SF027 1 UNIT 10: PHOTONS AND UNIT 10: PHOTONS AND QUANTIZED ENERGY QUANTIZED ENERGY SF027 2 Fig. 10.1a Fig. 10.1a 10.1 Planck’s Quantum Theory The foundation of the Planck’s quantum theory is a theory of black theory of black body radiation body radiation. Black body is defined as an ideal system that absorbs all the an ideal system that absorbs all the radiation incident on it radiation incident on it. The electromagnetic radiation emitted by electromagnetic radiation emitted by the black body the black body is called black body radiation black body radiation. The spectrum of electromagnetic radiation emitted by the black body (experimental result) is shown in figure 10.1a. From the fig. 10.1a, the Rayleigh-Jeans and Wien’s theories failed to fit the experimental curve because this two theories based on classical ideas. The classical ideas are Energy Energy of the e.m. radiation is not depend not depend on its frequency frequency orwavelength wavelength. Energy Energy of the e.m. radiation is continuously continuously. Experimental Experimental result result Rayleigh Rayleigh - - Jeans theory Jeans theory Wien Wien’ s s theory theory Classical Classical physics physics
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10.1 Planck’s Quantum Theory The foundation of the Planck’s quantum theory is a theory of blacktheory of black
body radiationbody radiation.
Black body is defined as an ideal system that absorbs all thean ideal system that absorbs all theradiation incident on itradiation incident on it. The electromagnetic radiation emitted byelectromagnetic radiation emitted by
the black bodythe black body is called black body radiationblack body radiation.
The spectrum of electromagnetic radiation emitted by the black body(experimental result) is shown in figure 10.1a.
From the fig. 10.1a, theRayleigh-Jeans and Wien’stheories failed to fit theexperimental curve because
In 1900, Max Planck proposed his theory that is fit with theexperimental curve in fig. 10.1a at all wavelengths known as Planck’squantum theory.
The assumptions made by Planck in his theory are :
The e.m. radiation emitted by the black body is a discretediscrete
(separate) packets of energy(separate) packets of energy known as quantaquanta. This means the
energy of e.m. radiation is quantisedquantised. The energy size of the radiation dependeddepended on its frequencyfrequency.
According to this assumptions, the quantum E of the energy for
radiation of frequency f is given by
Since the speed of electromagnetic wave in a vacuum is ,
then eq. (10.1a) can be written as
From the eq. (10.1b), the quantum E of the energy for radiation is
inversely proportional to its wavelength.
hf E =
where constantPlanck :h J s10636 34 . −×=
(10.1a)(10.1a) PlanckPlanck’’ss
quantum theoryquantum theory
λ f c =
λ hc E = (10.1b)(10.1b)
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It is convenient to express many quantum energies in electronvolts.
The electronvoltelectronvolt ((eVeV)) is a unit of energyunit of energy that can be defined as thethe
kinetic energy gained by an electron in being accelerated by akinetic energy gained by an electron in being accelerated by apotential difference (voltage) of 1 voltpotential difference (voltage) of 1 volt.
Unit conversion :
In 1905, Albert Einstein extended Planck’s idea by proposing thatelectromagnetic radiation is also quantised. It consists of particle likepackets (bundles) of energy called photonsphotons of electromagneticradiation.
Photon is defined as a particle with zero mass consisting of aa particle with zero mass consisting of aquantum of electromagnetic radiation where its energy isquantum of electromagnetic radiation where its energy is
concentrated.concentrated.
A photon may also be regarded as a unit of energy equal to hf . Photons travel at the speed of lightspeed of light in a vacuum. They are required to
explain the photoelectric effect and other phenomena that require lightto have particle property.
10.3 The Photoelectric Effect Definition – is defined as the emission of electron from the surfaceemission of electron from the surface
of a metal when theof a metal when the e.me.m. radiation (light) of higher . radiation (light) of higher
frequency strikes its surface.frequency strikes its surface.
Figure 10.3a 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 the surface of an electron emitted from the surface of
the metal when light strikes its surface.the metal when light strikes its surface. The photoelectric effect can be studied through the experiment made
by Hertz in 1887.
--lightlight photoelectronphotoelectron
-- -- -- -- -- -- -- -- -- --
MetalMetal
Free electronsFree electronsFig. 10.3aFig. 10.3a
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10.3.1 Experiment of Photoelectric Effect
Figure 10.3b shows a schematic diagram of an experimentalarrangement for studying the photoelectric effect.
The set-up as follows :
Two conducting electrodes, the anode (positive electric potential)and the cathode (negative electric potential) are encased in anevacuated tube (vacuum).
The monochromatic light of known frequency and intensity areincident on the cathode.
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 a
photoelectric current or photocurrent I which is detected by the
galvanometer.
When the positive voltage (potential difference) is increased, morephotoelectrons reach the anode , hence the photoelectric currentalso increase.
As positive voltage becomes sufficiently large, the photoelectric
current reaches a maximum constant value I m, called saturationsaturation
currentcurrent.
Saturation current is defined as the maximum constant valuethe maximum constant value
of photocurrent when all the photoelectrons have reachedof photocurrent when all the photoelectrons have reachedthe anode.the anode.
If the positive voltage is gradually decreased, the photoelectric
current I
also decreases slowly. Even at zero voltage there are still
some photoelectrons with sufficient energy reach the anode and
the photoelectric current flows is I 0.
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Finally, when the voltage is made negative by reversing the power
supply terminal as shown in figure 10.3c, the photoelectric currentdecreases even further to very low values since mostphotoelectronsphotoelectrons are repelledrepelled by anodeanode which is now negativenegativeelectric potential.
As the potential of the anode becomes more negative, lessphotoelectrons 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) V s. Stopping potential is defined as the minimum value of the minimum value of
negative voltage when there are no photoelectronsnegative voltage when there are no photoelectrons
reaching the anode.reaching the anode.
anodeanodecathodecathode
photoelectronphotoelectronvacuumvacuum
glassglass
----
--
GG
VV
rheostatrheostatpower supplypower supply
e.me.m. radiation (light). radiation (light)
Fig. 10.3c : reversing power supply terminalFig. 10.3c : reversing power supply terminal
The potential energy U due to this retarding voltage V s now
equals the maximum kinetic energy K max of the photoelectron.
The variation of photoelectric current I as a function of the voltage
V can be shown through the graph in figure 10.3d.
max K U =
(10.3a)(10.3a)2
s mv
2
1eV =
m I
0 I
sV −
I current ric Photoelect ,
V Voltage,0
Fig. 10.3dFig. 10.3d
Before reversingBefore reversing
the terminalthe terminal
After After
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10.3.2 Einstein’s theory of Photoelectric Effect
A photon is a ‘‘packetpacket’’ of electromagnetic radiationelectromagnetic radiation with particleparticle--likelike
characteristiccharacteristic and carries energy E given by
and this energy is not spread out through the mediumnot spread out through the medium.
Work functionWork function W 0 of a metal
Is defined as the minimum energy of minimum energy of e.me.m. radiation required to. radiation required toemit an electron from the surface of the metalemit an electron from the surface of the metal.
It depends on the metal used.
Equation :
where f 0 is called threshold frequencythreshold frequency and is defined as the
minimum frequencyminimum frequency of of e.me.m. radiation required to emit an. radiation required to emit anelectron from the surface of the metalelectron from the surface of the metal.
where λ 0 is called threshold wavelengththreshold wavelength and is defined as
the maximum wavelengthmaximum wavelength of of e.me.m. radiation required to emit. radiation required to emit
an electron from the surface of the metal.an electron from the surface of the metal.
Table 10.3a shows the work functions of several elements.
Einstein’s photoelectric equation :
In photoelectric effect, Einstein summarizes that some of the
energyenergy E E imparted by a photonimparted by a photon is actually used to release anrelease an
electronelectron from the surface of a metal (i.e. to overcome the bindingforce) and that the rest appears as the maximum kinetic energymaximum kinetic energy
of the emitted electron (photoelectron). It given by
4.3Silver
5.1Gold
4.7Copper
2.7Sodium
4.3Aluminum
Work function (Work function (eVeV))ElementElement
Table 10.3aTable 10.3a
0W K E += max
2mv2
1 K =maxwhere hf E = and
0
2 W mv2
1hf += (10.3d)(10.3d) EinsteinEinstein’’ss
photoelectricphotoelectric eqeq..
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Since then eq. (10.3d) can be written as
Note :
First case : hf >W 0 or f >f 0
0 s W eV hf += (10.3e)(10.3e)
s
2
eV mv2
1
=
where voltagestopping: sV chargeelectrontheof magnitude:e
--hf hf vvmax max
--MetalMetalW W 00
Second case : hf=W 0 or f =f 0
--hf hf
v=0v=0
--MetalMetalW W 00
Third case : hf<W 0 or f <f 0
hf hf
--MetalMetalW W 00
Electron is emitted withElectron is emitted with
maximum kinetic energy.maximum kinetic energy.
K K max max
K K max max =0=0
Electron is emitted but maximumElectron is emitted but maximum
Variation of photoelectric current I with voltage V for the radiation of different intensitiesdifferent intensities but its frequency is fixedfrequency is fixed.
Explanation: From the experiment, the photoelectric currentphotoelectric current isdirectly proportionaldirectly proportional to the intensityintensity of the radiation asshown in figure 10.3f.
Intensity 2xIntensity 2x
m I
sV −
I current ric Photoelect ,
V Voltage,0
Fig. 10.3e : graphFig. 10.3e : graph
of of I I againstagainst V V Intensity 1xIntensity 1x
m I 2
I current ric Photoelect ,
intensityLight0 ×1
m I 2
×2
m I
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For the radiation of different frequenciesdifferent frequencies but its intensity is fixedintensity is fixed.
Explanation: From the Einstein’s photoelectric equation,
For the different metals of cathodedifferent metals of cathode but the intensity andintensity andfrequencyfrequency of the radiation are fixedfixed.
Explanation: From the Einstein’s photoelectric equation,
W W 0101
1 sV −
m I
I current ric Photoelect ,
V Voltage,0
Fig. 10.3g : graphFig. 10.3g : graph
of of I I againstagainst V V
2 sV −
W W 0202
W W 0202 >> W W 0101
0 s W eV hf +=
+
−=
e
hf W
e
1V 0 s
X C +=Y e
hf
0W
sV voltageStopping ,
0 hf E =01W
1 sV
02W
2 sV
Energy of a photonEnergy of a photon
inin e.me.m. radiation. radiation
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Variation of stopping voltage V s with frequency f of the radiation for different metals of cathodedifferent metals of cathode but the intensityintensity is fixedfixed.
Experimental observations deviate from classical predictions based onMaxwell’s e.m. theory. Hence the classical physics cannot explain thephenomenon of photoelectric effect.
The modern theory based on Einstein’s photon theory of light canexplain the phenomenon of photoelectric effect.
It is because Einstein postulated that light is quantized and light isemitted, transmitted and reabsorbed as photons.
Classical predictions Experimental
observation
Modern theory
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Example 8 :
In a photoelectric experiments, a graph of the light frequency f isplotted against the maximum kinetic energy K max of the photoelectronas shown in figure below.
Based on the graph, for the light frequency of 6.00 x 1014 Hz, calculate
a. the threshold frequency.
b. the maximum kinetic energy of the photoelectron.
c. the maximum velocity of the photoelectron.
(Given c = 3.00 x 108 m s-1, h = 6.63 x 10-34 J s , 1 eV=1.60 x 10-19 J,mass of electron m = 9.11 x 10-31 kg, e = 1.60 x 10-19 C)
Solution: f=6.00x1014 Hz a. By rearranging Einstein’s photoelectric equation,
From the graph, W 0=(2.0)(1.60x10-19 )=3.20x10-19 J The threshold frequency is
b. By applying the Einstein’s photoelectric equation, thus
c. The maximum velocity of the photoelectron is
0W K hf += max
max K W 0 −=
0W hf K −=max
Hz 10834 f 14
0 . ×=
=Y C +
WhenWhen f=0, f=0,
00 hf W =
0W 0h K −= )(max
Hz 10 f 14×
02.−)(max eV K
J 10787 K 20 .max
−×=0
W K hf +=max
1-5 sm10134v . ×=2mv2
1 K =max
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Example 9 : (exercise)
A photocell with cathode and anode made of the same metalconnected in a circuit as shown in the figure below. Monochromaticlight of wavelength 365 nm shines on the cathode and the photocurrent
I is measured for various values of voltage V across the cathode andanode. The result is shown in the graph.
a. Calculate the maximum kinetic energy of the 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.
(Given c = 3.00 x 108 m s-1, h = 6.63 x 10-34 J s , 1 eV=1.60 x 10-19 J,mass of electron m = 9.11 x 10-31 kg, e = 1.60 x 10-19 C)