chapter24 student

8/10/2019 Chapter24 Student

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PHYSICS CHAPTER 24

1

CHAPTER 24:

Quantization of light(3 Hours)


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PHYSICS CHAPTER 24

Learning Outcome:

At the end of this chapter, students should be able to:

a. Distinguish between Planks quantum theory and

classical theory of energy

b. Use Einsteins formulae for photon energy,

2

24.1 Plancks quantum theory (1/2 hour)


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PHYSICS CHAPTER 24

24.1 Plancks quantum theory

24.1.1 Classical theory of black body radiation

Black body is defined as an ideal system that absorbs all the

radiation incident on it. The electromagnetic (EM) radiation

emitted by the black body is called black body radiation.

From the black body experiment, the distribution of energy inblack body, Edepends only on the temperature, T.

If the temperature increases thus the energy of the black body

increases and vice versa.

3

(24.1)

constantsBoltzmann':Bkwhere

kelvininetemperatur:T


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PHYSICS CHAPTER 24

The spectrum of EM radiation emitted by the black body

(experimental result) is shown in Figure 24.1.

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. 4

Figure 24.1

Experimental

result

Rayleigh -Jeans

theoryWiens theory

Classical

physics


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PHYSICS CHAPTER 24

The Rayleigh-Jeans and Wiens theories failed to fit the

experimental curve because this two theories based on classical

ideas which are Energy of the EM radiation is not depend on its frequency

or wavelength.

Energy of the EM radiation is continuously.

24.1.2 Plancks quantum theory In 1900, Max Planck proposed his theory that is fit with the

experimental curve in Figure 24.1 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 discrete

(separate) packets of energy. Each packet is called a

quantum of energy. This means the energy of EM radiation

is quantised.

The energy size of the radiation depends on its frequency.

5


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PHYSICS CHAPTER 24

According to this assumptions, the quantum of the energy E

for radiation of frequency fis given by

Since the speed of EM radiation in a vacuum is

then eq. (24.2) can be written as

From eq. (24.3), the quantum of the energy Efor radiation is

inversely proportional to its wavelength.

6

where

(24.2)

(24.3)


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PHYSICS CHAPTER 24

It is convenient to express many quantum energies in electron-

volts.

The electron-volt (eV) is a unit of energy that can be definedas the kinetic energy gained by an electron in being

accelerated 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 photons of

electromagnetic radiation.

7

J101.60eV119

Note:

For EM radiation of n packets, the energyEn is given by

(24.4)

1,2,3,...numberreal: nwhere


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PHYSICS CHAPTER 24

24.1.3 Photon

Photon is defined as a particle with zero mass consisting of aquantum of electromagnetic radiation where its energy is

concentrated.

A photon may also be regarded as a unit of energy equal to

hf.

Photons travel at the speed of light in a vacuum. They arerequired to explain the photoelectric effect and other

phenomena that require light to have particle property.

Table 9.1 shows the differences between the photon andelectromagnetic wave.

8


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PHYSICS CHAPTER 24

EM Wave Photon

9

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 24.2a.

Its energy is discrete asshown in Figure 24.2b.

Table 24.1

2AI

fE

Photon

Figure 24.2a Figure 24.2b


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PHYSICS CHAPTER 24

10

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 =3.00108 m s1 and

Plancks constant, h =6.631034 J s)

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 24.1 :

m107409

fc f98 107401000.3

hfE 1434 1005.41063.6 E

101.60

1069.2

19

19

E


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PHYSICS CHAPTER 24

11

For a gamma radiation of wavelength 4.621012 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 =3.00108 m s1 and

Plancks constant, h =6.631034 J s)

Solution :

By applying the Plancks quantum theory, thus the energy of a

photon in electron-volt is

Example 24.2 :

m1062.4

12

hcE

12

834

1062.4

1000.31063.6

E

J1031.4 14E

101.60

1031.419

14


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PHYSICS CHAPTER 24

Learning Outcome:


a) Explain the phenomenon of photoelectric effect.

b) Define threshold frequency, work function and stopping

potential.

c) Describe and sketch diagram of the photoelectric effect

experimental set-up.

d) Explain the failure of wave theory to justify the

photoelectric effect.

12

24.2 The photoelectric effect (3 hours)

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PHYSICS CHAPTER 24

Learning Outcome ( Cont..):


c) Explain by using graph and equations the

observation of photoelectric effect experiment in

terms of the dependence of :

i. Kinetic energy of photoelectron on the frequency of

light

ii. Photoelectric current on the intensity of incident

light

iii. Work function and threshold frequency on the types

of metal surface

13


0s

2

max2

1hfhfeVmv


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PHYSICS CHAPTER 24

Learning Outcome ( Cont..):


f. Use Einsteins photoelectric equation

14


WhfeVK s max


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PHYSICS CHAPTER 24

24.2 The photoelectric effect

is defined as the emission of electron from the surfaceof a metal when the EM radiation (light) of higher frequency

strikes its surface.

Figure 24.3 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 the

surface of the metal when the EM radiation (light) strikes itssurface. 15

Figure 24.3

EM

radiation- photoelectron

- - - - - - - - - -

Metal

Free electrons


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PHYSICS CHAPTER 24

24.2.1 Photoelectric experiment

The photoelectric effect can be studied through the experiment

made by Franck Hertz in 1887.

Figure 24.4a shows a schematic diagram of an experimental

arrangement for studying the photoelectric effect.

16

--

-

EM radiation (light)

anodecathode

glass

rheostatpower supply

vacuumphotoelectron

Figure 24.4a

G

V


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PHYSICS CHAPTER 24

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 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 bythe galvanometer.

When the positive voltage (potential difference) across the

cathode and anode is increased, more photoelectrons reach the

anode , thus the photoelectric current increases.

17


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PHYSICS CHAPTER 24

As positive voltage becomes sufficiently large, the photoelectric

current reaches a maximum constant valueIm

, called

saturation current. Saturation current is defined as the maximum constant

value of photocurrent when all the photoelectrons havereached 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 24.4b, the

photoelectric current decreases even further to very low valuessince most photoelectrons are repelled by anode which isnow negative electric potential.

18


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PHYSICS CHAPTER 24

As the potential of the anode becomes more negative, less

photoelectrons reach the anode thus the photoelectric currentdrops until its value equals zero which the electric potential at

this moment is called stopping potential (voltage)Vs.

Stopping potential is defined as the minimum value of

negative voltage when there are no photoelectrons

reaching the anode. 19

Figure 24.4b: reversing power supply terminal

--

-

EM radiation (light)

anodecathode

glass

rheostatpower supply

vacuumphotoelectron

G

V


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PHYSICS CHAPTER 24

The potential energy Udue to this retarding voltage Vs

now

equals the maximum kinetic energyKmax

of the photoelectron.

The variation of photoelectric currentIas a function of the

voltage Vcan be shown through the graph in Figure 9.4c.

20

maxKU(24.5)

electrontheofmass:mwhere

mI

0I

sV

I,currentricPhotoelect

V,Voltage0

Before reversing the terminalAfterFigure 24.4c

Simulation 9.1
http://localhost/var/www/apps/conversion/tmp/scratch_7/AF_4009.swfhttp://localhost/var/www/apps/conversion/tmp/scratch_7/AF_4009.swf


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PHYSICS CHAPTER 24

24.2.2 Einsteins theory of photoelectric effect

A photon is a packet of electromagnetic radiation with

particle-like characteristic and carries the energyEgiven by

and this energy is not spread out through the medium.

Work function W0

of a metal

Is defined as the minimum energy of EM radiation requiredto emit an electron from the surface of the metal.

It depends on the metal used.

Its formulae is

wheref0

is called threshold frequency and is defined as the

minimum frequency of EM radiation required to emit an

electron from the surface of the metal. 21

hfE

min0 EW and 0min hfE

(24.6)


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PHYSICS CHAPTER 24

Since c=f then the eq. (24.6) can be written as

where 0

is called threshold wavelength and is defined as the

maximum wavelength of EM radiation required to emit anelectron from the surface of the metal.

Table 24.2 shows the work functions of several elements.

22

(24.7)

Element Work function (eV)

Aluminum 4.3

Sodium 2.3Copper 4.7

Gold 5.1

Silver 4.3

Table 24.2


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PHYSICS CHAPTER 24Einsteins photoelectric equation

In the photoelectric effect, Einstein summarizes that some of the

energy Eimparted by a photon is actually used to release anelectron from the surface of a metal (i.e. to overcome the

binding force) and that the rest appears as the maximum

kinetic energy of the emitted electron (photoelectron). It is

given by

where eq. (24.8) is known as Einsteins photoelectric equation.

SinceKmax

=eVsthen the eq. (24.8) can be written as

23

where and0max WKE hfE

(24.8)

(24.9)

voltagestopping:sVwhere

electronofchargeformagnitude:e


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PHYSICS CHAPTER 24

1st case:

24

Note:

OR0Whf 0ff

Electron is emitted with maximum

kinetic energy.-Metal

hf

0W

-maxv maxK

2nd case: OR0Whf 0ff

Electron is emitted but maximum

kinetic energy is zero.

- 0v 0max K

3rd case: OR0Whf 0ff

No electron is emitted.

-Metal

hf

0W

-Metal 0

W

hf

Figure 24.5a

Figure 24.5b

Figure 24.5c


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PHYSICS CHAPTER 24

25

Cadmium has a work function of 4.22 eV. Calculate

a. its threshold frequency,b. the maximum speed of the photoelectrons when the cadmium is

shined by UV radiation of wavelength 275 nm,

c. the stopping potential.

(Given c =3.00

108

m s1

, h =6.63

1034

J s, me=9.11

1031

kg ande=1.601019 C)

Solution :

a. By using the equation of the work function, thus

Example 24.3 :

J1075.61060.122.4 19190 W

00 hfW

03419 1063.61075.6 f


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PHYSICS CHAPTER 24

26

Solution :

b. Given

By applying the Einsteins photoelectric equation, thus

c. The stopping potential is given by

m10275 9

0

2

max2

1Wmv

hc

0max WKE

J1075.61060.122.4 19190 W

192max319834

1075.61011.92

1

10275

1000.31063.6

v

2

maxs2

1mveV

2

maxmax2

1mvK

2531s19 1026.31011.92

11060.1 V


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PHYSICS CHAPTER 24

27

A beam of white light containing frequencies between 4.00

10

14

Hzand 7.90 1014 Hz is incident on a sodium surface, which has a

work function of 2.28 eV.

a. Calculate the threshold frequency of the sodium surface.

b. What is the range of frequencies in this beam of light for which

electrons are ejected from the sodium surface?c. Determine the highest maximum kinetic energy of the

photoelectrons that are ejected from this surface.

(Given c =3.00108 m s1, h =6.631034 J s, me=9.111031 kg and

e=1.601019

C)

Example 24.4 :


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PHYSICS CHAPTER 24

28

Solution :

a. The threshold frequency is

b. The range of the frequencies that eject electrons is

c. For the highestKmax

, take

By applying the Einsteins photoelectric equation, thus

03419 1063.61065.3 f 00 hfW

J1065.31060.128.2 19190 W

Hz1090.7 14f

0

2

max2

1 Wmvhf

0max WKE

19max1434 1065.31090.71063.6 K


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PHYSICS CHAPTER 24

29

Exercise 24.1 :Given c =3.00108 m s1, h =6.631034 J s, m

e=9.111031 kg and

e=1.601019 C1. The energy of a photon from an electromagnetic wave is

2.25 eV

a. Calculate its wavelength.

b. If this electromagnetic wave shines on a metal, electrons

are emitted with a maximum kinetic energy of 1.10 eV.Calculate the work function of this metal in joules.

ANS. : 553 nm; 1.841019 J

2. In a photoelectric effect experiment it is observed that nocurrent flows when the wavelength of EM radiation is greaterthan 570 nm. Calculate

a. the work function of this material in electron-volts.

b. the stopping voltage required if light of wavelength 400 nmis used.

(Physics for scientists & engineers, 3rd edition, Giancoli, Q15,p.974)

ANS. : 2.18 eV; 0.92 V


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PHYSICS CHAPTER 24

30

Exercise 24.1 :

3. In an experiment on the photoelectric effect, the following data

were collected.

a. Calculate the maximum velocity of the photoelectrons

when the wavelength of the incident radiation is 350 nm.

b. Determine the value of the Planck constant from the above

data.ANS. : 7.73105 m s1; 6.721034 J s

Wavelength of EM

radiation, (nm)

Stopping potential,

Vs(V)

350 1.70

450 0.900


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PHYSICS CHAPTER 24

24.2.3 Graph of photoelectric experiment

Variation of photoelectric currentI

with voltageV

for the radiation of different intensities but its frequency is

fixed.

Reason:

From the experiment, the photoelectric current is directly

proportional to the intensity of the radiation as shown in

Figure 24.6b. 31

Intensity 2x

mI

I

V0sV

Intensity 1x

m2I

Figure 24.6a


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PHYSICS CHAPTER 24

for the radiation of different frequencies but its intensity is

fixed.

32

Figure 24.6b

I

intensityLight0 1

mIm2I

2

mI

Figure 24.7a

I

V

0s1V

f1

f2

s2V

f2> f

1


33/46

PHYSICS CHAPTER 24

Reason:

From the Einsteins photoelectric equation,

33

Figure 24.7b

0s WeVhf e

Wf

e

hV 0s

y xm c

e

W0

f,frequency

s,voltageStopping V

02

f

s2V

1f

s1V

IfVs=0, 0)0( Wehf

hfW 0 0f

0f


34/46

PHYSICS CHAPTER 24

For the different metals of cathode but the intensity and

frequency of the radiation are fixed.

Reason: From the Einsteins photoelectric equation,

34

Figure 24.8a

mI

s1V

01W

s2V

02W

W02> W

01

0s WeVhf

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 24.8b


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PHYSICS CHAPTER 24

Variation of stopping voltage Vs

with frequency fof the radiation

for different metals of cathode but the intensity is fixed.

Reason: Since W0=hf0 then

35

Figure 24.9W03 >W02 > W01

01f

W01

02f

W02

03f

W03

f

sV

0

00 fW

0s WeVhf e

Wf

e

hV 0s

y xm c

IfVs=0, 0)0( Wehf

hfW 0 0f

Threshold (cut-off)frequency

PHYSICS CHAPTER 24


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PHYSICS CHAPTER 24

24.2.4 Failure of wave theory of light

Table 24.3 shows the classical predictions (wave theory),

photoelectric experimental observation and modern theoryexplanation about photoelectric experiment.

36

Classical predictions Experimental

observation

Modern theory

Emission of

photoelectrons occurfor all frequencies of

light. Energy of light is

independent of

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 of

photoelectrons depend on

the light frequency

PHYSICS CHAPTER 24


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PHYSICS CHAPTER 24

37


observation

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 light is thenumber of photonsradiated per unit time on aunit surface area.

Based on the Einsteins

photoelectric equation:

The maximum kineticenergy of photoelectrondepends only on the lightfrequency and the workfunction. If the lightintensity is doubled, thenumber of electrons emittedalso doubled but themaximum kinetic energy

remains unchanged.

0WhfK max

PHYSICS CHAPTER 24


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PHYSICS CHAPTER 24

38


observation

Modern theory

Light energy is spreadover the wavefront, the

amount of energy

incident on any one

electron is small. An

electron must gathersufficient energy

before emission, hence

there is time interval

between absorption of

light energy and

emission. Time interval

increases if the light

intensity is low.

Photoelectrons areemitted from the

surface of the metal

almost

instantaneously

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 time

interval between

absorption of light energy

and emission.

PHYSICS CHAPTER 24


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PHYSICS CHAPTER 24

39


observation

Modern theory

Energy of lightdepends only on

amplitude ( or

intensity) and not on

frequency.

Energy of lightdepends on

frequency.

According to Plancksquantum theory which is

E=hf

Energy of light depends on

its frequency.

Table 24.3Note:

Experimental observations deviate from classical predictions based onwave theory of light. Hence the classical physics cannot explain thephenomenon of photoelectric effect.

The modern theory based on Einsteins 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.

PHYSICS CHAPTER 24


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PHYSICS CHAPTER 24

40

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 :

a. Wave theory predicts that the photoelectric effect should occur atany 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 energy

from 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 24.5 :

PHYSICS CHAPTER 24


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PHYSICS CHAPTER 24

41

In a photoelectric experiments, a graph of the light frequencyfisplotted against the maximum kinetic energyK

maxof the

photoelectron as shown in Figure 24.10.

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 =3.00108 m s1, h =6.631034 J s, me=9.111031 kg and

e=1.601019 C)

Example 24.6 :

Hz1014f

83.4

)eV(maxK0Figure 24.10

PHYSICS CHAPTER 24


42/46

PHYSICS CHAPTER 24

42

Solution :

a. By rearranging Einsteins photoelectric equation,

From the graph,

Therefore the threshold wavelength is given by

Hz1014.7 14f

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

PHYSICS CHAPTER 24


43/46

PHYSICS CHAPTER 24

43

Solution :

b. By using the Einsteins photoelectric equation, thus

Hz1014.7 14f

02

max21 Wmvhf

0

2

max2

1hfmvhf

02

max2

1ffhmv

1414342max31 1083.41014.71063.61011.92

1 v

PHYSICS CHAPTER 24


44/46

PHYSICS CHAPTER 24

44

Exercise 24.2 :

Given c =3.00108 m s1, h =6.631034 J s, me=9.111031 kg and

e=1.601019 C

1. A photocell with cathode and anode made of the same metalconnected in a circuit as shown in the Figure 24.11a.Monochromatic light of wavelength 365 nm shines on the

cathode and the photocurrentIis measured for various values

of voltage Vacross the cathode and anode. The result isshown in Figure 24.11b

365 nm

V

G 5

1

)nA(I

)V(V0

Figure 24.11a Figure 24.11b

PHYSICS CHAPTER 24


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PHYSICS CHAPTER 24

45

Exercise 24.2 :

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. : 1.60

10

19

J, 3.85

10

19

J; 1.57 V2. 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 emittedonly when 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, 7th edition, Nelkon&Parker, Q6, p.835)

PHYSICS CHAPTER 24


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PHYSICS CHAPTER 24

Next ChapterCHAPTER 25 :

Wave properties of particle

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