SlideShare une entreprise Scribd logo
1  sur  4
Télécharger pour lire hors ligne
APHO II 2001 Theoretical Question 3 2013/09/28 00:19 A9/P9 p. 1 / 4
[Solution] Theoretical Question 3
Thermal Vibration of Surface Atoms
(1) (a) The wavelength of the incident electron is

A53.11053.1
0.641060.11011.92
1063.6
2
10
1931
34
=×=
×××××
×
=
==
−
−−
−
m
meV
h
p
h
λ
(b) Consider the interference between the atomic rows on the surface as shown in
Fig. 3c.
The path difference between electron beam 1 and 2 is
λφφ nb =−=∆ )sin(sin 
Given 
 0.15=φ , λ=

A35.1 and

A77.2
2
92.3
2
===
a
b , two solutions
are possible.
(i) When n = 0, φ φ= o = 15.0
(Answer 1)
(ii) When n =1
53.11)15sin(sin77.2 ×=−=∆ 
 φ
812.0
77.2
72.053.1
sin =
+
=φ
[Solution] (continued) Theoretical Question 3
Vibration of Surface Atoms

3.54=φ (Answer 2)
1
Fig.3c
φ
φ
e-
1
2
[011]b
e-
φ
φ
n

n

APHO II 2001 Theoretical Question 3 2013/09/28 00:19 A9/P9 p. 2 / 4
For n = 2, no solution exists as 531215772 .)sin(sin. ×=−= 
 φ∆ and φsin > 1.
(2) 〉⋅〈−= 2
0 )Ku(expII

∆
For the specularly reflected beam, we have from Fig. 3d
θcos2KKKK =−′=∆

xˆ
where xˆ is the unit vector in the direction of the surface normal. Take the x-
component of u

, we then obtain
><−>⋅<−
== )t(ucosKcosK)t(u xx
eIeII
222222
4
0
4
0
θθ (2)
The vibration in the direction of the surface normal of the surface atoms is
simple harmonic, take
tAtux ωcos)( =
 22
11 2
0 0
2
2222 AA
dttcosAdtu)t(ux =⋅===〉〈 ∫ ∫
τ
τ
ω
ττ
τ τ
∴ 〉〈= )(2
22
tuA x
The total energy E is thus given by
><⋅== )(2
2
1
2
1 22
tuCCAE x = >< )(
2
tuC x
= ><′ )(
22
tum xω
2
Fig. 3d
surface
θK

K

′
K∆
APHO II 2001 Theoretical Question 3 2013/09/28 00:19 A9/P9 p. 3 / 4
[Solution] (continued) Theoretical Question 3
Vibration of Surface Atoms
Therefore, one obtains
>< )(
2
tux
= E / ( 2
ωm′ )
Tku'mE Bx =><=
22
ω
where 'm is the mass of the atom. From either of the above two equations,
one then has the following equality
222
2
4 fm
Tk
m
Tk
u BB
x
πω ′
=
′
>=< (3)
From eq. (3) and eq. (2), one obtains
22
22
4
cos4
0
fm
Tk
K B
eII π
θ
′
−
=
where
λ
ππ 22
==
h
p
K . Accordingly,
TM
T
fm
k
eIeII
B
′−
−
== 0
'
cos4
0
22
2
λ
θ
(4)
and
TM
I
I
n ′−=
0

From the plot of
0I
I
n versus T,one obtains the slope
22
2
cos4
λ
θ
fm
k
M B
′
=′ (5)
The slope of the curve can be estimated from Fig. 3b and leads to the result
3
103.2 −
×=′M .
Using the following data in Eq.(5),
K/J.kB
23
10381 −
×=
m10
1053.1 −
×=λ
m′ = 195.1 3
10−
× /(6.02 23
10× ) = 3.24 25
10−
× kg/atom
[Solution] (continued) Theoretical Question 3
Vibration of Surface Atoms
3
APHO II 2001 Theoretical Question 3 2013/09/28 00:19 A9/P9 p. 4 / 4
one finds
2102
23
3
223
3
10531
10026
101195
15103814
1032
).(f
.
.
cos.
.
−
−
−
−
×××
×
×
⋅××
=×

The solution for frequency is then
242
100.3 ×=f (new) Hzf 12
107.1 ×=⇒ Answer (a)
From 22
2
4 f'm
Tk
u B
x
π
=>< , KT 300= , one finally obtains
222
242
23
3
23
2
101.1
100.34
1002.6
101.195
3001038.1
mux
−
−
−
×=
×××
×
×
⋅×
>=<
π
(new)
and

A10.0100.1 112
=×=>< −
mux
(new)
Ans
4

Contenu connexe

Tendances

Capitulo 9, 7ma edición
Capitulo 9, 7ma ediciónCapitulo 9, 7ma edición
Capitulo 9, 7ma ediciónSohar Carr
 
(Neamen)solution manual for semiconductor physics and devices 3ed
(Neamen)solution manual for semiconductor physics and devices 3ed(Neamen)solution manual for semiconductor physics and devices 3ed
(Neamen)solution manual for semiconductor physics and devices 3edKadu Brito
 
Capitulo 6, 7ma edición
Capitulo 6, 7ma ediciónCapitulo 6, 7ma edición
Capitulo 6, 7ma ediciónSohar Carr
 
Stress&strain part 2
Stress&strain part 2Stress&strain part 2
Stress&strain part 2AHMED SABER
 
Capitulo 3, 7ma edición
Capitulo 3, 7ma ediciónCapitulo 3, 7ma edición
Capitulo 3, 7ma ediciónSohar Carr
 
L5 determination of natural frequency & mode shape
L5 determination of natural frequency & mode shapeL5 determination of natural frequency & mode shape
L5 determination of natural frequency & mode shapeSam Alalimi
 
Kites team l5
Kites team l5Kites team l5
Kites team l5aero103
 
solution-manual-3rd-ed-metal-forming-mechanics-and-metallurgy-chapter-1-3
 solution-manual-3rd-ed-metal-forming-mechanics-and-metallurgy-chapter-1-3 solution-manual-3rd-ed-metal-forming-mechanics-and-metallurgy-chapter-1-3
solution-manual-3rd-ed-metal-forming-mechanics-and-metallurgy-chapter-1-3dean129
 
Magnetic Materials Assignment Help
Magnetic Materials Assignment HelpMagnetic Materials Assignment Help
Magnetic Materials Assignment HelpEdu Assignment Help
 
Cubic Spline Interpolation
Cubic Spline InterpolationCubic Spline Interpolation
Cubic Spline InterpolationVARUN KUMAR
 
Cap 03
Cap 03Cap 03
Cap 03UO
 

Tendances (20)

Capitulo 9, 7ma edición
Capitulo 9, 7ma ediciónCapitulo 9, 7ma edición
Capitulo 9, 7ma edición
 
Deflection and member deformation
Deflection and member deformationDeflection and member deformation
Deflection and member deformation
 
(Neamen)solution manual for semiconductor physics and devices 3ed
(Neamen)solution manual for semiconductor physics and devices 3ed(Neamen)solution manual for semiconductor physics and devices 3ed
(Neamen)solution manual for semiconductor physics and devices 3ed
 
Capitulo 6, 7ma edición
Capitulo 6, 7ma ediciónCapitulo 6, 7ma edición
Capitulo 6, 7ma edición
 
Stress&strain part 2
Stress&strain part 2Stress&strain part 2
Stress&strain part 2
 
Capitulo 3, 7ma edición
Capitulo 3, 7ma ediciónCapitulo 3, 7ma edición
Capitulo 3, 7ma edición
 
Velocity of Neutrino
Velocity of NeutrinoVelocity of Neutrino
Velocity of Neutrino
 
Multi degree of freedom systems
Multi degree of freedom systemsMulti degree of freedom systems
Multi degree of freedom systems
 
Solution manual 4 6
Solution manual 4 6Solution manual 4 6
Solution manual 4 6
 
L5 determination of natural frequency & mode shape
L5 determination of natural frequency & mode shapeL5 determination of natural frequency & mode shape
L5 determination of natural frequency & mode shape
 
Solution manual 1 3
Solution manual 1 3Solution manual 1 3
Solution manual 1 3
 
H.w. #7
H.w. #7H.w. #7
H.w. #7
 
Kites team l5
Kites team l5Kites team l5
Kites team l5
 
solution-manual-3rd-ed-metal-forming-mechanics-and-metallurgy-chapter-1-3
 solution-manual-3rd-ed-metal-forming-mechanics-and-metallurgy-chapter-1-3 solution-manual-3rd-ed-metal-forming-mechanics-and-metallurgy-chapter-1-3
solution-manual-3rd-ed-metal-forming-mechanics-and-metallurgy-chapter-1-3
 
Problemas estatica.
Problemas estatica.Problemas estatica.
Problemas estatica.
 
Magnetic Materials Assignment Help
Magnetic Materials Assignment HelpMagnetic Materials Assignment Help
Magnetic Materials Assignment Help
 
H#8
H#8H#8
H#8
 
Cubic Spline Interpolation
Cubic Spline InterpolationCubic Spline Interpolation
Cubic Spline Interpolation
 
Cap 03
Cap 03Cap 03
Cap 03
 
Undeterminate problems
Undeterminate problemsUndeterminate problems
Undeterminate problems
 

Similaire à Solution 3 a ph o 2

Dynamics of structures 5th edition chopra solutions manual
Dynamics of structures 5th edition chopra solutions manualDynamics of structures 5th edition chopra solutions manual
Dynamics of structures 5th edition chopra solutions manualSchneiderxds
 
Pages from Rao S.S. - Mechanical vibrations in SI units-Pearson (2018).pptx
Pages from Rao S.S. - Mechanical vibrations in SI units-Pearson (2018).pptxPages from Rao S.S. - Mechanical vibrations in SI units-Pearson (2018).pptx
Pages from Rao S.S. - Mechanical vibrations in SI units-Pearson (2018).pptxebookslist1
 
Dynamic response to harmonic excitation
Dynamic response to harmonic excitationDynamic response to harmonic excitation
Dynamic response to harmonic excitationUniversity of Glasgow
 
Aircraft Structures for Engineering Students 5th Edition Megson Solutions Manual
Aircraft Structures for Engineering Students 5th Edition Megson Solutions ManualAircraft Structures for Engineering Students 5th Edition Megson Solutions Manual
Aircraft Structures for Engineering Students 5th Edition Megson Solutions ManualRigeler
 
Dynamic response of oscillators to general excitations
Dynamic response of oscillators to general excitationsDynamic response of oscillators to general excitations
Dynamic response of oscillators to general excitationsUniversity of Glasgow
 
JEE Main Mock Test - Physics
JEE Main Mock Test - Physics JEE Main Mock Test - Physics
JEE Main Mock Test - Physics Ednexa
 
Deformation of structures
Deformation of structuresDeformation of structures
Deformation of structuresAhmed zubydan
 

Similaire à Solution 3 a ph o 2 (15)

Dynamics of structures 5th edition chopra solutions manual
Dynamics of structures 5th edition chopra solutions manualDynamics of structures 5th edition chopra solutions manual
Dynamics of structures 5th edition chopra solutions manual
 
Pages from Rao S.S. - Mechanical vibrations in SI units-Pearson (2018).pptx
Pages from Rao S.S. - Mechanical vibrations in SI units-Pearson (2018).pptxPages from Rao S.S. - Mechanical vibrations in SI units-Pearson (2018).pptx
Pages from Rao S.S. - Mechanical vibrations in SI units-Pearson (2018).pptx
 
Solution 3 i ph o 34
Solution 3 i ph o 34Solution 3 i ph o 34
Solution 3 i ph o 34
 
Dynamic response to harmonic excitation
Dynamic response to harmonic excitationDynamic response to harmonic excitation
Dynamic response to harmonic excitation
 
Solution 3 a ph o 8
Solution 3 a ph o 8 Solution 3 a ph o 8
Solution 3 a ph o 8
 
Aircraft Structures for Engineering Students 5th Edition Megson Solutions Manual
Aircraft Structures for Engineering Students 5th Edition Megson Solutions ManualAircraft Structures for Engineering Students 5th Edition Megson Solutions Manual
Aircraft Structures for Engineering Students 5th Edition Megson Solutions Manual
 
Problem and solution a ph o 6
Problem and solution a ph o 6Problem and solution a ph o 6
Problem and solution a ph o 6
 
Dynamic response of oscillators to general excitations
Dynamic response of oscillators to general excitationsDynamic response of oscillators to general excitations
Dynamic response of oscillators to general excitations
 
Base excitation of dynamic systems
Base excitation of dynamic systemsBase excitation of dynamic systems
Base excitation of dynamic systems
 
Electrostatic10 end
Electrostatic10 endElectrostatic10 end
Electrostatic10 end
 
Solution a ph o 3
Solution a ph o 3Solution a ph o 3
Solution a ph o 3
 
Sect5 4
Sect5 4Sect5 4
Sect5 4
 
JEE Main Mock Test - Physics
JEE Main Mock Test - Physics JEE Main Mock Test - Physics
JEE Main Mock Test - Physics
 
Deformation of structures
Deformation of structuresDeformation of structures
Deformation of structures
 
Ch03 9
Ch03 9Ch03 9
Ch03 9
 

Plus de eli priyatna laidan

Up ppg daljab latihan soal-pgsd-set-2
Up ppg daljab latihan soal-pgsd-set-2Up ppg daljab latihan soal-pgsd-set-2
Up ppg daljab latihan soal-pgsd-set-2eli priyatna laidan
 
Soal up sosial kepribadian pendidik 5
Soal up sosial kepribadian pendidik 5Soal up sosial kepribadian pendidik 5
Soal up sosial kepribadian pendidik 5eli priyatna laidan
 
Soal up sosial kepribadian pendidik 4
Soal up sosial kepribadian pendidik 4Soal up sosial kepribadian pendidik 4
Soal up sosial kepribadian pendidik 4eli priyatna laidan
 
Soal up sosial kepribadian pendidik 3
Soal up sosial kepribadian pendidik 3Soal up sosial kepribadian pendidik 3
Soal up sosial kepribadian pendidik 3eli priyatna laidan
 
Soal up sosial kepribadian pendidik 2
Soal up sosial kepribadian pendidik 2Soal up sosial kepribadian pendidik 2
Soal up sosial kepribadian pendidik 2eli priyatna laidan
 
Soal up sosial kepribadian pendidik 1
Soal up sosial kepribadian pendidik 1Soal up sosial kepribadian pendidik 1
Soal up sosial kepribadian pendidik 1eli priyatna laidan
 
Soal sospri ukm ulang i 2017 1 (1)
Soal sospri ukm ulang i 2017 1 (1)Soal sospri ukm ulang i 2017 1 (1)
Soal sospri ukm ulang i 2017 1 (1)eli priyatna laidan
 
Soal perkembangan kognitif peserta didik
Soal perkembangan kognitif peserta didikSoal perkembangan kognitif peserta didik
Soal perkembangan kognitif peserta didikeli priyatna laidan
 
Soal latihan utn pedagogik plpg 2017
Soal latihan utn pedagogik plpg 2017Soal latihan utn pedagogik plpg 2017
Soal latihan utn pedagogik plpg 2017eli priyatna laidan
 
Bank soal pedagogik terbaru 175 soal-v2
Bank soal pedagogik terbaru 175 soal-v2Bank soal pedagogik terbaru 175 soal-v2
Bank soal pedagogik terbaru 175 soal-v2eli priyatna laidan
 

Plus de eli priyatna laidan (20)

Up ppg daljab latihan soal-pgsd-set-2
Up ppg daljab latihan soal-pgsd-set-2Up ppg daljab latihan soal-pgsd-set-2
Up ppg daljab latihan soal-pgsd-set-2
 
Soal utn plus kunci gurusd.net
Soal utn plus kunci gurusd.netSoal utn plus kunci gurusd.net
Soal utn plus kunci gurusd.net
 
Soal up sosial kepribadian pendidik 5
Soal up sosial kepribadian pendidik 5Soal up sosial kepribadian pendidik 5
Soal up sosial kepribadian pendidik 5
 
Soal up sosial kepribadian pendidik 4
Soal up sosial kepribadian pendidik 4Soal up sosial kepribadian pendidik 4
Soal up sosial kepribadian pendidik 4
 
Soal up sosial kepribadian pendidik 3
Soal up sosial kepribadian pendidik 3Soal up sosial kepribadian pendidik 3
Soal up sosial kepribadian pendidik 3
 
Soal up sosial kepribadian pendidik 2
Soal up sosial kepribadian pendidik 2Soal up sosial kepribadian pendidik 2
Soal up sosial kepribadian pendidik 2
 
Soal up sosial kepribadian pendidik 1
Soal up sosial kepribadian pendidik 1Soal up sosial kepribadian pendidik 1
Soal up sosial kepribadian pendidik 1
 
Soal up akmal
Soal up akmalSoal up akmal
Soal up akmal
 
Soal tkp serta kunci jawabannya
Soal tkp serta kunci jawabannyaSoal tkp serta kunci jawabannya
Soal tkp serta kunci jawabannya
 
Soal tes wawasan kebangsaan
Soal tes wawasan kebangsaanSoal tes wawasan kebangsaan
Soal tes wawasan kebangsaan
 
Soal sospri ukm ulang i 2017 1 (1)
Soal sospri ukm ulang i 2017 1 (1)Soal sospri ukm ulang i 2017 1 (1)
Soal sospri ukm ulang i 2017 1 (1)
 
Soal perkembangan kognitif peserta didik
Soal perkembangan kognitif peserta didikSoal perkembangan kognitif peserta didik
Soal perkembangan kognitif peserta didik
 
Soal latihan utn pedagogik plpg 2017
Soal latihan utn pedagogik plpg 2017Soal latihan utn pedagogik plpg 2017
Soal latihan utn pedagogik plpg 2017
 
Rekap soal kompetensi pedagogi
Rekap soal kompetensi pedagogiRekap soal kompetensi pedagogi
Rekap soal kompetensi pedagogi
 
Bank soal pedagogik terbaru 175 soal-v2
Bank soal pedagogik terbaru 175 soal-v2Bank soal pedagogik terbaru 175 soal-v2
Bank soal pedagogik terbaru 175 soal-v2
 
Bank soal ppg
Bank soal ppgBank soal ppg
Bank soal ppg
 
Soal cpns-paket-17
Soal cpns-paket-17Soal cpns-paket-17
Soal cpns-paket-17
 
Soal cpns-paket-14
Soal cpns-paket-14Soal cpns-paket-14
Soal cpns-paket-14
 
Soal cpns-paket-13
Soal cpns-paket-13Soal cpns-paket-13
Soal cpns-paket-13
 
Soal cpns-paket-12
Soal cpns-paket-12Soal cpns-paket-12
Soal cpns-paket-12
 

Dernier

Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxChapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxesiyasmengesha
 
Plano de marketing- inglês em formato ppt
Plano de marketing- inglês  em formato pptPlano de marketing- inglês  em formato ppt
Plano de marketing- inglês em formato pptElizangelaSoaresdaCo
 
Intellectual Property Licensing Examples
Intellectual Property Licensing ExamplesIntellectual Property Licensing Examples
Intellectual Property Licensing Examplesamberjiles31
 
Boat Trailers Market PPT: Growth, Outlook, Demand, Keyplayer Analysis and Opp...
Boat Trailers Market PPT: Growth, Outlook, Demand, Keyplayer Analysis and Opp...Boat Trailers Market PPT: Growth, Outlook, Demand, Keyplayer Analysis and Opp...
Boat Trailers Market PPT: Growth, Outlook, Demand, Keyplayer Analysis and Opp...IMARC Group
 
To Create Your Own Wig Online To Create Your Own Wig Online
To Create Your Own Wig Online  To Create Your Own Wig OnlineTo Create Your Own Wig Online  To Create Your Own Wig Online
To Create Your Own Wig Online To Create Your Own Wig Onlinelng ths
 
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessQ2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessAPCO
 
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfGraham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfAnhNguyen97152
 
Developing Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursDeveloping Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursKaiNexus
 
Data skills for Agile Teams- Killing story points
Data skills for Agile Teams- Killing story pointsData skills for Agile Teams- Killing story points
Data skills for Agile Teams- Killing story pointsyasinnathani
 
A flour, rice and Suji company in Jhang.
A flour, rice and Suji company in Jhang.A flour, rice and Suji company in Jhang.
A flour, rice and Suji company in Jhang.mcshagufta46
 
Live-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarLive-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarNathanielSchmuck
 
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003believeminhh
 
Cracking the ‘Business Process Outsourcing’ Code Main.pptx
Cracking the ‘Business Process Outsourcing’ Code Main.pptxCracking the ‘Business Process Outsourcing’ Code Main.pptx
Cracking the ‘Business Process Outsourcing’ Code Main.pptxWorkforce Group
 
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...Brian Solis
 
Amazon ppt.pptx Amazon about the company
Amazon ppt.pptx Amazon about the companyAmazon ppt.pptx Amazon about the company
Amazon ppt.pptx Amazon about the companyfashionfound007
 
Team B Mind Map for Organizational Chg..
Team B Mind Map for Organizational Chg..Team B Mind Map for Organizational Chg..
Team B Mind Map for Organizational Chg..dlewis191
 
Lecture_6.pptx English speaking easyb to
Lecture_6.pptx English speaking easyb toLecture_6.pptx English speaking easyb to
Lecture_6.pptx English speaking easyb toumarfarooquejamali32
 
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHelene Heckrotte
 
Borderless Access - Global B2B Panel book-unlock 2024
Borderless Access - Global B2B Panel book-unlock 2024Borderless Access - Global B2B Panel book-unlock 2024
Borderless Access - Global B2B Panel book-unlock 2024Borderless Access
 

Dernier (20)

Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptxChapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
Chapter_Five_The_Rural_Development_Policies_and_Strategy_of_Ethiopia.pptx
 
Plano de marketing- inglês em formato ppt
Plano de marketing- inglês  em formato pptPlano de marketing- inglês  em formato ppt
Plano de marketing- inglês em formato ppt
 
Intellectual Property Licensing Examples
Intellectual Property Licensing ExamplesIntellectual Property Licensing Examples
Intellectual Property Licensing Examples
 
Boat Trailers Market PPT: Growth, Outlook, Demand, Keyplayer Analysis and Opp...
Boat Trailers Market PPT: Growth, Outlook, Demand, Keyplayer Analysis and Opp...Boat Trailers Market PPT: Growth, Outlook, Demand, Keyplayer Analysis and Opp...
Boat Trailers Market PPT: Growth, Outlook, Demand, Keyplayer Analysis and Opp...
 
To Create Your Own Wig Online To Create Your Own Wig Online
To Create Your Own Wig Online  To Create Your Own Wig OnlineTo Create Your Own Wig Online  To Create Your Own Wig Online
To Create Your Own Wig Online To Create Your Own Wig Online
 
WAM Corporate Presentation Mar 25 2024.pdf
WAM Corporate Presentation Mar 25 2024.pdfWAM Corporate Presentation Mar 25 2024.pdf
WAM Corporate Presentation Mar 25 2024.pdf
 
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for BusinessQ2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
Q2 2024 APCO Geopolitical Radar - The Global Operating Environment for Business
 
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdfGraham and Doddsville - Issue 1 - Winter 2006 (1).pdf
Graham and Doddsville - Issue 1 - Winter 2006 (1).pdf
 
Developing Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, OursDeveloping Coaching Skills: Mine, Yours, Ours
Developing Coaching Skills: Mine, Yours, Ours
 
Data skills for Agile Teams- Killing story points
Data skills for Agile Teams- Killing story pointsData skills for Agile Teams- Killing story points
Data skills for Agile Teams- Killing story points
 
A flour, rice and Suji company in Jhang.
A flour, rice and Suji company in Jhang.A flour, rice and Suji company in Jhang.
A flour, rice and Suji company in Jhang.
 
Live-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry WebinarLive-Streaming in the Music Industry Webinar
Live-Streaming in the Music Industry Webinar
 
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
The Vietnam Believer Newsletter_MARCH 25, 2024_EN_Vol. 003
 
Cracking the ‘Business Process Outsourcing’ Code Main.pptx
Cracking the ‘Business Process Outsourcing’ Code Main.pptxCracking the ‘Business Process Outsourcing’ Code Main.pptx
Cracking the ‘Business Process Outsourcing’ Code Main.pptx
 
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
The End of Business as Usual: Rewire the Way You Work to Succeed in the Consu...
 
Amazon ppt.pptx Amazon about the company
Amazon ppt.pptx Amazon about the companyAmazon ppt.pptx Amazon about the company
Amazon ppt.pptx Amazon about the company
 
Team B Mind Map for Organizational Chg..
Team B Mind Map for Organizational Chg..Team B Mind Map for Organizational Chg..
Team B Mind Map for Organizational Chg..
 
Lecture_6.pptx English speaking easyb to
Lecture_6.pptx English speaking easyb toLecture_6.pptx English speaking easyb to
Lecture_6.pptx English speaking easyb to
 
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptxHELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
HELENE HECKROTTE'S PROFESSIONAL PORTFOLIO.pptx
 
Borderless Access - Global B2B Panel book-unlock 2024
Borderless Access - Global B2B Panel book-unlock 2024Borderless Access - Global B2B Panel book-unlock 2024
Borderless Access - Global B2B Panel book-unlock 2024
 

Solution 3 a ph o 2

  • 1. APHO II 2001 Theoretical Question 3 2013/09/28 00:19 A9/P9 p. 1 / 4 [Solution] Theoretical Question 3 Thermal Vibration of Surface Atoms (1) (a) The wavelength of the incident electron is  A53.11053.1 0.641060.11011.92 1063.6 2 10 1931 34 =×= ××××× × = == − −− − m meV h p h λ (b) Consider the interference between the atomic rows on the surface as shown in Fig. 3c. The path difference between electron beam 1 and 2 is λφφ nb =−=∆ )sin(sin  Given   0.15=φ , λ=  A35.1 and  A77.2 2 92.3 2 === a b , two solutions are possible. (i) When n = 0, φ φ= o = 15.0 (Answer 1) (ii) When n =1 53.11)15sin(sin77.2 ×=−=∆   φ 812.0 77.2 72.053.1 sin = + =φ [Solution] (continued) Theoretical Question 3 Vibration of Surface Atoms  3.54=φ (Answer 2) 1 Fig.3c φ φ e- 1 2 [011]b e- φ φ n  n 
  • 2. APHO II 2001 Theoretical Question 3 2013/09/28 00:19 A9/P9 p. 2 / 4 For n = 2, no solution exists as 531215772 .)sin(sin. ×=−=   φ∆ and φsin > 1. (2) 〉⋅〈−= 2 0 )Ku(expII  ∆ For the specularly reflected beam, we have from Fig. 3d θcos2KKKK =−′=∆  xˆ where xˆ is the unit vector in the direction of the surface normal. Take the x- component of u  , we then obtain ><−>⋅<− == )t(ucosKcosK)t(u xx eIeII 222222 4 0 4 0 θθ (2) The vibration in the direction of the surface normal of the surface atoms is simple harmonic, take tAtux ωcos)( =  22 11 2 0 0 2 2222 AA dttcosAdtu)t(ux =⋅===〉〈 ∫ ∫ τ τ ω ττ τ τ ∴ 〉〈= )(2 22 tuA x The total energy E is thus given by ><⋅== )(2 2 1 2 1 22 tuCCAE x = >< )( 2 tuC x = ><′ )( 22 tum xω 2 Fig. 3d surface θK  K  ′ K∆
  • 3. APHO II 2001 Theoretical Question 3 2013/09/28 00:19 A9/P9 p. 3 / 4 [Solution] (continued) Theoretical Question 3 Vibration of Surface Atoms Therefore, one obtains >< )( 2 tux = E / ( 2 ωm′ ) Tku'mE Bx =><= 22 ω where 'm is the mass of the atom. From either of the above two equations, one then has the following equality 222 2 4 fm Tk m Tk u BB x πω ′ = ′ >=< (3) From eq. (3) and eq. (2), one obtains 22 22 4 cos4 0 fm Tk K B eII π θ ′ − = where λ ππ 22 == h p K . Accordingly, TM T fm k eIeII B ′− − == 0 ' cos4 0 22 2 λ θ (4) and TM I I n ′−= 0  From the plot of 0I I n versus T,one obtains the slope 22 2 cos4 λ θ fm k M B ′ =′ (5) The slope of the curve can be estimated from Fig. 3b and leads to the result 3 103.2 − ×=′M . Using the following data in Eq.(5), K/J.kB 23 10381 − ×= m10 1053.1 − ×=λ m′ = 195.1 3 10− × /(6.02 23 10× ) = 3.24 25 10− × kg/atom [Solution] (continued) Theoretical Question 3 Vibration of Surface Atoms 3
  • 4. APHO II 2001 Theoretical Question 3 2013/09/28 00:19 A9/P9 p. 4 / 4 one finds 2102 23 3 223 3 10531 10026 101195 15103814 1032 ).(f . . cos. . − − − − ××× × × ⋅×× =×  The solution for frequency is then 242 100.3 ×=f (new) Hzf 12 107.1 ×=⇒ Answer (a) From 22 2 4 f'm Tk u B x π =>< , KT 300= , one finally obtains 222 242 23 3 23 2 101.1 100.34 1002.6 101.195 3001038.1 mux − − − ×= ××× × × ⋅× >=< π (new) and  A10.0100.1 112 =×=>< − mux (new) Ans 4