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PHYSICS CHAPTER 9
CHAPTER 9:CHAPTER 9:
Quantization of lightQuantization of light(4 Hours)(4 Hours)
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PHYSICS CHAPTER 9
2
At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
Explain brieflyExplain briefly Plancks quantum theory and classicalPlancks quantum theory and classical
theory of energy.theory of energy.
Write and useWrite and use Einsteins formulae for photon energy,Einsteins formulae for photon energy,
Learning Outcome:
9.1 Plancks quantum theory (1 hour)
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hchfE ==
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PHYSICS CHAPTER 9
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9.1.1 Classical theory of black body radiation Black body is defined as an ideal system that absorbs all thean ideal system that absorbs all the
radiation incident on itradiation incident on it. The electromagnetic (EM) radiationelectromagnetic (EM) radiation
emitted by the black bodyemitted by the black body is called black body radiationblack body radiation.
From the black body experiment, the distribution ofenergy inenergy inblack body,black body,EEdepends only on the temperature,depends only on the temperature, TT.
If the temperature increases thus the energy of the black body
increases and vice versa.
9.1 Plancks quantum theory
TkE B= (9.1)(9.1)
constantsBoltzmann':Bkwhere
kelvininetemperatur:T
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PHYSICS CHAPTER 9
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The spectrum of EM radiation emitted by the black body
(experimental result) is shown in Figure 9.1.
From the curve, Wiens theory was accurate at short
wavelengths but deviated at longer wavelengths whereas the
reverse was true for the Rayleigh-Jeans theory.
Figure 9.1Figure 9.1
Experimental
result
Rayleigh -Jeans
theoryWiens theory
ClassicalClassical
physicsphysics
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PHYSICS CHAPTER 9
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The Rayleigh-Jeans and Wiens theories failed to fit the
experimental curve because this two theories based on classical
ideas which are EnergyEnergy of the EM radiation is not dependnot depend on its frequencyfrequency
orwavelengthwavelength.
EnergyEnergy of the EM radiation is continuouslycontinuously.
9.1.2 Plancks quantum theory In 1900, Max Planck proposed his theory that is fit with the
experimental curve in Figure 9.1 at all wavelengths known as
Plancks quantum theory.
The assumptions made by Planck in his theory are :
The EM radiation emitted by the black body is in discretediscrete
(separate) packets of energy(separate) packets of energy. Each packet is called a
quantum of energyquantum of energy. This means the energy of EM radiation
is quantisedquantised.
The energy size of the radiation dependsdepends on its frequencyfrequency.
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PHYSICS CHAPTER 9
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According to this assumptions, the quantum of the energyquantum of the energyEE
for radiation of frequencyfor radiation of frequencyff is given by
Since the speed of EM radiation in a vacuum is
then eq. (9.2) can be written as
From eq. (9.3), the quantumquantum of the energyEEfor radiation isinversely proportional to its wavelengthinversely proportional to its wavelength.
hfE=
sJ1063.6constantsPlanck': 34=hwhere
(9.2)(9.2)
fc =
hc
E=
(9.3)(9.3)
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PHYSICS CHAPTER 9
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It is convenient to express many quantum energies in electron-
volts.
The electron-volt (eV)electron-volt (eV) is a unit of energyunit of energy that can be definedas the kinetic energy gained by an electron in beingthe kinetic energy gained by an electron in being
accelerated by a potential difference (voltage) of 1 voltaccelerated by a potential difference (voltage) of 1 volt.
Unit conversion:
In 1905, Albert Einstein extended Plancks idea by proposing
that electromagnetic radiation is also quantised. It consists of
particle like packets (bundles) of energy called photonsphotons of
electromagnetic radiation.
J101.60eV1 19=
Note:Note:
For EM radiation ofn packets, the energyEnis given by
nhfEn = (9.4)(9.4)
1,2,3,...numberreal: =nwhere
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PHYSICS CHAPTER 9
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Photon is defined as a particle with zero mass consisting ofa particle with zero mass consisting ofa quantum of electromagnetic radiation where its energy isa quantum of electromagnetic radiation where its energy is
concentratedconcentrated.
A photon may also be regarded as a unit of energy equal tounit of energy equal to
hfhf.
Photons travel at the speed of lightspeed of light in a vacuum. They arerequired to explain the photoelectric effectexplain the photoelectric effect and other
phenomena that require light to have particle propertylight to have particle property.
Table 9.1 shows the differences between the photon andelectromagnetic wave.
9.1.3 Photon
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PHYSICS CHAPTER 9
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EM Wave Photon
Energy of the EM wavedepends on the intensityof the wave. Intensity of
the waveIis proportionalto the squared of its
amplitudeA2 where
Energy of a photon isproportional to thefrequency of the EMwave where
Its energy is continuouslyand spread out throughthe medium as shown inFigure 9.2a.
Its energy is discrete asshown in Figure 9.2b.
Table 9.1Table 9.1
2AI
fE
Photon
Figure 9.2aFigure 9.2a Figure 9.2bFigure 9.2b
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PHYSICS CHAPTER 9
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A photon of the green light has a wavelength of 740 nm. Calculate
a. the photons frequency,b. the photons energy in joule and electron-volt.
(Given the speed of light in the vacuum, c =3.00 108 m s1and
Plancks constant, h =6.63 1034 J s)
Solution :Solution :a. The frequency of the photon is given by
b. By applying the Plancks quantum theory, thus the photons
energy in joule is
and its energy in electron-volt is
Example 1 :
m10740
9
=
fc = ( ) f98 107401000.3 =Hz1005.4 14=f
hfE= ( )( )1434 1005.41063.6 = EJ1069.2 19=E
101.60
1069.2
19
19
=E eV66.1
=E
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PHYSICS CHAPTER 9
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For a gamma radiation of wavelength 4.62 1012 m propagates in
the air, calculate the energy of a photon for gamma radiation inelectron-volt.
(Given the speed of light in the vacuum, c =3.00 108 m s1and
Plancks constant, h =6.63 1034 J s)
Solution :Solution :
By applying the Plancks quantum theory, thus the energy of a
photon in electron-volt is
Example 2 :
m1062.4
12
=
hcE= ( )( )
12
834
1062.4
1000.31063.6
=E
J1031.4 14=E
101.60
1031.419
14
=
eV1069.2
5
=E
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PHYSICS CHAPTER 9
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At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
ExplainExplain the phenomenon of photoelectric effect.the phenomenon of photoelectric effect.
DefineDefine threshold frequency, work function and stoppingthreshold frequency, work function and stopping
potential.potential. Describe and sketchDescribe and sketch diagram of the photoelectric effectdiagram of the photoelectric effect
experimental set-up.experimental set-up.
Explain by using graph and equationsExplain by using graph and equations the observationsthe observations
of photoelectric effect experiment in terms of theof photoelectric effect experiment in terms of the
dependence of :dependence of :
kinetic energy of photoelectron on the frequency ofkinetic energy of photoelectron on the frequency of
light;light;
Learning Outcome:
9.2 The photoelectric effect (3 hours)
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0s
2
max2
1hfhfeVmv ==
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PHYSICS CHAPTER 9
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At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
photoelectric current on intensity of incident light;photoelectric current on intensity of incident light;
work function and threshold frequency on the typeswork function and threshold frequency on the types
of metal surface.of metal surface.
ExplainExplain the failure of wave theory to justify thethe failure of wave theory to justify the
photoelectric effect.photoelectric effect.
Learning Outcome:
9.2 The photoelectric effect (3 hours)
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00 hfW =
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PHYSICS CHAPTER 9
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is defined as the emission of electron from the surfaceemission of electron from the surfaceof a metal when the EM radiation (light) of higherof a metal when the EM radiation (light) of higher
frequency strikes its surfacefrequency strikes its surface.
Figure 9.3 shows the emission of the electron from the surface of
the metal after shining by the light.
Photoelectron is defined as an electron emitted from thean electron emitted from the
surface of the metal when the EM radiation (light) strikes itssurface of the metal when the EM radiation (light) strikes itssurfacesurface.
9.2 The photoelectric effect
Figure 9.3Figure 9.3
EM
radiation-- photoelectronphotoelectron
-- -- -- -- -- -- -- -- -- --
MetalMetal
Free electronsFree electrons
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PHYSICS CHAPTER 9
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The photoelectric effect can be studied through the experiment
made by Franck Hertz in 1887.
Figure 9.4a shows a schematic diagram of an experimental
arrangement for studying the photoelectric effect.
9.2.1 Photoelectric experiment
----
--
EM radiation (light)
anodecathode
glass
rheostatpower supply
vacuumphotoelectron
Figure 9.4aFigure 9.4a
GG
VV
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PHYSICS CHAPTER 9
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The set-up apparatus as follows:
Two conducting electrodes, the anode (positive electric
potential) and the cathode (negative electric potential) areencased in an evacuated tube (vacuum).
The monochromatic light of known frequency and intensity is
incident on the cathode.
Explanation of the experimentExplanation of the experiment
When a monochromatic light of suitable frequency (or
wavelength) shines on the cathode, photoelectrons are emitted.
These photoelectrons are attracted to the anode and give rise to
the photoelectric current or photocurrentIwhich is measured by
the galvanometer. When the positive voltage (potential difference) across the
cathode and anode is increased, more photoelectrons reach the
anode , thus the photoelectric current increases.
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PHYSICS CHAPTER 9
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As positive voltage becomes sufficiently large, the photoelectric
current reaches a maximum constant valueIm, called saturationsaturation
currentcurrent. Saturation current is defined as the maximum constantthe maximum constant
value of photocurrent when all the photoelectrons havevalue of photocurrent when all the photoelectrons have
reached the anodereached the anode.
If the positive voltage is gradually decreased, the photoelectric
currentIalso decreases slowly. Even at zero voltage there arestill some photoelectrons with sufficient energy reach the anode
and the photoelectric current flows isI0.
Finally, when the voltage is made negative by reversing thepower supply terminal as shown in Figure 9.4b, the
photoelectric current decreases even further to very low valuessince most photoelectronsphotoelectrons are repelledrepelled by anodeanode which isnow negativenegative electric potential.
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PHYSICS CHAPTER 9
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As the potential of the anode becomes more negative, less
photoelectrons reach the anode thus the photoelectric currentphotoelectric currentdrops until its value equals zerozero which the electric potential at
this moment is called stopping potential (voltage)stopping potential (voltage)Vs.
Stopping potential is defined as the minimum value ofthe minimum value of
negative voltage when there are no photoelectronsnegative voltage when there are no photoelectrons
reaching the anodereaching the anode.
Figure 9.4b: reversing power supply terminalFigure 9.4b: reversing power supply terminal
----
--
EM radiation (light)
anodecathode
glass
rheostatpower supply
vacuumphotoelectron
GG
VV
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PHYSICS CHAPTER 9
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The potential energy Udue to this retarding voltage Vsnow
equals the maximum kinetic energyKmax
of the photoelectron.
The variation of photoelectric currentIas a function of thevoltage Vcan be shown through the graph in Figure 9.4c.
maxKU =2
maxs2
1mveV = (9.5)(9.5)
electrontheofmass:mwhere
mI
0I
sV
I,currentricPhotoelect
V,Voltage0
Before reversing the terminalBefore reversing the terminalAfterAfterFigure 9.4cFigure 9.4c
Stimulation 9.1
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PHYSICS CHAPTER 9
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A photon is apacketpacket of
electromagnetic radiationelectromagnetic radiation with
particle-like characteristicparticle-like characteristic and carries the energyEgiven by
and this energy is not spread out through the mediumnot spread out through the medium.
Work functionWork function WW00of a metalof a metal
Is defined as the minimum energy of EM radiation requiredminimum energy of EM radiation required
to emit an electron from the surface of the metalto emit an electron from the surface of the metal.
It depends on the metal usedmetal used.
Its formulae is
wheref0is called threshold frequencythreshold frequencyand is defined as the
minimum frequency of EM radiation required to emit anminimum frequency of EM radiation required to emit an
electron from the surface of the metalelectron from the surface of the metal.
9.2.2 Einsteins theory of photoelectric effect
hfE=
min0 EW =
00 hfW =
and 0min hfE =
(9.6)(9.6)
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PHYSICS CHAPTER 9
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Since c= f then the eq. (9.6) can be written as
where 0is called threshold wavelengththreshold wavelength and is defined as the
maximum wavelengthmaximum wavelengthof EM radiation required to emit anof EM radiation required to emit an
electron from the surface of the metalelectron from the surface of the metal. Table 9.2 shows the work functions of several elements.
0
0
hcW = (9.7)(9.7)
ElementElement Work function (eV)Work function (eV)
Aluminum 4.3
Sodium 2.3
Copper 4.7
Gold 5.1
Silver 4.3
Table 9.2Table 9.2
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PHYSICS CHAPTER 9
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Einsteins photoelectric equationEinsteins photoelectric equation
In the photoelectric effect, Einstein summarizes that some of the
energyenergyEEimparted by a photonimparted by a photon is actually used to release anrelease anelectronelectron from the surface of a metal (i.e. to overcome the
binding force) and that the rest appears as the maximummaximum
kinetic energykinetic energy of the emitted electron (photoelectronphotoelectron). It is
given by
where eq. (9.8) is known as Einsteins photoelectric equation. SinceK
max=eV
sthen the eq. (9.8) can be written as
where and0max WKE += hfE=
0
2
max2
1Wmvhf +=
2
maxmax2
1mvK =
(9.8)(9.8)
0s WeVhf += (9.9)(9.9)
voltagestopping:sVwhere
electronofchargeformagnitude:e
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PHYSICS CHAPTER 9
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Note:Note:
1st case: OR0Whf> 0ff>
Electron is emitted with maximumElectron is emitted with maximum
kinetic energykinetic energy.--MetalMetal
hf
0W
--maxv maxK
2nd case: OR0Whf= 0ff=
Electron is emitted but maximumElectron is emitted but maximum
kinetic energy is zerokinetic energy is zero.
-- 0=v 0max =K
3rd case: OR0Whf< 0ff>ff
11
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PHYSICS CHAPTER 9
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Reason:
From the Einsteins photoelectric equation,
Figure 9.7bFigure 9.7b
0s WeVhf +=e
Wf
e
hV 0s
=
=y xm c+
e
W0
f,frequency
s,voltageStopping V
02
f
s2V
1f
s1V
IfVVss=0=0,, 0)0( Wehf +=
hfW =0 0f
0f
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PHYSICS CHAPTER 9
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For the different metals of cathodedifferent metals of cathode but the intensity andintensity and
frequencyfrequency of the radiation are fixedfixed.
Reason: From the Einsteins photoelectric equation,
Figure 9.8aFigure 9.8a
mI
s1V
01W
s2V02W
WW0202>> WW
0101
0sWeVhf
+=
+
=e
hfW
eV
0s
1
e
hf
0W
sV
0 Ehf=
01W
1sV
02W
s2VEnergy of a photon
in EM radiation
I
V0
=y xm c+Figure 9.8bFigure 9.8b
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PHYSICS CHAPTER 9
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Variation of stopping voltageVariation of stopping voltage VVsswith frequencywith frequencyffof the radiationof the radiation
fordifferent metals of cathodedifferent metals of cathode but the intensityintensity is fixedfixed.
Reason: Since W0=hf0 then
Figure 9.9Figure 9.9WW0303 >>WW0202 >>WW0101
01f
WW0101
02f
WW0202
03f
WW0303
f
sV
0
00 fW 0s WeVhf +=
e
Wf
e
hV 0s
=
=y xm c+
IfVVss=0=0,, 0)0( Wehf +=
hfW =0 0f
Threshold (cut-off)Threshold (cut-off)frequencyfrequency
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PHYSICS CHAPTER 9
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Table 9.3 shows the classical predictions (wave theory),
photoelectric experimental observation and modern theoryexplanation about photoelectric experiment.
9.2.4 Failure of wave theory of light
Classical predictions Experimentalobservation
Modern theory
Emission of
photoelectrons occurfor all frequencies of
light. Energy of light is
independent ofindependent of
frequency.frequency.
Emission of
photoelectrons occuronly when frequency
of the light exceeds
the certain frequency
which value is
characteristic of thematerial being
illuminated.
When the light frequency is
greater than thresholdfrequency, a higher rate of
photons striking the metal
surface results in a higher
rate of photoelectrons
emitted. If it is less thanthreshold frequency no
photoelectrons are emitted.
Hence the emission ofemission of
photoelectronsphotoelectronsdependdepend on
the light frequencylight frequency
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PHYSICS CHAPTER 9
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Classical predictions Experimentalobservation
Modern theory
The higher theintensity, the greater
the energy imparted to
the metal surface for
emission of
photoelectrons. Whenthe intensity is low, the
energy of the radiation
is too small for
emission of electrons.
Very low intensity buthigh frequency
radiation could emit
photoelectrons. The
maximum kinetic
energy ofphotoelectrons is
independent of light
intensity.
The intensity of lightintensity of light is thenumber of photonsnumber of photons
radiated per unit time on aradiated per unit time on a
unit surface areaunit surface area.
Based on the Einsteins
photoelectric equation:
The maximum kinetickinetic
energyenergy of photoelectrondepends only on the light
frequencyfrequency and the workwork
functionfunction. If the lightintensity is doubled, thenumber of electrons emittedalso doubled but themaximum kinetic energy
remains unchanged.
0WhfK =max
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
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Classical predictions Experimentalobservation
Modern theory
Light energy is spreadover the wavefront, the
amount of energy
incident on any one
electron is small. An
electron must gather
sufficient energy beforeemission, hence there isthere is
time intervaltime interval between
absorption of light
energy and emission.
Time interval increases ifthe light intensity is low.
Photoelectrons areemitted from the
surface of the metal
almost
instantaneouslyinstantaneously
after the surface isilluminated, even at
very low light
intensities.
The transfer of photonsenergy to an electron is
instantaneous as its energy
is absorbed in its entirely,
much like a particle to
particle collision. Theemission of photoelectron
is immediate and no timeno time
intervalinterval between
absorption of light energy
and emission.
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
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Classical predictions Experimentalobservation
Modern theory
Energy of lightdepends only ondepends only on
amplitudeamplitude ( or
intensityintensity) and not on
frequency.
Energy of lightdepends on
frequency.
According to Plancksquantum theory which is
E=hf
Energy of light depends ondepends on
its frequency.its frequency.
Table 9.3Table 9.3Note:Note:
Experimental observations deviate from classical predictions based on
wave theory of lightwave theory of light. Hence the classical physics cannot explain thephenomenon of photoelectric effect.
The modern theory based on Einsteins photon theory of lightmodern theory based on Einsteins photon theory of light canexplain the phenomenon of photoelectric effect.
It is because Einstein postulated that light is quantizedlight is quantized and light isemitted, transmitted and reabsorbed as photonsphotons.
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
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a. Why does the existence of a threshold frequency in the
photoelectric effect favor a particle theory for light over a wavetheory?
b. In the photoelectric effect, explains why the stopping potential
depends on the frequency of light but not on the intensity.
Solution :Solution :
a. Wave theory predicts that the photoelectric effect should occur at
any frequency, provided the light intensity is high enough.However, as seen in the photoelectric experiments, the light must
have a sufficiently high frequency (greater than the threshold
frequency) for the effect to occur.
b. The stopping voltage measures the kinetic energy of the most
energetic photoelectrons. Each of them has gotten its energyfrom a single photon. According to Plancks quantum theory , the
photon energy depends on the frequency of the light. The
intensity controls only the number of photons reaching a unit area
in a unit time.
Example 5 :
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
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In a photoelectric experiments, a graph of the light frequencyfisplotted against the maximum kinetic energyK
maxof the photoelectron
as shown in Figure 9.10.
Based on the graph, for the light of frequency 7.14 1014 Hz, calculate
a. the threshold wavelength,
b. the maximum speed of the photoelectron.
(Given c =3.00 108 m s1, h =6.63 1034 J s, me=9.11 1031 kg and
e=1.60 1019 C)
Example 6 :
Hz1014
f
83.4
)eV(maxK0Figure 9.10Figure 9.10
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
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Solution :Solution :
a. By rearranging Einsteins photoelectric equation,
From the graph,
Therefore the threshold wavelength is given by
Hz1014.7 14=f
Hz1014f
83.4
)eV(maxK0
0max WKhf += hWK
hf 0max
1 +
=
=y xm c+
0max
1fK
hf +
=
Hz1083.4 140 =f
0
0f
c=
14
8
1083.4
1000.3
=
m1021.6 70 =
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
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Solution :Solution :
b. By using the Einsteins photoelectric equation, thus
Hz1014.7 14=f
02
max21 Wmvhf +=
0
2
max2
1hfmvhf +=
( )02
max2
1ffhmv =
( ) ( )1414342max31 1083.41014.71063.61011.92
1 = v15
max sm1080.5=v
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
43
Exercise 9.2 :
Given c =3.00 108 m s1, h =6.63 1034 J s, me=9.11 1031 kg and
e=1.60 1019 C1. A photocell with cathode and anode made of the same metal
connected in a circuit as shown in the Figure 9.11a.Monochromatic light of wavelength 365 nm shines on the
cathode and the photocurrentIis measured for variousvalues of voltage Vacross the cathode and anode. The resultis shown in Figure 9.11b.
365 nm365 nm
VV
GG 5
1
)nA(I
)V(V0
Figure 9.11aFigure 9.11a Figure 9.11bFigure 9.11b
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
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Exercise 9.2 :
1. a. Calculate the maximum kinetic energy of photoelectron.
b. Deduce the work function of the cathode.
c. If the experiment is repeated with monochromatic light of
wavelength 313 nm, determine the new intercept with the V-axis for the new graph.
ANS. :ANS. : 1.601.60 1010 1919 J, 3.85J, 3.85 1010 1919 J;J; 1.57 V1.57 V
2. When EM radiation falls on a metal surface, electrons may be
emitted. This is photoelectric effect.
a. Write Einsteins photoelectric equation, explaining the
meaning of each term.
b. Explain why for a particular metal, electrons are emitted onlywhen the frequency of the incident radiation is greater
than a certain value?
c. Explain why the maximum speed of the emitted electrons
is independent of the intensity of the incident radiation?
(Advanced Level Physics, 7(Advanced Level Physics, 7
thth
edition, Nelkon&Parker, Q6, p.835)edition, Nelkon&Parker, Q6, p.835)
PHYSICS CHAPTER 9
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PHYSICS CHAPTER 9
Next ChapterCHAPTER 10 :
Wave properties of particle