Particle Physics - Measurements and Theory
|
|
|
- Elvin Theodore Ray
- 9 years ago
- Views:
Transcription
1 Paticle Physics - Measueents and Theoy Outline Natual Units Relativistic Kineatics Paticle Physics Measueents Lifeties Resonances and Widths Scatteing Coss section Collide and Fixed Taget xeients Consevation Laws Chage, Leton and Bayon nube, Paity, Quak flavous Theoetical Concets Quantu Field Theoy Klein-Godon quation Anti-aticles Yukawa Potential Scatteing Alitude - Fei s Golden Rule Matix eleents Nuclea and Paticle Physics Fanz Muhei
2 Paticle Physics Units Paticle Physics is elativistic and quantu echanical c /s ħ h/π Js Length size of oton: f 0-5 Lifeties as shot as 0-3 s Chage e C negy Units: GeV 0 9 ev -- ev J use also MeV, kev Mass in GeV/c, est ass is c Natual Units Set ħ c Mass [GeV/c ], enegy [GeV] and oentu [GeV/c] in GeV Tie [(GeV/ħ) - ], Length [(GeV/ħc) - ] in /GeV aea [(GeV/ħc) - ] Useful elations ħc 97 MeV f ħ MeV s Nuclea and Paticle Physics Fanz Muhei
![60 0-9 J use also MeV, kev Mass in GeV/c, est ass is c Natual Units Set ħ c Mass [GeV/c ], enegy [GeV] and oentu [GeV/c]](/docs-images/47/20901128/images/page_2.jpg "in GeV Tie [(GeV/ħ) - ], Length [(GeV/ħc) - ] in /GeV aea [(GeV/ħc) - ] Useful elations ħc 97 MeV f ħ 6.")
3 Paticle Physics Measueents How do we easue aticle oeties and inteaction stengths? Static oeties Mass How do you weigh an electon? Magnetic oent coules to agnetic field Sin, Paity Paticle decays Lifeties Foce Lifeties Resonances & Widths Stong s Allowed/fobidden l.ag s Decays Weak s Consevation laws Scatteing lastic scatteing e- e- Inelastic annihilation e+ e- + - Coss section total σ Foce Coss sections Diffeential dσ/dω Stong O(0 b) Luinosity L l.ag. O(0 - b) Paticle flux vent ate N Weak O(0 - b) Nuclea and Paticle Physics Fanz Muhei 3
4 Nuclea and Paticle Physics Fanz Muhei 4 Relativistic Kineatics Relativistic Kineatics Basics 4-oentu Invaiant ass Fou-vecto notation Useful Loentz boosts elations set ħ c invaiant ass γ /c / γβ c/c / γ / (- β ) β c/ / β ( -/γ ) -body decays P 0 P P wok in P 0 est fae xale: π + + ν wok in π + est fae use ν 0 ( ) /,,, c c c z y x ( ) ( ) ( ) ( ) ,,, ( ) ( ) ( ) 9.8 MeV/c 09.8 MeV,,,0 + π π ν π v
5 Lifeties Decay tie distibution Mean lifetie τ <dγ/dt> aka oe tie, eigen-tie of a aticle Lifetie easueents In laboatoy fae Decay Length L γβcτ xale: B d π + π - in LHCb exeient <L> 7 Aveage B eson enegy < B > 80 GeV τ.54 s xale: π + discovey Decay sequence π + + ν + e + ν eν ulsions exosed to Cosic ays dγ t Γ ex Γ dt τ τ π <L> + + ν + e + ν eν Nuclea and Paticle Physics Fanz Muhei 5
6 Resonances and Widths Stong Inteactions Poduction and decay of aticles Lifetie τ ~ 0-3 s cτ ~ O(0-5 ) uneasuable Heisenbeg s Uncetainty Pincile t h Tie and enegy easueents ae elated Natual width negy width Γ and lifetie τ of a aticle Γ ħ/τ Width Γ O(00 MeV) easuable xale - Delta(3) Resonance Poduction + π ++ + π Peak at negy.3 GeV (Cente-of-Mass) Width Γ 0 MeV Lifetie τ ħ/γ s Nuclea and Paticle Physics Fanz Muhei 6
7 Scatteing Fixed Taget xeients a + b c + d + n a v a n b # of bea aticles velocity of bea aticles # of taget aticles e unit aea Incident flux F n a v a Coss Section effective aea of any scatteing haening noalised e unit of incident flux deends on undelying hysics What you want to study dn # of scatteed aticles in solid angle dω dσ/dω diffeential coss section in solid angle dω σ total coss section d σ dndn dn na vanbdσ Fnbdσ Ldσ L dω L Luinosity dω L dω dσ N N vent ate σ dω N σl σ Luinosity dω Incident flux ties nube of tagets Deends on you exeiental setu ban b 0 c Luinosity [ L] 0 c s vent Rate Luinosity ties Coss Section vent L Rate N Nuclea and Paticle Physics Fanz Muhei 7
8 Scatteing Cente-of-Mass negy a + b c + d + s is invaiant quantity s CoM Collision of two aticles cente-of-ass enegy Mandelsta vaiable Total available enegy in cente-of-ass fae CoM is invaiant in any fae, e.g. laboatoy negy Theshold ( + ) ( + ) ( + ) s ( cosθ ) fo aticle oduction Fixed Taget xeients + CoM s j j c, d,... ( lab ), (,0) CoM s + + lab CoM lab if lab >> i xale: 00 GeV oton onto oton at est CoM s ( ) 4 GeV Most of bea enegy goes into CoM oentu and is not available fo inteactions Nuclea and Paticle Physics Fanz Muhei 8
9 Scatteing Collide xeients Head-on collisions of two aticles θ 80 0 ( + ) CoM 4 if i i + + >> CoM s ( cosθ ) + + All of bea enegy available fo aticle oduction xale LP - Lage lecton Positon Collide at CRN 00 GeV e- onto 00 GeV e+ Cente-of-ass enegy CoM s 00 GeV Coss section σ(e+ e- + -). b Luinosity Ldt 400 b - Nube of ecoded events N σ Ldt 870 Nuclea and Paticle Physics Fanz Muhei 9
10 Consevation Laws Noethe s Theoe vey syety has associated with it a consevation law and vice-vesa negy and Moentu, Angula Moentu conseved in all inteactions Syeties tanslations in sace and tie, otations in sace Chage consevation Well established q + q e < e Valid fo all ocesses Syety gauge tansfoation Leton and Bayon nube (L and B) L+B consevation atte consevation Poton decay not obseved (B violation) Leton faily nubes L e, L, L τ conseved Syety ystey Quak Flavous, Isosin, Paity conseved in stong and electoagn ocesses Violated in weak inteactions Syety unknown Nuclea and Paticle Physics Fanz Muhei 0
11 Theoetical Concets Standad Model of Paticle Physics Standad Model of Paticle Physics Quantu Field Theoy (QFT) Descibes fundaental inteactions of leentay aticles Cobines quantu echanics and secial elativity Classical Physics Vey sall x ħc Quantu echanics Vey fast v c Secial elativity Quantu field theoy Natual exlanation fo antiaticles and fo Pauli exclusion incile Full QFT is beyond scoe of this couse Intoduction to Majo QFT concets Tansition Rate Matix eleents Feynan Diagas Foce ediated by exchange of bosons Nuclea and Paticle Physics Fanz Muhei
12 Klein-Godon quation Schoedinge quation Fo fee aticle non-elativistic st ode in tie deivative nd ode in sace deivatives not Loentz-invaiant Klein-Godon (K-G) quation Stat with elativistic equation + (ħ c ) ih t Aly quantu echanical oeatos ˆ ψ ˆ ψ h ψ ih ψ t ih t + ψ ψ o t + ψ 0 nd ode in sace and tie deivatives Loentz invaiant Plane wave solutions of K-G equation ψ ν ( x ) N ex( i x ) ± + ν negative enegies ( < 0) also negative obability densities ( ψ < 0) Negative negy solutions Diac quation, but ve enegies eain Antiatte Nuclea and Paticle Physics Fanz Muhei
13 Klein-Godon quation Inteetation K-G quation is fo sinless aticles Solutions ae wave-functions fo bosons Tie-Indeendent Solution Conside static case, i.e. no tie deivative ψ ψ Solution is sheically syetic g ψ ( ) ex 4π Inteetation - Potential analogous to Coulob otential Foce is ediated by exchange of assive bosons Yukawa Potential Intoduced to exlain nuclea foce g V ( ) ex 4π g stength of foce stong nuclea chage ass of boson R Range of foce ( ) R h c see also nuclea hysics Fo 0 and g e Coulob Potential R Nuclea and Paticle Physics Fanz Muhei 3
14 Antiaticles Klein-Godon & Diac quations edict negative enegy solutions Inteetation - Diac Vacuu filled with < 0 electons electons with oosite sins e enegy state - Diac Sea Hole of < 0, -ve chage in Diac sea -> antiaticle > 0, +ve chage -> ositon, e + discovey (93) Pedicts e + e - ai oduction and annihilation Moden Inteetation Feynan-Stueckelbeg < 0 solutions: Negative enegy aticle oving backwads in sace and tie coesond to ex ex Antiaticles Positive enegy, oosite chage oving fowad in sace and tie [ i( ( )( t) ( ) ( x) )] [ i( ( t x) ] Nuclea and Paticle Physics Fanz Muhei 4
15 Scatteing Alitude Tansition Rate W Scatteing eaction a + b c + d W σ F Inteaction ate e taget aticle elated to hysics of eaction Fei s Golden Rule W π h M fi non-elativistic st ode tie-deendent etubation theoy see e.g. Halzen&Matin,. 80, Quantu Physics Matix leent Contains all hysics of the inteaction M ψ H ) ψ fi f Hailtonian H is etubation st ode Incoing and outgoing lane waves woks if etubation is sall ρ f i Matix leent M fi scatteing alitude Density ρ f # of ossible final states hase sace Bon Aoxiation Nuclea and Paticle Physics Fanz Muhei 5
16 Matix leent Scatteing in Potential xale: e- e- Incoing and outgoing lane waves Matix eleent Moentu tansfe M fi fi ψ 3 V ( ) ψ d 3 N N * f ex ex ( i ) V ( )ex( i ) 3 ( iq ) V ( ) d q i f M fi (q) is Fouie tansfo of Potential V() Scatteing in Yukawa Potential V ( ) g π π ex ( ) ( ) M fi ex i q cosθ M fi 4π g i q 0 0 g 0 i 0 ( + q ) f q i f i d 3 ( ex( i q ) ex( i q ) ) ex( ) Poagato g ex 4π d sinθdθdφ d te in M fi /( +q ) ( ) Coss section dσ M dω Result still holds elativistically 4-oentu tansfe q ( + q ) dσ dω ( ), i f i f 4 q 0 Nuclea and Paticle Physics Fanz Muhei 6
Mechanics 1: Motion in a Central Force Field
Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.
(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of
Homewok VI Ch. 7 - Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the
12.1. FÖRSTER RESONANCE ENERGY TRANSFER
ndei Tokmakoff, MIT epatment of Chemisty, 3/5/8 1-1 1.1. FÖRSTER RESONNCE ENERGY TRNSFER Föste esonance enegy tansfe (FR) efes to the nonadiative tansfe of an electonic excitation fom a dono molecule to
Solution Derivations for Capa #8
Solution Deivations fo Capa #8 1) A ass spectoete applies a voltage of 2.00 kv to acceleate a singly chaged ion (+e). A 0.400 T field then bends the ion into a cicula path of adius 0.305. What is the ass
Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined
12. Rolling, Torque, and Angular Momentum
12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.
The Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C
![The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C](/thumbs/40/21051327.jpg "The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C")
Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit
Exam 3: Equation Summary
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P
Physics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.
Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming
Gauss Law. Physics 231 Lecture 2-1
Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2
F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,
Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
Forces & Magnetic Dipoles. r r τ = μ B r
Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent
Quark Model. Quark Model
Quark odel Outline Hadrons Isosin Strangeness Quark odel Flavours u d s esons Pseudoscalar and vector mesons Baryons Deculet octet Hadron asses Sin-sin couling Heavy Quarks Charm bottom Heavy quark esons
2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
Classical Mechanics (CM):
Classical Mechanics (CM): We ought to have some backgound to aeciate that QM eally does just use CM and makes one slight modification that then changes the natue of the oblem we need to solve but much
Phys 2101 Gabriela González. cos. sin. sin
1 Phys 101 Gabiela González a m t t ma ma m m T α φ ω φ sin cos α τ α φ τ sin m m α τ I We know all of that aleady!! 3 The figue shows the massive shield doo at a neuton test facility at Lawence Livemoe
PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013
PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0
On Efficiently Updating Singular Value Decomposition Based Reduced Order Models
On Efficiently dating Singula alue Decoosition Based Reduced Ode Models Ralf Zieann GAMM oksho Alied and Nueical Linea Algeba with Secial Ehasis on Model Reduction Been Se..-3. he POD-based ROM aoach.
PY1052 Problem Set 8 Autumn 2004 Solutions
PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what
Chapter 17 The Kepler Problem: Planetary Mechanics and the Bohr Atom
Chapte 7 The Keple Poblem: Planetay Mechanics and the Boh Atom Keple s Laws: Each planet moves in an ellipse with the sun at one focus. The adius vecto fom the sun to a planet sweeps out equal aeas in
FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
Gravitation. AP Physics C
Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What
Lecture L9 - Linear Impulse and Momentum. Collisions
J. Peraire, S. Widnall 16.07 Dynaics Fall 009 Version.0 Lecture L9 - Linear Ipulse and Moentu. Collisions In this lecture, we will consider the equations that result fro integrating Newton s second law,
Displacement, Velocity And Acceleration
Displacement, Velocity And Acceleation Vectos and Scalas Position Vectos Displacement Speed and Velocity Acceleation Complete Motion Diagams Outline Scala vs. Vecto Scalas vs. vectos Scala : a eal numbe,
Chapter 4: Matrix Norms
EE448/58 Vesion.0 John Stensby Chate 4: Matix Noms The analysis of matix-based algoithms often equies use of matix noms. These algoithms need a way to quantify the "size" of a matix o the "distance" between
Excitation energies for molecules by Time-Dependent. based on Effective Exact Exchange Kohn-Sham potential
Excitation enegies fo molecules by Time-Dependent Density-Functional Theoy based on Effective Exact Exchange Kohn-Sham potential Fabio Della Sala National Nanotechnology Laboatoies Lecce Italy A. Göling
Newton s Law of Universal Gravitation and the Scale Principle
Newton s Law of Univesal avitation and the ale iniple RODOLO A. RINO July 0 Eletonis Enginee Degee fo the National Univesity of Ma del lata - Agentina ([email protected]) Ealie this yea I wote a pape
α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =
Experiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION
MISN-0-34 TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION shaft TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION by Kiby Mogan, Chalotte, Michigan 1. Intoduction..............................................
VISCOSITY OF BIO-DIESEL FUELS
VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
Mechanics 1: Work, Power and Kinetic Energy
Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).
Gravity. A. Law of Gravity. Gravity. Physics: Mechanics. A. The Law of Gravity. Dr. Bill Pezzaglia. B. Gravitational Field. C.
Physics: Mechanics 1 Gavity D. Bill Pezzaglia A. The Law of Gavity Gavity B. Gavitational Field C. Tides Updated: 01Jul09 A. Law of Gavity 3 1a. Invese Squae Law 4 1. Invese Squae Law. Newton s 4 th law
8.4. Motion of Charged Particles in Magnetic Fields
Motion of Chaged Paticles in Magnetic Fields Atos and olecules ae paticles that ae the building blocks of ou uniese. How do scientists study the natue of these sall paticles? The ass spectoete shown in
2. Orbital dynamics and tides
2. Obital dynamics and tides 2.1 The two-body poblem This efes to the mutual gavitational inteaction of two bodies. An exact mathematical solution is possible and staightfowad. In the case that one body
Relativistic Quantum Mechanics
Chapte Relativistic Quantum Mechanics In this Chapte we will addess the issue that the laws of physics must be fomulated in a fom which is Loentz invaiant, i.e., the desciption should not allow one to
A new Definition of Graviton
A new Definition of Graviton H.Javadi a, F.Forouzbakhsh b, H.Pour Iani c a)invited Professor of the Faculty of Science at Azad Islaic University Tehran capuses, Tehran, Iran [email protected] b)acadeic
Deflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
A comparison result for perturbed radial p-laplacians
A comaison esult fo etubed adial -Lalacians Raul Manásevich and Guido Swees Diectoy Table of Contents Begin Aticle Coyight c 23 Last Revision Date: Ail 1, 23 Table of Contents 1. Intoduction and main esult
Absorption and Emission of Radiation by an Atomic Oscillator
hysics ssays volue 6 nube bsoption and ission of Radiation by an toic Oscillato Milan ekovac bstact The theoy of absoption and eission of electoagnetic adiation by an oscillato consisting of the atoic
Voltage ( = Electric Potential )
V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
Controlling the Money Supply: Bond Purchases in the Open Market
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
University of Maryland Fraternity & Sorority Life Spring 2015 Academic Report
University of Maryland Fraternity & Sorority Life Academic Report Academic and Population Statistics Population: # of Students: # of New Members: Avg. Size: Avg. GPA: % of the Undergraduate Population
Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 10 Solutions
Peason Physics Level 30 Unit VI Foces and Fields: hapte 10 Solutions Student Book page 518 oncept heck 1. It is easie fo ebonite to eove electons fo fu than fo silk.. Ebonite acquies a negative chage when
Voltage ( = Electric Potential )
V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
Charges, Coulomb s Law, and Electric Fields
Q&E -1 Chages, Coulomb s Law, and Electic ields Some expeimental facts: Expeimental fact 1: Electic chage comes in two types, which we call (+) and ( ). An atom consists of a heavy (+) chaged nucleus suounded
Multiple choice questions [60 points]
![Multiple choice questions [60 points]](/thumbs/40/20623569.jpg "Multiple choice questions [60 points]")
1 Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect bubble on you scanton sheet. Each question has exactly one coect answe. All questions
F G r. Don't confuse G with g: "Big G" and "little g" are totally different things.
G-1 Gavity Newton's Univesal Law of Gavitation (fist stated by Newton): any two masses m 1 and m exet an attactive gavitational foce on each othe accoding to m m G 1 This applies to all masses, not just
F en = mω 0 2 x. We should regard this as a model of the response of an atom, rather than a classical model of the atom itself.
The Electron Oscillator/Lorentz Atom Consider a simple model of a classical atom, in which the electron is harmonically bound to the nucleus n x e F en = mω 0 2 x origin resonance frequency Note: We should
Scalars, Vectors and Tensors
Scalars, Vectors and Tensors A scalar is a physical quantity that it represented by a dimensional number at a particular point in space and time. Examples are hydrostatic pressure and temperature. A vector
Chapter 15 Collision Theory
Chapter 15 Collision Theory 151 Introduction 1 15 Reference Frames Relative and Velocities 1 151 Center of Mass Reference Frame 15 Relative Velocities 3 153 Characterizing Collisions 5 154 One-Dimensional
Solutions to Problems in Goldstein, Classical Mechanics, Second Edition. Chapter 7
Solutions to Problems in Goldstein, Classical Mechanics, Second Edition Homer Reid April 21, 2002 Chapter 7 Problem 7.2 Obtain the Lorentz transformation in which the velocity is at an infinitesimal angle
NUCLEAR MAGNETIC RESONANCE
19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic
Perfect Fluids: From Nano to Tera
Perfect Fluids: From Nano to Tera Thomas Schaefer North Carolina State University 1 2 Perfect Fluids sqgp (T=180 MeV) Neutron Matter (T=1 MeV) Trapped Atoms (T=0.1 nev) 3 Hydrodynamics Long-wavelength,
Introduction to Fluid Mechanics
Chapte 1 1 1.6. Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = 3.174 ft/s. (a) What is its mass in kg? (b) What will the weight of this body
Concepts in Theoretical Physics
Concepts in Theoretical Physics Lecture 6: Particle Physics David Tong e 2 The Structure of Things 4πc 1 137 e d ν u Four fundamental particles Repeated twice! va, 9608085, 9902033 Four fundamental forces
Suggested solutions, FYS 500 Classical Mechanics and Field Theory 2014 fall
UNIVERSITETET I STAVANGER Institutt for matematikk og naturvitenskap Suggested solutions, FYS 500 Classical Mecanics and Field Teory 014 fall Set 11 for 17/18. November 014 Problem 59: Te Lagrangian for
Supplementary Material for EpiDiff
Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module
Free Electron Fermi Gas (Kittel Ch. 6)
Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals -- they are the glue that hold the nuclei together Types of binding (see next slide)
The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
Moment and couple. In 3-D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r
Moment and couple In 3-D, because the detemination of the distance can be tedious, a vecto appoach becomes advantageous. o k j i M k j i M o ) ( ) ( ) ( + + M o M + + + + M M + O A Moment about an abita
Masses in Atomic Units
Nuclear Composition - the forces binding protons and neutrons in the nucleus are much stronger (binding energy of MeV) than the forces binding electrons to the atom (binding energy of ev) - the constituents
Matter Waves. Home Work Solutions
Chapter 5 Matter Waves. Home Work s 5.1 Problem 5.10 (In the text book) An electron has a de Broglie wavelength equal to the diameter of the hydrogen atom. What is the kinetic energy of the electron? How
Chapter 4: Fluid Kinematics
4-1 Lagangian g and Euleian Desciptions 4-2 Fundamentals of Flow Visualization 4-3 Kinematic Desciption 4-4 Reynolds Tanspot Theoem (RTT) 4-1 Lagangian and Euleian Desciptions (1) Lagangian desciption
Do Vibrations Make Sound?
Do Vibations Make Sound? Gade 1: Sound Pobe Aligned with National Standads oveview Students will lean about sound and vibations. This activity will allow students to see and hea how vibations do in fact
Detectors in Nuclear and Particle Physics
Detectors in Nuclear and Particle Physics Prof. Dr. Johanna Stachel Deartment of Physics und Astronomy University of Heidelberg June 17, 2015 J. Stachel (Physics University Heidelberg) Detectorhysics June
Measuring relative phase between two waveforms using an oscilloscope
Measuring relative hase between two waveforms using an oscilloscoe Overview There are a number of ways to measure the hase difference between two voltage waveforms using an oscilloscoe. This document covers
Physics 111 Homework Solutions Week #9 - Tuesday
Physics 111 Homework Solutions Week #9 - Tuesday Friday, February 25, 2011 Chapter 22 Questions - None Multiple-Choice 223 A 224 C 225 B 226 B 227 B 229 D Problems 227 In this double slit experiment we
An Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom
UNIVERSITETET I OSLO
UNIVERSITETET I OSLO Det matematisk-naturvitenskapelige fakultet Exam in: FYS 310 Classical Mechanics and Electrodynamics Day of exam: Tuesday June 4, 013 Exam hours: 4 hours, beginning at 14:30 This examination
R&DE (Engineers), DRDO. Theories of Failure. [email protected]. Ramadas Chennamsetti
heories of Failure ummary Maximum rincial stress theory Maximum rincial strain theory Maximum strain energy theory Distortion energy theory Maximum shear stress theory Octahedral stress theory Introduction
Second Order Systems
Second Order Systems Second Order Equations Standard Form G () s = τ s K + ζτs + 1 K = Gain τ = Natural Period of Oscillation ζ = Damping Factor (zeta) Note: this has to be 1.0!!! Corresponding Differential
Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!
1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the
1. Degenerate Pressure
. Degenerate Pressure We next consider a Fermion gas in quite a different context: the interior of a white dwarf star. Like other stars, white dwarfs have fully ionized plasma interiors. The positively
Lecture 09 Nuclear Physics Part 1
Lecture 09 Nuclear Physics Part 1 Structure and Size of the Nucleus Νuclear Masses Binding Energy The Strong Nuclear Force Structure of the Nucleus Discovered by Rutherford, Geiger and Marsden in 1909
Financing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 [email protected] August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
0.33 d down 1 1. 0.33 c charm + 2 3. 0 0 1.5 s strange 1 3. 0 0 0.5 t top + 2 3. 0 0 172 b bottom 1 3
Chapter 16 Constituent Quark Model Quarks are fundamental spin- 1 particles from which all hadrons are made up. Baryons consist of three quarks, whereas mesons consist of a quark and an anti-quark. There
Fluids Lecture 15 Notes
Fluids Lectue 15 Notes 1. Unifom flow, Souces, Sinks, Doublets Reading: Andeson 3.9 3.12 Unifom Flow Definition A unifom flow consists of a velocit field whee V = uî + vĵ is a constant. In 2-D, this velocit
PHY2061 Enriched Physics 2 Lecture Notes Relativity 4. Relativity 4
PHY6 Enriched Physics Lectre Notes Relativity 4 Relativity 4 Disclaimer: These lectre notes are not meant to replace the corse textbook. The content may be incomplete. Some topics may be nclear. These
Standard Model of Particle Physics
Standard Model of Particle Physics Chris Sachrajda School of Physics and Astronomy University of Southampton Southampton SO17 1BJ UK SUSSP61, St Andrews August 8th 3rd 006 Contents 1. Spontaneous Symmetry
Lecture L26-3D Rigid Body Dynamics: The Inertia Tensor
J. Peraire, S. Widnall 16.07 Dynaics Fall 008 Lecture L6-3D Rigid Body Dynaics: The Inertia Tensor Version.1 In this lecture, we will derive an expression for the angular oentu of a 3D rigid body. We shall
Feynman diagrams. 1 Aim of the game 2
Feynman diagrams Contents 1 Aim of the game 2 2 Rules 2 2.1 Vertices................................ 3 2.2 Anti-particles............................. 3 2.3 Distinct diagrams...........................
PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8 - TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
Carter-Penrose diagrams and black holes
Cate-Penose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
Coordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
Phys101 Lectures 14, 15, 16 Momentum and Collisions
Phs0 Lectures 4, 5, 6 Moentu and ollisions Ke points: Moentu and ipulse ondition for conservation of oentu and wh How to solve collision probles entre of ass Ref: 9-,,3,4,5,6,7,8,9. Page Moentu is a vector:
0.1 Phase Estimation Technique
Phase Estimation In this lecture we will describe Kitaev s phase estimation algorithm, and use it to obtain an alternate derivation of a quantum factoring algorithm We will also use this technique to design
Episode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
Linearized quantum transport equations: ac conductance of a quantum wire with an electron-phonon interaction
PHYSICAL REVIEW B VOLUME 53, NUMBER 16 15 APRIL 1996-II Lineaized quantum tanspot equations: ac conductance of a quantum wie with an electon-phonon inteaction Pet Kál Institute of Physics, Academy of Sciences,
CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer
CRRC- Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the