3.00
×
10
8
m/s
__
3.44
×
10
9
Hz
Substitute c
=
3.00
×
10
8
m/s and
ν =
3.44
×
10
9
Hz.
Note that hertz is equivalent to 1/s or s
-
1
.
λ
=
3.00
×
10
8
m/s
__
3.44
×
10
9
s
-
1
Divide numbers and units.
λ
=
8.72
×
10
-
2
m
3
EVALUATE THE ANSWER
The answer is correctly expressed in a unit of wavelength (m). Both of the known values in
the problem are expressed with three significant figures, so the answer should have three
significant figures, which it does. The value for the wavelength is within the wavelength range
for microwaves shown in
Figure 5.
ADDITIONAL PRACTICE
110
Module 4 • Electrons in Atoms