Chapter 38
7
(a) Let
R
be the rate of photon emission (number of photons emitted per unit time) and let
E
be
the energy of a single photon. Then the power output of a lamp is given by
P
=
RE
if all the
power goes into photon production. Now
E
=
hf
=
hc=¸
,whe
re
h
is the Planck constant,
f
is
the frequency of the light emitted, and
¸
is the wavelength. Thus
P
=
Rhc=¸
and
R
=
¸P=hc
.
The lamp emitting light with the longer wavelength (the 700nm lamp) emits more photons per
unit time. The energy of each photon is less so it must emit photons at a greater rate.
(b) Let
R
be the rate of photon production for the 700 nm lamp Then
R
=
¸P
hc
=
(700
£
10
¡
9
m)(400 J
=
s)
(6
:
626
£
10
¡
34
J
¢
s)(2
:
9979
£
10
8
m
=
s)
=1
:
41
£
10
21
photon
=
s
:
17
The energy of an incident photon is
E
=
hf
=
hc=¸
,whe
re
h
is the Planck constant,
f
is the
frequency of the electromagnetic radiation, and
¸
is its wavelength. The kinetic energy of the
most energetic electron emitted is
K
m
=
E
¡
©
=(
hc=¸
)
¡
©
,whe
re
©
is the work function for
sodium. The stopping potential
V
0
is related to the maximum kinetic energy by
eV
0
=
K
m
,so
eV
0
=(
hc=¸
)
¡
©
and
¸
=
hc
eV
0
+
©
=
(6
:
626
£
19
¡
34
J
¢
s)(2
:
9979
£
10
8
m
=
s)
(5
:
0eV+2
:
2eV)(1
:
602
£
10
¡
19
J
=
eV)
=1
:
7
£
10
¡
7
m
:
Here
eV
0
=5
:
0eV was used.
21
(a) The kinetic energy
K
m
of the fastest electron emitted is given by
K
m
=
hf
¡
©
=(
hc=¸
)
¡
©
,
where
©
is the work function of aluminum,
f
is the frequency of the incident radiation, and
¸
is
its wavelength. The relationship
f
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 Fall '98
 Heckman
 Physics, Energy, Kinetic Energy, Power, Photon, Wavelength

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