Chapter25 Student

8/10/2019 Chapter25 Student

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1

is aphenomenon where under certainphenomenon where under certain

circumstances a particle exhibits wavecircumstances a particle exhibits wave

properties and under other conditions aproperties and under other conditions a

wave exhibits properties of a particle.wave exhibits properties of a particle.

CHAPTER 25CHAPTER 25

!ave properties of particle!ave properties of particle

"2 Hours#"2 Hours#


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$earnin% &utcome

2

p

h=

25.' de (ro%lie wavelen%th "1hour#

At the end of this chapter) students should be able toAt the end of this chapter) students should be able to

"a# *tate"a# *tate wave+particle dualit,.wave+particle dualit,.

"b# -se de (ro%lie wvelen%th)"b# -se de (ro%lie wvelen%th)


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25.' de (ro%lie wavelen%th From the Plancks quantum theory, the energy of a photon is

given by

From the Einsteins special theory of relativity, the energy of a

photon is given by

By equating eqs. (1.1! an" (1.#!, hence

3

hcE= "'/.'#"'/.'#

2mcE="'/.2#"'/.2#

an" pmc=pcE=

pchc =

hp=particle aspectparticle aspect

wave aspectwave aspect"'/.0#"'/.0#

$here momentum:p


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From the eq. (1.%!, thus light has momentum an" e&hibitsparticle property. 'his also sho$ light is dualistic in naturedualistic in nature,

behaving in some situations li1e wavesome situations li1e wavean" in others li1e particleothers li1e particle"photon#"photon#an" this phenomenon is calle" wave particle dualit, ofwave particle dualit, of

li%htli%ht.

'able 1.1 sho$s the e&periment evi"ences to sho$ $aveparticle "uality of light.

Base" on the $ave particle "uality of light, ouis "e Brogliesuggeste" that matter such as electron and proton mi%ht alsoelectron and proton mi%ht also

have a dual naturehave a dual nature.

!ave Particle

)oungs "ouble slit

e&periment

Photoelectric effect

*iffraction e&periment +ompton effect

Table '/.'


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e propose" that for an, particle of momentumfor an, particle of momentumppshouldshould

have a wavelen%thhave a wavelen%th

%iven b,%iven b,

Eq. (1.-! is kno$n as de (ro%lie relation "principle#de (ro%lie relation "principle#.

'his $ave properties of matter is calle" de (ro%lie wavesde (ro%lie wavesor

matter wavesmatter waves.

'he "e Broglie relation $as confirme" in 1#/ $hen *avisson

an" 0ermer succee"e" in diffractin% electrondiffractin% electron$hich sho$s

that electrons have wave propertieselectrons have wave properties.

5

mv

h

p

h==

$here

"'/.#"'/.#

hwavelengtBrogliede:

particleaofmass:mparticleaofvelocity:v

constantsPlanck':h


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6

n a photoelectric effect e&periment, a light source of

$avelength 22 nm is inci"ent on a so"ium surface. *etermine themomentum an" the energy of a photon use".

(0iven the spee" of light in the vacuum, c3%.14m s1 an"

Plancks constant, h35.5%1%-6 s!

*olution *olution By using the "e Broglie relation, thus

an" the energy of the photon is given by

Example 25.'

m10550

9

=

p

h=

p

!9 10"#"10550

=

hcE=

( )( )9

$!

10550

1000#10"#"

=E


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7

+alculate the "e Broglie $avelength for

a. a 7ogger of mass // kg runs $ith at spee" of -.1 m s1.

b. an electron of mass .111%1 kg moving at %.#212m s1.

(0iven the Plancks constant, h35.5%1%-6 s!

*olution *olution

a. 0iven'he "e Broglie $avelength for the 7ogger is

b. 0iven

'he "e Broglie $avelength for the electron is

Example 25.2

1

sm1#!kg%&&

== vm

mv

h=

( ) ( )1#!&&10"#" !

=

151 sm1025#kg%1011#9 == vm

( )( )51

!

1025#1011#9

10"#"

=


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8

8n electron an" a proton have the same spee".

a. 9hich has the longer "e Broglie $avelength: E&plain.

b. +alculate the ratio of e' p.

(0iven c3%.14m s1, h35.5%1%-6 s, me3.111%1kg,

mp31.5/1#/kg an" e31.511+!

*olution *olution

a. From "e Broglie relation,

the "e Broglie wavelen%th is inversel, proportional to thewavelen%th is inversel, proportional to themassmass of the particle. ;ince the electron li%hter than the masselectron li%hter than the mass

of the protonof the protontherefore the electron has the lon%er de (ro%lieelectron has the lon%er de (ro%lie

wavelen%thwavelen%th.

Example 25.0

vvv == pe

mv

h=


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9

*olution *olution

'herefore the ratio of their "e Broglie $avelengths is

e

p

m

m=

1

2&

1011#910"

=

vvv == pe

=

vm

h

vm

h

p

e

p

e


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$earnin% &utcome

At the end of this chapter) students should be able toAt the end of this chapter) students should be able to

3escribe3escribethe observations ofthe observations of electron diffraction.inelectron diffraction.in

3avisson+4ermer experiment.3avisson+4ermer experiment. ExplainExplainthe wave behaviour of electron in an electronthe wave behaviour of electron in an electron

microscopemicroscope

*tate the advanta%es of electron microscope compared*tate the advanta%es of electron microscope compared

to optical microscope.to optical microscope.

"Relate de (ro%lie wavelen%th of electron with the"Relate de (ro%lie wavelen%th of electron with theresolvin% power of the electron microscope#resolvin% power of the electron microscope#

10

25.2 Electron diffraction "1hour#


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25.2.' 3avisson+4ermer experiment

Figure 1.1 sho$s a tube for "emonstrating electron "iffractionby *avisson an" 0ermer.

8 beam of accelerate" electrons strikes on a layer of graphite$hich is e&tremely thin an" a "iffraction pattern consisting ofrings is seen on the tube face.

screen "iffraction

pattern

electron

"iffraction

graphite film

ano"e

catho"e

6i%ure '/.' electron diffraction tube


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'his e&periment proves that the "e Broglie relation $as right

an" the $avelength of the electron is given by

f the velocit, of electrons is increasedvelocit, of electrons is increased, the rin%srin%sare seen tobecome narrowernarrowersho$ing that the wavelen%th ofwavelen%th of

electrons decreaseselectrons decreases$ith increasin% velocit,increasin% velocit,as pre"icte"by "e broglie (eq. 1.2!.

'he velocity of electrons are controlle" by the applie" voltage V

across ano"e an" catho"e i.e.

12

mvh=

$here electronanofmass:m

"'/.5#"'/.5#

electronanofvelocity:v

KU= 22

1mveV =

m

eVv

2= "'/.#"'/.#


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By substituting the eq. (1.5! into eq. (1.2!, thus

13

=m

eVm

h

2

meV

h

2= "'/.7#"'/.7#8ote8ote

Electrons are not the only particles $hich behave as $aves.

'he diffraction effects are lessdiffraction effects are lessnoticeable $ith more massivemassive

particlesparticlesbecause their momentatheir momentaare generally much hi%hermuch hi%heran"so the wavelen%thwavelen%this correspon"ingly shortershorter.

*iffraction of the particles are observe" $hen the wavelen%th is ofwavelen%th is of

the same order as the spacin% between plane of the atomthe same order as the spacin% between plane of the atom.


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14

a. 8n electron is accelerate" from rest through a potential

"ifferenceof #

the photon.

(0iven c3%.14m s1, h35.5%1%-6 s, me3.111%1kg an"

e31.511+!

*olution *olution

a. 0iven

'he "e Broglie $avelength for the electron is

Example 25.

(2000=V

meV

h

2= ( )( )200010"0#11011#92

10"#"

191

!

=


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15

*olution *olution

b. 0iven

For an electron,

ts momentum is

an" its energy is

m1021#0 9pe==

e

hp

=

9

!

1021#0

10"#"

=p12! smkg101"# =p

2e2

1vmK=

( )( )122!

1011#92

101"#

=

19

1$

10"0#1

10!$#5

=

an"em

pv=

e

2

2m

p=


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16

*olution *olution

b. 0iven

For a photon,

ts momentum is

an" its energy is

m1021#0 9pe==

12! smkg101"# =p

p

hcE=

( )( )9

$!

1021#0

1000#10"#"

=

19

1"

10"0#1

10!

=


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17

+ompare the "e Broglie $avelength of an electron an" a proton if

they have the same kinetic energy.(0iven c3%.14m s1, h35.5%1%-6 s, me3.111

%1kg,

mp31.5/1#/kg an" e31.511+!

*olution *olution

By using the "e Broglie $avelength formulae, thus

Example 25.5

KKK == pe

meV

h

2=

mK

h

2

=

an" KeV=


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18

*olution *olution

'herefore the ratio of their "e Broglie $avelengths is

KKK == pe

=

Km

h

Km

h

e

p

p

e

2

2

e

p

m

m=

1

2&

1011#9

10"

=


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25.2.2 Electron microscope 8 practical "evice that relies on the $ave properties of electrons

is electron microscope.

t is similar to optical compoun" microscope in many aspects.

'he advanta%eadvanta%eof the electron microscope over the optical

microscope is the resolvin% powerresolvin% powerof the electronelectron

microscopemicroscopeis much hi%hermuch hi%herthan that of an opticalopticalmicroscopemicroscope.

'his is becausebecausethe electrons can be accelerate" to a very high

kinetic energy giving them a ver, short wavelen%thver, short wavelen%th

typically 1 times shorter thanthanthose of visible li%htvisible li%ht.

'herefore the diffraction effectdiffraction effectof electronselectronsas a $ave ismuch lessmuch lessthan that of li%htli%ht.

8s a result, electron microscopes are able to "istinguish "etails

about 1 times smaller.

19


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n operation, a beam of electrons falls on a thin slice of sample.

'he sample (specimen! to be e&amine" must be very thin (a fe$

micrometres! to minimi=e the effects such as absorption orscattering of the electrons.

'he electron beam is controlle" by electrostatic or ma%neticelectrostatic or ma%netic

lenseslensesto focusfocusthe beambeamto an image.

'he image is forme" on a fluorescent screen.

'here are t$o types of electron microscopes>

l TransmissionTransmission? pro"uces a two+dimensional ima%etwo+dimensional ima%e.

l *cannin%*cannin%? pro"uces images $ith a three+dimensionalthree+dimensional

9ualit,9ualit,.

Figures 1.# an" 1.% are "iagram of the transmission electronmicroscope an" the scanning electron microscope.

20


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216i%ure '/.26i%ure '/.2 6i%ure '/.06i%ure '/.0


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22

Exercise 25.' 0iven c3%.14m s1, h35.5%1%-6 s, me3.111

%1kg an"

e31.511+

1. a. 8n electron an" a photon have the same $avelengthsan" the total energy of the electron is 1. @e

Chapter25 Student

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