26771259 Matriculation Physics Quantization of Light

7/29/2019 26771259 Matriculation Physics Quantization of Light

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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

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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:

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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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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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
http://opt/scribd/conversion/tmp/scratch2518/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://opt/scribd/conversion/tmp/scratch2518/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://af_4009.html/


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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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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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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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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.


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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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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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

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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

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26771259 Matriculation Physics Quantization of Light