Download Topic 7_1_Ext B__Photons and the photoelectric effect

Topic 7.1 Extended
B –Photons and the Photoelectric Effect
In the last lesson you found out about Planck's
hypothesis that radiant energy came in discrete packets
called quanta, and that for each frequency or
wavelength of radiant energy
En = nhf, for n = 1,2,3,...
Planck's Hypothesis
where
h = 6.6310-34 Js
Planck's Constant
Using the relationship
c = f
where
c = 3.00108 m/s
Relation between  and
f for radiant energy
Speed of Light
we can restate Planck's hypothesis in terms of
wavelength:
nhc
Planck's
En =

Hypothesis
FYI: In short, light has particle-like properties.
Topic
7.1
Extended
FYI: But light also has
wave-like
properties
since frequency is a
property
of a wave. and the Photoelectric Effect
B –Photons
FYI: The ramifications of the particle-wave duality of light will be
explored later.
calculations agree with experimental observations.
In 1905 Elbert Einstein published a paper on the
photoelectric effect, in which he postulated that
energy quantization is a fundamental property of
electromagnetic waves (including visible light and
heat).
He called the energy packet a photon, each photon
having an energy given by
Planck's hypothesis was made to make theoretical
E = hf
Energy of a Photon
In his paper Einstein said
...the radiant energy from a point source is not
distributed continuously throughout an
increasingly larger region, but, instead, this
energy consists of a finite number of spatially
localized energy quanta which, moving without
subdividing, can only be absorbed and created in
whole units.
Topic 7.1 Extended
B –Photons and the Photoelectric Effect
THE PHOTOELECTRIC EFFECT
Einstein based his reasoning on an experiment he
conducted in 1905, describing the photoelectric effect.
Certain metals are photosensitive - meaning that
when they are struck by radiant energy, they emit
electrons from their surface.
In order for this to happen, the light must have
done work on the electron.
FYI: If we reverse the voltage (and it is big enough), we can stop the
photoelectrons from Topic
making it to7.1
the opposite
plate. In other words, we
Extended
can
the photocurrent.
B stop
–Photons
and the Photoelectric Effect
THE PHOTOELECTRIC EFFECT
We can enhance this process if we add another metal
electrode, and apply a voltage like so:
-
+
+
-
(+) anode
A
(-) cathode
In fact, you can read the ammeter to determine the
current of the emitted photoelectrons.
As with all positively and negatively charged
plates, we have the anode and the cathode.
Ip
FYI: The negative voltage necessary
7.1 Extended
to stop the photocurrentTopic
is called the
STOPPING
POTENTIAL.and the Photoelectric
B –Photons
Effect
-V0
V
We can enclose our anode and cathode in an evacuated
glass envelope, and hook it up as shown:
If we adjust the voltage on the
phototube using the variable resistor
FYI: we
Point
(1) is predicted
by classical
theory.
and
limit
the radiant
energy
to a
The morefrequency
intense the barrage
of light, the more
single
(monochromatic
light)
and
intensity,
we get the
I
electrons
will be emitted.
E X Pfollowing
ECTED
vs. V graph:
Ip
FYI: Point (2) is NOT predicted by classical
If we reverse the polarity of the
theory. According
to classical
theory,
more
voltage,
our graph
looks
likethethis:
A
V
intense
the
barrage
of
light,
the
faster
electrons
If we increase the intensity of the
will bemonochromatic
emitted, and therefore
the larger
the this
same
light,
we get
required stopping potential. N O T E X P E C T E D
graph:
Two important observations can be
made regarding the graphs:
+
(1) The photoelectric current is
proportional to the intensity.
(2) The cutoff voltage is
independent of the intensity.
THE PHOTOELECTRIC EFFECT
+
-
K
Topic 7.1 Extended
B –Photons and the Photoelectric Effect
THE PHOTOELECTRIC EFFECT
f0
cutoff
frequency
The stopping potential V0 is related to the maximum
kinetic energy of the emitted electrons by
Kmax = eV0
If we change the frequency of our monochromatic
light, we observe that the maximum kinetic energy of
the emitted electrons increases linearly with the
frequency:
We also observe that below a certain frequency no
more electrons are emitted no matter how intense the
light.
We call this lower limit the cutoff frequency.
We also observe that above this frequency the
electron emissions begin instantaneously, even at
extremely low intensities.
f
Topic 7.1 Extended
B –Photons and the Photoelectric Effect
THE PHOTOELECTRIC EFFECT
The following table summarizes the problems classical
theory has with the photoelectric effect:
Photoelectric Effect and Classical Theory
Characteristics
The photocurrent is proportional to the intensity of
the light.
Classical Prediction?
YES
The maximum kinetic energy of the emitted
electrons is dependent on the frequency of the
light but not on its intensity.
NO
No photoemission occurs for light with a frequency
below a certain cutoff frequency f0 regardless of its
intensity.
NO
A photocurrent is observed immediately when the
light frequency is greater than f0 even if the light
intensity is low.
NO
Topic 7.1 Extended
B –Photons and the Photoelectric Effect
THE PHOTOELECTRIC EFFECT
The last effect is a very serious problem classically
because classical wave theory predicts that at low
intensities, times of the order of minutes are required
to dislodge an electron. But Einstein's observation
was that
"A photocurrent is observed immediately when
the light frequency is greater than f0 even if
the light intensity is low."
Thus, if light were treated as a wave, current
theory failed to predict this result.
Einstein thus suggested that light was a particle and
he called it a photon. It was a particle having an
associated energy of E = hf.
Topic 7.1 Extended
B –Photons and the Photoelectric Effect
THE PHOTOELECTRIC EFFECT
Einstein also stated that an electron was held in its
photomaterial by "cohesive forces" that needed a
minimum amount of work to be overcome. He called the
energy needed to dislodge the electron the work
function 0.
Thus, the photon must overcome the work function in
order to cause the electron to become free, or a
photoelectron. The following relationship follows:
hf = Kmax + 0
incident
photon
maximum
kinetic
energy of
dislodged
electron
The Work Function
minimum
work
needed to
dislodge
electron
FYI: This relationship satisfactorily addresses all of the failures of
classical theory regarding the photoelectric effect.
Topic 7.1 Extended
B –Photons and the Photoelectric Effect
THE PHOTOELECTRIC EFFECT
Suppose the work function for a particular metal is
1.00 eV.
(a) If the metal is illuminated with a monochromatic
light having a wavelength of 600 nm, what will be the
maximum kinetic energy of the emitted electrons?
Since c = f we can easily find f:
f = c /  = 3108 / 60010-9 = 51014 Hz
Furthermore, since 0 = 1.00 eV = 1.610-19 J we
have
hf = Kmax + 0
Kmax = hf - 0
Kmax = 6.6310-34(51014) - 1.610-19
Kmax = 1.7210-19 J
Topic 7.1 Extended
B –Photons and the Photoelectric Effect
THE PHOTOELECTRIC EFFECT
Suppose the work function for a particular metal is
1.00 eV.
(b) What, then, is the maximum speed of the emitted
electron?
1
Since m = 9.1110-31 kg and Kmax = 2 mv2 we have
vmax =
vmax =
2Kmax
m
2(1.7210-19)
9.1110-31
vmax = 6.14105 m s-1
(c) What is the cutoff voltage for this metal?
Kmax = eV0
1.7210-19 = (1.610-19)V0
V0 = 1.075 V
FYI: This corresponds to a wavelength given by
Topic 7.1 Extended
=c/f
14
B –Photons
and
Photoelectric
= 3108 / 2.41
10the
= 1243 nm.
Effect
THE PHOTOELECTRIC EFFECT
Suppose the work function for a particular metal is
1.00 eV.
(d) What is the cutoff frequency f0 for this metal?
From hf = Kmax + 0 we have
0
hf0 = Kmax + 0
f0 =
0
h
Cutoff
Frequency
FYI: This relationship gives you the minimum frequency that will
dislodge electrons from a metal.
1.610-19
f0 =
6.6310-34
f0 = 2.411014 Hz