|
|
- Virgil Caldwell
- 6 years ago
- Views:
Transcription
1 ดร. สมศ กด แดงต บ ห องพ ก 617 โทร 5777 ห องว จ ย k46 โทร Psonal Wbsit : Cous (1 st alf wbsit: Lctu 6 Raioactiv Dcay ค าถามทบทวน July 9 SCPY 415: Nucla Pysics Lctu 1
2 การสลายต ว// ร งส อ ลฟ า รงสอลฟา ร งส แกมมา ร งส บ ตา July 9 SCPY 415: Nucla Pysics Lctu 1 Ala cay Consi T Z9 fm R7.6 fm E4 V E Z Z 1 4πε c c R Engy of α: E α 4.8 V Qustion: How os t α sca? Answ: Q tunnlling July 9 SCPY 415: Nucla Pysics Lctu 1 4
3 Ala cay aial wav function in ala cay I II III Exonntial cay of ψ nuclus bai (ngativ KE small flux of al α July 9 SCPY 415: Nucla Pysics Lctu 1 5 ψ I x( ikx + Ax( ikx ψ B x( Kx + C x( Kx II ψ III D x(ikx Q tunnlling k me K m ( V E E t BC B.C. at x an xt fo Kt>>1 an k~k Kgivs fo 1D ctangula bai ticknss t givs T D x( Kt Intgat ov Coulomb bai fom R to t July 9 SCPY 415: Nucla Pysics Lctu 1 6
4 Ala cay ΔE s 6V nuclon fo avy nucli ΔE bin ( 4 α8. V > 4*6V Nutons Potons Alas July 9 SCPY 415: Nucla Pysics Lctu 1 7 T t x K( x R Z V ( 4πε E α Z 4πε t Ala cay ( V ( E 1/ t 1/ Z G πε R 1/ 1 Z 1/ G t sin ϑ ϑ πε α x( G ( 1/ 1/ t ; t cos ϑ t cosϑ sinϑϑ ϑ sin ϑ ϑ (1/ ϑ sinϑcosϑ [ ] 1/ Z t >> ;cos ϑ / ; cosϑ ; ϑ π /; 4 πε t R R t G π July 9 SCPY 415: Nucla Pysics Lctu 1 8
5 Ala cay ats 1/ Z t π G Gamow facto 4 πε t Z 4πε E α Z G 4ε E α 1/ Numb of its, on sufac of nuclus aius R ~ v/r.dcay at (Eα / m ω RR x( G July 9 SCPY 415: Nucla Pysics Lctu 1 9 Eximntal tsts Pict log cay at ootional to (E a 1/ Ags ~ wit ata fo nucli. Angula momntum ffcts: Aitional bai l(l l + 1( c E l c Small coma to Coulomb o but still gnats lag agta xta xonntial sussion. E.g l1, R15 fm E l ~.5 V cf fo Z 9 Ec~17 V. Sin/aity i ΔJL aity cang( L July 9 SCPY 415: Nucla Pysics Lctu 1 1
6 Eximntal tsts 1 18 Half-lif (s Engy E (V July 9 SCPY 415: Nucla Pysics Lctu 1 11 Fmi Bta Dcay Toy Consi simlst cas: n cay. At quak lvl: l u+w follow by cay of vitual W. n ν ; n u u u - u ν W - ( ν July 9 SCPY 415: Nucla Pysics Lctu 1 1
7 Fmi Toy 4 oint intaction (low ngy aoximation. if * * * Gβ ψ ( ψν ( ψ ( ψ n ( ψ ( x( ik. ; ( x( ik. ; q k + k ( ψ ν ν ν q ~ 1 V / c R ~ 5 fm > q. ~ 1/ 4 > x( iq. 1 if G β * ψ ( ψ ( n July 9 SCPY 415: Nucla Pysics Lctu 1 1 Fmi Toy istibution tmin by as sac (nglct nucla coil ngy N N 4π / ; Nν 4πν ν / ( 4π / ( 4π / ν ν ( E f E / c ; / E f 1/ c ν ν N 16π 6 c ( E f E E f Us FGR : as sac &.E. cay at July 9 SCPY 415: Nucla Pysics Lctu 1 14
8 Kui Plot I( A I ( ( E f E A( E f E Coulomb coction Fmi function K(Z, Continuous sctum nutino En oint givs limit on nutino mass Intnsity Titium β cay (I I(/ K(Z, 1/ Elcton ngy (kv 18 Elcton ngy(kv July 9 SCPY 415: Nucla Pysics Lctu 1 15 Fmi Tansitions: Slction Ruls n coul to giv sin: ΔS Allow tansitions ΔL ΔJ. Gamow Tll tansitions: n coul to giv 1 unit of sin: ΔS o ± 1. Allow tansitions ΔL ΔJ o ± 1. Fobin tansitions: x( iq. 1 + ( iq. + O ( q Hig o tms coson to non zo ΔL. Tfo suss ning on (q (q. L Usual Q uls giv: JL+S July 9 SCPY 415: Nucla Pysics Lctu 1 16
9 Can comt wit β + cay Elcton catu + if G n + ν R β * * ψ ( ψ ( ψ n ( ψ ν ( Fo allow tansitions. ii if * Gβψ ( ψν ( ψ ( ψ n ( R Only l. n1 lagst. ψ ( / 1 / Zm x( ik. π ; ( / 4 ψν πε L if Gβ Zm πl 4 πε F F R * ψ n ( ψ ( July 9 SCPY 415: Nucla Pysics Lctu 1 17 Dnsity of stats: Elcton catu (II N 4π q N N q L L ; ; Eν qc ν q E q E N E 4π q L c q L Fmi s Goln Rul: ππ w w G β F N E 16π E c ν 4 Zm 4 πε July 9 SCPY 415: Nucla Pysics Lctu 1 18
10 Discovy of Anti nutino + Invs Bta Dcay n ν ; ν n Sam matix lmnts 6 β F G L Fmi Goln Rul: w w π N E π N Gβ F E July 9 SCPY 415: Nucla Pysics Lctu 1 19 Discovy of Anti nutino(ii Pas sac facto Nglct nucla coil Combin wit FGR N E 4π L E ; E / c E 4 E c + m c w π G πe c L F c / L ; R 4 β F σ G Fσ 16π E β F 4 c July 9 SCPY 415: Nucla Pysics Lctu 1
11 Eximnt to vify Anti nutino Fo E~ 1 V s~1 47 cm Pauli iction an Cowan an Rins. ν + n + γ (omt n + C γs(9v,lay Liqui Scint. 1 GW Nucla Racto H +CCl PTs Siling July 9 SCPY 415: Nucla Pysics Lctu 1 1 Paity Dfinitions ; P[ ψ ( ] ψ ( P [ ψ ( ] ψ ( Pv ( v ; Pvv ( 1. vv 1. L x P( L L Eignvalus of aity a ± 1. If aity is consv: [H,P] ignstats of H a ignstats of aity. If aity violat can av stats wit mix aity. If Paity is consv sult of an ximnt soul b uncang by aity oation. July 9 SCPY 415: Nucla Pysics Lctu 1
12 Paity Consvation If aity is consv fo action a+b c+. η L a η b ( 1 η c η ( 1 IN L FINAL Nb absolut aity of stats tat can b ouc fom vacuum (.g. otons can b fin. Fo ot aticls w can fin lativ aity..g. fin η +1, η n +1 tn can tmin aity of ot nucli. If aity is consv <suo scala> (s nxt tansancy. July 9 SCPY 415: Nucla Pysics Lctu 1 < > O ψ Oψ ψ POψ ψ ψ ψ ψ * * < O > ψ PO P ψ * * < O > ( η ψ Oψ < O > ψ O ψ <O > QED * July 9 SCPY 415: Nucla Pysics Lctu 1 4
13 Is aity consv? Fynman s bt. Ys in lctomagntic an stong intactions. Big suis was tat aity is violat in wak intactions. July 9 SCPY 415: Nucla Pysics Lctu 1 5 Paity Tst: m Wo s Eximnt 6 6 * Co(J 5 Ni (J 4 ν ; Ni Ni+γ 6 * 6 Align sins of 6 Co wit magntic fil. Aiabatic magntisation to gt T ~ 1 mk asu angula istibution of lctons an otons lativ lti to B fil. Cla fowa backwa asymmty Paity violation. July 9 SCPY 415: Nucla Pysics Lctu 1 6
14 T ximnt July 9 SCPY 415: Nucla Pysics Lctu 1 7 Imov aity tst ximnt θ is angl wt sin of 6 Co. July 9 SCPY 415: Nucla Pysics Lctu 1 8
15 Gamma cay Wn o ty occu? Nucli av xcit stats cf atoms. Don t woy about tails E,J P (n sll mol to unstan. E intaction << stong intaction Low ngy stats E < 6 V abov goun stat can t cay by stong intaction ti E. Imotant in casca cays α an β. Pactical consquncs Fission. Significant ngy las in γ cays. Raiotay: γ fom Co 6 cays. ical imaging g Tc. July 9 SCPY 415: Nucla Pysics Lctu 1 9 Gamma cay β cay lavs Tc in xcit stat. Usful fo mical imaging July 9 SCPY 415: Nucla Pysics Lctu 1
16 Gamma cay toy ost common cay mo fo nucla xcit stats (blow tsol fo bak u is γ cay. Liftims vay fom yas to 1 16 s. nb long liftims can asily b obsv unlik in atomic. Wy? Angula momntum consvation in g cays. intinsic sin of g is1 an obital angula momntum intg J is intg. Only intg cangs in J of nuclus allow. Q aition of J: J J J J + J i f Absolutly fobin (wy?: i f July 9 SCPY 415: Nucla Pysics Lctu 1 1 Gamma cay Elctic tansitions E E x[ i ( k. ω t ] E E (1 + ik. + ( k. + O( k. Tyically k~1 V/c ~ 1 fm k~1/ k.~1/ us multiol xansion. Lowst tm is lctic iol tansitions, L1. H * ψ f ψ i Paity cang fo lctic iol. July 9 SCPY 415: Nucla Pysics Lctu 1
17 Fobin Tansition If lctic iol tansitions fobin by angula momntum o aity can av fobin tansitions, g lctic quaool. Rat suss cf iol by ~ (k. agntic tansitions also ossibl: Classically: E μ.b 1 tansition at small tan E1 by ~ 1. Hig o magntic tansitions also ossibl. Paity slction uls: Elctic: Δ( 1 L agntic: Δ( 1 L+1 July 9 SCPY 415: Nucla Pysics Lctu 1 Intnal convsion absolutly l fobin: Wat ans to a + xcit stat? Dcays by it: Intnal convsion: nuclus mits a vitual oton wic kicks k out an atomic lcton. Rquis ovla of t lcton wit t nuclus only l. Pobability of lcton ovla wit nuclus incass as Z. Fo ig Z can comt wit ot γ cays. Intnal ai convsion: nuclus mits a vitual oton wic convts to + ai. July 9 SCPY 415: Nucla Pysics Lctu 1 4
Shape parameterization
Shap paatization λ ( θ, φ) α ( θ ) λµ λµ, φ λ µ λ axially sytic quaupol axially sytic octupol λ α, α ± α ± λ α, α ±,, α, α ±, Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7 Octupol collctivity coupling
More informationNeutrino mass in tritium and rhenium single beta decay
Nutino mass in titium and hnium singl bta dcay Rastislav Dvonicky Comnius Univsity, Batislava Slovakia in collaboation with.simkovic, K. Muto & R. Hodak Nutinos in Cosmology, in Asto-, Paticl- and Nucla
More informationThe angle between L and the z-axis is found from
Poblm 6 This is not a ifficult poblm but it is a al pain to tansf it fom pap into Mathca I won't giv it to you on th quiz, but know how to o it fo th xam Poblm 6 S Figu 6 Th magnitu of L is L an th z-componnt
More informationMon. Tues. Wed. Lab Fri Electric and Rest Energy
Mon. Tus. Wd. Lab Fi. 6.4-.7 lctic and Rst ngy 7.-.4 Macoscoic ngy Quiz 6 L6 Wok and ngy 7.5-.9 ngy Tansf R 6. P6, HW6: P s 58, 59, 9, 99(a-c), 05(a-c) R 7.a bing lato, sathon, ad, lato R 7.b v. i xal
More informationHydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals
Hydogn atom Engy lvls and wav functions Obital momntum, lcton spin and nucla spin Fin and hypfin intaction Hydogn obitals Hydogn atom A finmnt of th Rydbg constant: R ~ 109 737.3156841 cm -1 A hydogn mas
More informationQ Q N, V, e, Quantum Statistics for Ideal Gas and Black Body Radiation. The Canonical Ensemble
Quantum Statistics fo Idal Gas and Black Body Radiation Physics 436 Lctu #0 Th Canonical Ensmbl Ei Q Q N V p i 1 Q E i i Bos-Einstin Statistics Paticls with intg valu of spin... qi... q j...... q j...
More informationFree carriers in materials
Lctu / F cais in matials Mtals n ~ cm -3 Smiconductos n ~ 8... 9 cm -3 Insulatos n < 8 cm -3 φ isolatd atoms a >> a B a B.59-8 cm 3 ϕ ( Zq) q atom spacing a Lctu / "Two atoms two lvls" φ a T splitting
More informationQ Q N, V, e, Quantum Statistics for Ideal Gas. The Canonical Ensemble 10/12/2009. Physics 4362, Lecture #19. Dr. Peter Kroll
Quantum Statistics fo Idal Gas Physics 436 Lctu #9 D. Pt Koll Assistant Pofsso Dpatmnt of Chmisty & Biochmisty Univsity of Txas Alington Will psnt a lctu ntitld: Squzing Matt and Pdicting w Compounds:
More information5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS
5.61 Fall 2007 Lctu #2 pag 1 Th DEMISE of CLASSICAL PHYSICS (a) Discovy of th Elcton In 1897 J.J. Thomson discovs th lcton and masus ( m ) (and inadvtntly invnts th cathod ay (TV) tub) Faaday (1860 s 1870
More informationKinetics. Central Force Motion & Space Mechanics
Kintics Cntal Foc Motion & Spac Mcanics Outlin Cntal Foc Motion Obital Mcanics Exampls Cntal-Foc Motion If a paticl tavls un t influnc of a foc tat as a lin of action ict towas a fix point, tn t motion
More informationSolid state physics. Lecture 3: chemical bonding. Prof. Dr. U. Pietsch
Solid stat physics Lctu 3: chmical bonding Pof. D. U. Pitsch Elcton chag dnsity distibution fom -ay diffaction data F kp ik dk h k l i Fi H p H; H hkl V a h k l Elctonic chag dnsity of silicon Valnc chag
More informationCollisionless Hall-MHD Modeling Near a Magnetic Null. D. J. Strozzi J. J. Ramos MIT Plasma Science and Fusion Center
Collisionlss Hall-MHD Modling Na a Magntic Null D. J. Stoi J. J. Ramos MIT Plasma Scinc and Fusion Cnt Collisionlss Magntic Rconnction Magntic connction fs to changs in th stuctu of magntic filds, bought
More informationNuclear and Particle Physics
Nucla and Paticl Physics Intoduction What th lmntay paticls a: a bit o histoy Th ida about th lmntay paticls has changd in th cous o histoy, in accodanc with th human s comphnsion and lat obsvation o natu.
More informationPhysics 111. Lecture 38 (Walker: ) Phase Change Latent Heat. May 6, The Three Basic Phases of Matter. Solid Liquid Gas
Physics 111 Lctu 38 (Walk: 17.4-5) Phas Chang May 6, 2009 Lctu 38 1/26 Th Th Basic Phass of Matt Solid Liquid Gas Squnc of incasing molcul motion (and ngy) Lctu 38 2/26 If a liquid is put into a sald contain
More informationMolecules and electronic, vibrational and rotational structure
Molculs and ctonic, ational and otational stuctu Max on ob 954 obt Oppnhim Ghad Hzbg ob 97 Lctu ots Stuctu of Matt: toms and Molculs; W. Ubachs Hamiltonian fo a molcul h h H i m M i V i fs to ctons, to
More informationSTATISTICAL MECHANICS OF DIATOMIC GASES
Pof. D. I. ass Phys54 7 -Ma-8 Diatomic_Gas (Ashly H. Cat chapt 5) SAISICAL MECHAICS OF DIAOMIC GASES - Fo monatomic gas whos molculs hav th dgs of fdom of tanslatoy motion th intnal u 3 ngy and th spcific
More informationElectromagnetic Schrödinger Equation of the Deuteron 2 H (Heavy Hydrogen)
Wold Jounal of Nucla Scinc and Tchnology, 14, 4, 8-6 Publishd Onlin Octob 14 in SciRs. htt://www.sci.og/jounal/wjnst htt://dx.doi.og/1.46/wjnst.14.449 Elctomagntic Schöding Equation of th Duton H (Havy
More informationCompton Scattering. There are three related processes. Thomson scattering (classical) Rayleigh scattering (coherent)
Comton Scattring Tr ar tr rlatd rocsss Tomson scattring (classical) Poton-lctron Comton scattring (QED) Poton-lctron Raylig scattring (cornt) Poton-atom Tomson and Raylig scattring ar lasticonly t dirction
More informationL N O Q F G. XVII Excitons From a many electron state to an electron-hole pair
XVII Excitons 17.1 Fom a many lcton stat to an lcton-ol pai In all pvious discussions w av bn considd t valnc band and conduction on lcton stats as ignfunctions of an ffctiv singl paticl Hamiltonian. Tis
More informationPhysics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM
Physics 0, Lctu 5 Today s Topics nnouncmnts: Homwok #3 on Wbssign by tonight Du (with Homwok #) on 9/4, 10 PM Rviw: (Ch. 5Pat I) Elctic Potntial Engy, Elctic Potntial Elctic Potntial (Ch. 5Pat II) Elctic
More informationEE243 Advanced Electromagnetic Theory Lec # 22 Scattering and Diffraction. Reading: Jackson Chapter 10.1, 10.3, lite on both 10.2 and 10.
Appid M Fa 6, Nuuth Lctu # V //6 43 Advancd ctomagntic Thoy Lc # Scatting and Diffaction Scatting Fom Sma Obcts Scatting by Sma Dictic and Mtaic Sphs Coction of Scatts Sphica Wav xpansions Scaa Vcto Rading:
More informationUGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r.
UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM Solution (TEST SERIES ST PAPER) Dat: No 5. Lt a b th adius of cicl, dscibd by th aticl P in fig. if, a th ola coodinats of P, thn acos Diffntial
More informationFrom Classical to Quantum mechanics
From Classical to Quantum mcanics Engl & Rid 99-300 vrij Univrsitit amstrdam Classical wav baviour Ligt is a wav Two-slit xprimnt wit potons (81-85) 1 On sourc Intrfrnc sourcs ttp://www.falstad.com/matpysics.tml
More informationQ. Obtain the Hamiltonian for a one electron atom in the presence of an external magnetic field.
Syed Ashad Hussain Lectue Deatment of Physics Tiua Univesity www.sahussaintu.wodess.com Q. Obtain the Hamiltonian fo a one electon atom in the esence of an extenal magnetic field. To have an idea about
More information5- Scattering Stationary States
Lctu 19 Pyscs Dpatmnt Yamou Unvsty 1163 Ibd Jodan Pys. 441: Nucla Pyscs 1 Pobablty Cunts D. Ndal Esadat ttp://ctaps.yu.du.jo/pyscs/couss/pys641/lc5-3 5- Scattng Statonay Stats Rfnc: Paagaps B and C Quantum
More informationPropagation of Light About Rapidly Rotating Neutron Stars. Sheldon Campbell University of Alberta
Ppagatin f Light Abut Rapily Rtating Nutn Stas Shln Campbll Univsity f Albta Mtivatin Tlscps a nw pcis nugh t tct thmal spcta fm cmpact stas. What flux is masu by an bsv lking at a apily tating lativistic
More informationMid Year Examination F.4 Mathematics Module 1 (Calculus & Statistics) Suggested Solutions
Mid Ya Eamination 3 F. Matmatics Modul (Calculus & Statistics) Suggstd Solutions Ma pp-: 3 maks - Ma pp- fo ac qustion: mak. - Sam typ of pp- would not b countd twic fom wol pap. - In any cas, no pp maks
More informationSpeed of light c = m/s. x n e a x d x = 1. 2 n+1 a n π a. He Li Ne Na Ar K Ni 58.
Physical Chemistry II Test Name: KEY CHEM 464 Spring 18 Chapters 7-11 Average = 1. / 16 6 questions worth a total of 16 points Planck's constant h = 6.63 1-34 J s Speed of light c = 3. 1 8 m/s ħ = h π
More informationPHYS 272H Spring 2011 FINAL FORM B. Duration: 2 hours
PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish.
More informationPHYS 272H Spring 2011 FINAL FORM A. Duration: 2 hours
PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish.
More informationThe local orthonormal basis set (r,θ,φ) is related to the Cartesian system by:
TIS in Sica Cooinats As not in t ast ct, an of t otntias tat w wi a wit a cnta otntias, aning tat t a jst fnctions of t istanc btwn a atic an so oint of oigin. In tis cas tn, (,, z as a t Coob otntia an
More information3.46 PHOTONIC MATERIALS AND DEVICES Lecture 10: LEDs and Optical Amplifiers
3.46 PHOTONIC MATERIALS AND DEVICES Lctu 0: LEDs and Optical Amplifis Lctu Rfncs:. Salh, M. Tich, Photonics, (John-Wily, Chapts 5-6. This lctu will viw how lctons and hols combin in smiconductos and nat
More informationChemical Engineering 412
Chical Enginring 4 Introductory Nuclar Enginring Lctur 6 Nuclar Radiation Typs Ky oints Typs of cay Na roprtis athatical scriptions Cavats cay Charts (KNOW HOW TO USE!) Nuclar Equation for cay -Valus for
More informationPhysics 43 HW #9 Chapter 40 Key
Pysics 43 HW #9 Captr 4 Ky Captr 4 1 Aftr many ours of dilignt rsarc, you obtain t following data on t potolctric ffct for a crtain matrial: Wavlngt of Ligt (nm) Stopping Potntial (V) 36 3 4 14 31 a) Plot
More informationcos kd kd 2 cosθ = π 2 ± nπ d λ cosθ = 1 2 ± n N db
. (Balanis 6.43) You can confim tat AF = e j kd cosθ + e j kd cosθ N = cos kd cosθ gives te same esult as (6-59) and (6-6), fo a binomial aay wit te coefficients cosen as in section 6.8.. Tis single expession
More informationQuantitative Model of Unilluminated Diode part II. G.R. Tynan UC San Diego MAE 119 Lecture Notes
Quantitativ Modl of Unilluminatd Diod part II G.R. Tynan UC San Digo MAE 119 Lctur Nots Minority Carrir Dnsity at dg of quasinutral rgion incrass EXPONENTIALLY forward bias p nb n pa = p n0 xp qv a kt
More information6.Optical and electronic properties of Low
6.Optical and lctonic poptis of Low dinsional atials (I). Concpt of Engy Band. Bonding foation in H Molculs Lina cobination of atoic obital (LCAO) Schoding quation:(- i VionV) E find a,a s.t. E is in a
More informationAtomic Physics. Final Mon. May 12, 12:25-2:25, Ingraham B10 Get prepared for the Final!
# SCORES 50 40 30 0 10 MTE 3 Rsults P08 Exam 3 0 30 40 50 60 70 80 90 100 SCORE Avrag 79.75/100 std 1.30/100 A 19.9% AB 0.8% B 6.3% BC 17.4% C 13.1% D.1% F 0.4% Final Mon. Ma 1, 1:5-:5, Ingraam B10 Gt
More informationGRAVITATION 4) R. max. 2 ..(1) ...(2)
GAVITATION PVIOUS AMCT QUSTIONS NGINING. A body is pojctd vtically upwads fom th sufac of th ath with a vlocity qual to half th scap vlocity. If is th adius of th ath, maximum hight attaind by th body
More informationAakash. For Class XII Studying / Passed Students. Physics, Chemistry & Mathematics
Aakash A UNIQUE PPRTUNITY T HELP YU FULFIL YUR DREAMS Fo Class XII Studying / Passd Studnts Physics, Chmisty & Mathmatics Rgistd ffic: Aakash Tow, 8, Pusa Road, Nw Dlhi-0005. Ph.: (0) 4763456 Fax: (0)
More informationProblem Set 4: Whither, thou turbid wave SOLUTIONS
PH 253 / LeClair Spring 2013 Problem Set 4: Witer, tou turbid wave SOLUTIONS Question zero is probably were te name of te problem set came from: Witer, tou turbid wave? It is from a Longfellow poem, Te
More informationTrigonometric functions
Robrto s Nots on Diffrntial Calculus Captr 5: Drivativs of transcndntal functions Sction 5 Drivativs of Trigonomtric functions Wat you nd to know alrady: Basic trigonomtric limits, t dfinition of drivativ,
More informationDual Nature of Matter and Radiation
Higr Ordr Tinking Skill Qustions Dual Natur of Mattr and Radiation 1. Two bas on of rd ligt and otr of blu ligt of t sa intnsity ar incidnt on a tallic surfac to it otolctrons wic on of t two bas its lctrons
More informationGMm. 10a-0. Satellite Motion. GMm U (r) - U (r ) how high does it go? Escape velocity. Kepler s 2nd Law ::= Areas Angular Mom. Conservation!!!!
F Satllt Moton 10a-0 U () - U ( ) 0 f ow g dos t go? scap locty Kpl s nd Law ::= Aas Angula Mo. Consaton!!!! Nwton s Unsal Law of Gaty 10a-1 M F F 1) F acts along t ln connctng t cnts of objcts Cntal Foc
More informationALLEN. è ø = MB = = (1) 3 J (2) 3 J (3) 2 3 J (4) 3J (1) (2) Ans. 4 (3) (4) W = MB(cosq 1 cos q 2 ) = MB (cos 0 cos 60 ) = MB.
at to Succss LLEN EE INSTITUTE KT (JSTHN) HYSIS 6. magntic ndl suspndd paalll to a magntic fild quis J of wok to tun it toug 60. T toqu ndd to mata t ndl tis position will b : () J () J () J J q 0 M M
More informationP a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
More informationWhile flying from hot to cold, or high to low, watch out below!
STANDARD ATMOSHERE Wil flying fom ot to cold, o ig to low, watc out blow! indicatd altitud actual altitud STANDARD ATMOSHERE indicatd altitud actual altitud STANDARD ATMOSHERE Wil flying fom ot to cold,
More informationChapter 1 The Dawn of Quantum Theory
Chapt 1 Th Dawn of Quantum Thoy * By th Lat 18 s - Chmists had -- gnatd a mthod fo dtmining atomic masss -- gnatd th piodic tabl basd on mpiical obsvations -- solvd th stuctu of bnzn -- lucidatd th fundamntals
More informationProblem Set 5: Universal Law of Gravitation; Circular Planetary Orbits
Poblem Set 5: Univesal Law of Gavitation; Cicula Planetay Obits Design Engineeing Callenge: Te Big Dig.007 Contest Evaluation of Scoing Concepts: Spinne vs. Plowe PROMBLEM 1: Daw a fee-body-diagam of a
More informationChapter 4. QUANTIZATION IN FIVE DIMENSIONS
Chat QUANTIZATION IN FIVE DIMENSIONS Th cding dvlomnt ovids a tmndous walth o mathmatical abstactions Howv th sms within it no adily aant mthod o intting th nw ilds I th aas to b no hysical ntity which
More informationDifferential Kinematics
Lctu Diffntia Kinmatic Acknowgmnt : Pof. Ouama Khatib, Robotic Laboato, tanfo Univit, UA Pof. Ha Aaa, AI Laboato, MIT, UA Guiing Qution In obotic appication, not on th poition an ointation, but th vocit
More informationEquilibria of a cylindrical plasma
// Miscellaneous Execises Cylinical equilibia Equilibia of a cylinical plasma Consie a infinitely long cyline of plasma with a stong axial magnetic fiel (a geat fusion evice) Plasma pessue will cause the
More information( V ) 0 in the above equation, but retained to keep the complete vector identity for V in equation.
Cuvlna Coodnats Outln:. Otogonal cuvlna coodnat systms. Dffntal opatos n otogonal cuvlna coodnat systms. Dvatvs of t unt vctos n otogonal cuvlna coodnat systms 4. Incompssbl N-S quatons n otogonal cuvlna
More informationD-Cluster Dynamics and Fusion Rate by Langevin Equation
D-Clust Dynamics an Fusion at by Langvin Equation kito Takahashi** an Noio Yabuuchi High Scintific sach Laboatoy Maunouchi-4-6, Tsu, Mi, 54-33 Japan **Osaka Univsity STCT Conns matt nucla ffct, spcially
More informationAddition of Angular Momentum
Addition of Angula Moentu We ve leaned tat angula oentu i ipotant in quantu ecanic Obital angula oentu L Spin angula oentu S Fo ultielecton ato, we need to lean to add angula oentu Multiple electon, eac
More informationGeneral Relativity Homework 5
Geneal Relativity Homewok 5. In the pesence of a cosmological constant, Einstein s Equation is (a) Calculate the gavitational potential point souce with = M 3 (). R µ Rg µ + g µ =GT µ. in the Newtonian
More information10 Derivatives ( )
Instructor: Micael Medvinsky 0 Derivatives (.6-.8) Te tangent line to te curve yf() at te point (a,f(a)) is te line l m + b troug tis point wit slope Alternatively one can epress te slope as f f a m lim
More informationADDITIVE INTEGRAL FUNCTIONS IN VALUED FIELDS. Ghiocel Groza*, S. M. Ali Khan** 1. Introduction
ADDITIVE INTEGRAL FUNCTIONS IN VALUED FIELDS Ghiocl Goza*, S. M. Ali Khan** Abstact Th additiv intgal functions with th cofficints in a comlt non-achimdan algbaically closd fild of chaactistic 0 a studid.
More informationVaiatin f. A ydn balln lasd n t n ) Clibs u wit an acclatin f 6x.8s - ) Falls dwn wit an acclatin f.8x6s - ) Falls wit acclatin f.8 s - ) Falls wit an acclatin f.8 6 s-. T wit f an bjct in t cal in, sa
More information( ) ( ) Last Time. 3-D particle in box: summary. Modified Bohr model. 3-dimensional Hydrogen atom. Orbital magnetic dipole moment
Last Time 3-dimensional quantum states and wave functions Couse evaluations Tuesday, Dec. 9 in class Deceasing paticle size Quantum dots paticle in box) Optional exta class: eview of mateial since Exam
More informationCollective Focusing of a Neutralized Intense Ion Beam Propagating Along a Weak Solenodial Magnetic Field
Havy Ion Fusion Scinc Vitual National Laoatoy Collctiv Focusing of a Nutalizd Intns Ion Bam Popagating Along a Wak Solnodial Magntic Fild M. Dof (LLNL) In collaoation with I. Kaganovich, E. Statsv, and
More informationElectrodynamics Subject Exam Prep Quiz, Tuesday, May 2, 2017
Electodynamics ubject Exam Pep Quiz, Tuesday, May, 017 a ( b c ) b( a c ) c ( a b), a ( b c ) b ( c a ) c ( a b), ( a b) ( c d) ( a c )( b d) ( a d)( b c ), ( ψ) 0, ( a ) 0, ( a ) ( a ) a, (ψ a) a ψ +
More informationElementary Mechanics of Fluids
CE 39 F an McKinny Elmntay Mcanics o Flui Flow in Pis Rynol Eximnt Rynol Num amina low: Fluid movs in smoot stamlins Tuulnt low: iolnt mixin, luid vlocity at a oint vais andomly wit tim Tansition to tuulnc
More informationsin sin 1 d r d Ae r 2
Diffction k f c f Th Huygn-Fnl Pincil tt: Evy unobtuct oint of vfont, t givn intnt, v ouc of hicl cony vlt (ith th m funcy tht of th imy v. Th mlitu of th oticl fil t ny oint byon i th uoition of ll th
More informationTest on Nuclear Physics
Test on Nuclear Pysics Examination Time - 40 minutes Answer all questions in te spaces provided Tis wole test involves an imaginary element called Bedlum wic as te isotope notation sown below: 47 11 Bd
More informationSUPPLEMENTARY INFORMATION
SUPPLMNTARY INFORMATION. Dtmin th gat inducd bgap cai concntation. Th fild inducd bgap cai concntation in bilay gaphn a indpndntly vaid by contolling th both th top bottom displacmnt lctical filds D t
More informationGauge Institute Journal, Vol. 11, No. 3, August 2015
Gaug Institut Jounal, Vol., o. 3, August 05 Th uton as a Collasd-Hydogn Atom: Zo Point Engy & ucla Binding Engy, X Rays & Gamma Rays, ucla Focs & Bonding utonic Elctons Oitals, and uton Stas vic0@comcast.nt
More informationOverview. 1 Recall: continuous-time Markov chains. 2 Transient distribution. 3 Uniformization. 4 Strong and weak bisimulation
Rcall: continuous-tim Makov chains Modling and Vification of Pobabilistic Systms Joost-Pit Katon Lhstuhl fü Infomatik 2 Softwa Modling and Vification Goup http://movs.wth-aachn.d/taching/ws-89/movp8/ Dcmb
More informationFourier transforms (Chapter 15) Fourier integrals are generalizations of Fourier series. The series representation
Pof. D. I. Nass Phys57 (T-3) Sptmb 8, 03 Foui_Tansf_phys57_T3 Foui tansfoms (Chapt 5) Foui intgals a gnalizations of Foui sis. Th sis psntation a0 nπx nπx f ( x) = + [ an cos + bn sin ] n = of a function
More informationForging Analysis - 2. ver. 1. Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
Foging Analysis - ve. 1 Pof. ames Sing, Notes by D. Sing/ D. Colton 1 Slab analysis fictionless wit fiction ectangula Cylindical Oveview Stain adening and ate effects Flas edundant wo Pof. ames Sing, Notes
More informationFI 3103 Quantum Physics
7//7 FI 33 Quantum Physics Axan A. Iskana Physics of Magntism an Photonics sach oup Institut Tknoogi Banung Schoing Equation in 3D Th Cnta Potntia Hyognic Atom 7//7 Schöing quation in 3D Fo a 3D pobm,
More informationAP Calculus Multiple-Choice Question Collection
AP Calculus Multipl-Coic Qustion Collction 985 998 . f is a continuous function dfind for all ral numbrs and if t maimum valu of f () is 5 and t minimum valu of f () is 7, tn wic of t following must b
More informationEE 5337 Computational Electromagnetics (CEM) Method of Lines
11/30/017 Instucto D. Ramon Rumpf (915) 747 6958 cumpf@utp.u 5337 Computational lctomagntics (CM) Lctu #4 Mto of Lins Lctu 4 Ts nots ma contain copigt matial obtain un fai us uls. Distibution of ts matials
More informationIntroduction. Learning Objectives. On completion of this chapter you will be able to:
Introduction Learning Objectives On completion of tis capter you will be able to: 1. Define Compton Effect. 2. Derive te sift in incident ligt wavelengt and Compton wavelengt. 3. Explain ow te Compton
More informationPhysics Courseware Electromagnetism
Pysics Cousewae lectomagnetism lectic field Poblem.- a) Find te electic field at point P poduced by te wie sown in te figue. Conside tat te wie as a unifom linea cage distibution of λ.5µ C / m b) Find
More information0.1 Differentiation Rules
0.1 Differentiation Rules From our previous work we ve seen tat it can be quite a task to calculate te erivative of an arbitrary function. Just working wit a secon-orer polynomial tings get pretty complicate
More informationThe Electron in a Potential
Te Electron in a Potential Edwin F. Taylor July, 2000 1. Stopwatc rotation for an electron in a potential For a poton we found tat te and of te quantum stopwatc rotates wit frequency f given by te equation:
More informationH 2+ : A Model System for Understanding Chemical Bonds
: Modl Sytm fo Undtanding Chmical ond a - b R Th fit iu w hav to dal with i th multipl nucli; now w can hav nucla vibation and otation fo th fit tim. Impotant digion: on-oppnhim appoximation. V NN E l
More informationLecture: Experimental Solid State Physics Today s Outline
Lecture: Experimental Solid State Pysics Today s Outline Te quantum caracter of particles : Wave-Particles dualism Heisenberg s uncertainty relation Te quantum structure of electrons in atoms Wave-particle
More informationNotes 24 Image Theory
ECE 3318 Applied Electricity and Magnetism Spring 218 Prof. David R. Jackson Dept. of ECE Notes 24 Image Teory 1 Uniqueness Teorem S ρ v ( yz),, ( given) Given: Φ=ΦB 2 ρv Φ= ε Φ=Φ B on boundary Inside
More informationLecture 23 Flux Linkage and Inductance
Lecture 3 Flux Linkage and nductance Sections: 8.10 Homework: See omework file te sum of all fluxes piercing te surfaces bounded by all turns (te total flux linking te turns) Λ= NΦ, Wb Flux Linkage in
More informationMagnetic effects and the peculiarity of the electron spin in Atoms
Magtic ffcts ad t pculiaity of t lcto spi i Atos Pit Za Hdik otz Nobl Piz 90 Otto t Nobl 9 Wolfgag Pauli Nobl 95 ctu Nots tuctu of Matt: Atos ad Molculs; W. Ubacs T obital agula otu of a lcto i obit iclassical
More informationThe Real Hydrogen Atom
T Ra Hydog Ato ov ad i fist od gt iddt of :.6V a us tubatio toy to dti: agti ffts si-obit ad yfi -A ativisti otios Aso av ab sift du to to sfitatio. Nd QD Dia q. ad dds o H wavfutio at sou of ti fid. Vy
More informationRE 11.e Mon. Review for Final (1-11) HW11: Pr s 39, 57, 64, 74, 78 Sat. 9 a.m. Final Exam (Ch. 1-11)
Mon. Tue. We. ab i..4-.6, (.) ngula Momentum Pincile & Toque.7 -.9, (.) Motion With & Without Toque Rotation Coue Eval.0 Quantization, Quiz RE.c EP RE. RE.e Mon. Review fo inal (-) HW: P 9, 57, 64, 74,
More informationPhoton Energy (Particle Like)
L8 Potovoltaic Lctu : Caactitic of Sunligt. Todd J. Kai tjkai@c.montana.du patmnt of lctical and Comput ngining Montana Stat Univity - Bozman Wav Paticl uality Ligt bav a bot a wav and a paticl Wav Popti
More informationQuantum Mechanics I - Session 5
Quantum Mechanics I - Session 5 Apil 7, 015 1 Commuting opeatos - an example Remine: You saw in class that Â, ˆB ae commuting opeatos iff they have a complete set of commuting obsevables. In aition you
More informationDifferential Equations
Pysics-based simulation xi Differential Equations xi+1 xi xi+1 xi + x x Pysics-based simulation xi Wat is a differential equation? Differential equations describe te relation between an unknown function
More informationShor s Algorithm. Motivation. Why build a classical computer? Why build a quantum computer? Quantum Algorithms. Overview. Shor s factoring algorithm
Motivation Sho s Algoith It appas that th univs in which w liv is govnd by quantu chanics Quantu infoation thoy givs us a nw avnu to study & tst quantu chanics Why do w want to build a quantu coput? Pt
More informationPath to static failure of machine components
Pat to static failure of macine components Load Stress Discussed last week (w) Ductile material Yield Strain Brittle material Fracture Fracture Dr. P. Buyung Kosasi,Spring 008 Name some of ductile and
More informationPhysics 122, Fall December 2012
Physics 1, Fall 01 6 Decembe 01 Toay in Physics 1: Examples in eview By class vote: Poblem -40: offcente chage cylines Poblem 8-39: B along axis of spinning, chage isk Poblem 30-74: selfinuctance of a
More information( )( )( ) ( ) + ( ) ( ) ( )
3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13
More informationCase Study 1 PHA 5127 Fall 2006 Revised 9/19/06
Cas Study Qustion. A 3 yar old, 5 kg patint was brougt in for surgry and was givn a /kg iv bolus injction of a muscl rlaxant. T plasma concntrations wr masurd post injction and notd in t tabl blow: Tim
More informationAPP-IV Introduction to Astro-Particle Physics. Maarten de Jong
APP-IV Introduction to Astro-Particl Physics Maartn d Jong 1 cosmology in a nut shll Hubbl s law cosmic microwav background radiation abundancs of light lmnts (H, H, ) Hubbl s law (199) 1000 vlocity [km/s]
More informationSection 15.6 Directional Derivatives and the Gradient Vector
Section 15.6 Directional Derivatives and te Gradient Vector Finding rates of cange in different directions Recall tat wen we first started considering derivatives of functions of more tan one variable,
More informationNotes on wavefunctions II: momentum wavefunctions
Notes on wavefunctions II: momentum wavefunctions and uncertainty Te state of a particle at any time is described by a wavefunction ψ(x). Tese wavefunction must cange wit time, since we know tat particles
More informationEXAMINATION IN 2C1134 Electrotechnical design December
SOLUTIONS: EXAMINATION IN C4 Electotechnical esign Decembe --6 Solution to oblem : The temeatue ise o staight conuctos buie in goun is given b Li D Ti Pi Pk πλ πλ g i k i g ik ik whee L i is thei eth une
More informationStructure of Hadrons. quarks d (down) s (strange) c (charm)
quaks Flavo A t t 0 S B T Q(e) Mc 2 (GeV) u (up) 1 3 1 2-1 2 0 0 0 0 2 3 0.002-0.008 d (down) 1 3 1 2 1 2 0 0 0 0-1 3 0.005-0.015 s (stange) 1 3 0 0-1 0 0 0-1 3 0.1-0.3 c (cham) 1 3 0 0 0 1 0 0 2 3 1.0-1.6
More informationAnyone who can contemplate quantum mechanics without getting dizzy hasn t understood it. --Niels Bohr. Lecture 17, p 1
Anyone who can contemplate quantum mechanics without getting dizzy hasn t undestood it. --Niels Boh Lectue 17, p 1 Special (Optional) Lectue Quantum Infomation One of the most moden applications of QM
More informationb) The array factor of a N-element uniform array can be written
to Eam in Antenna Theo Time: 18 Mach 010, at 8.00 13.00. Location: Polacksbacken, Skivsal You ma bing: Laboato epots, pocket calculato, English ictiona, Råe- Westegen: Beta, Noling-Östeman: Phsics Hanbook,
More information2 Lecture 2: The Bohr atom (1913) and the Schrödinger equation (1925)
1 Lectue 1: The beginnings of quantum physics 1. The Sten-Gelach expeiment. Atomic clocks 3. Planck 1900, blackbody adiation, and E ω 4. Photoelectic effect 5. Electon diffaction though cystals, de Boglie
More information