Physics 2D Lecture Slides Lecture 14: Feb 3 rd 2004

Transcription

1 Bria Wcht, th TA is back! Pl. giv all rgrad rqusts to him Quiz 4 is This Friday Physics D Lctur Slids Lctur 14: Fb 3 rd 004 Vivk Sharma UCSD Physics

2 Whr ar th lctros isid th atom? Early Thought: Plum puddig modl Atom has a homogous distributio of Positiv charg with lctros mbddd i thm (atom is utral) Positivly chargd mattr or +? + Cor How to tst ths hypothss? Shoot bullts at th atom ad watch thir trajctory. What Kid of bullts? Idstructibl chargd bullts Ioizd H ++ atom = α ++ particls Q = +, Mass M α =4amu >> m, V α = x 10 7 m/s (o-rlavistic) [chargd to prob charg & mass distributio isid atom] Plum Puddig Modl of Atom No-rlativistic mchaics (V α /c = 0.1) I Plum-puddig modl, α-rays hardly scattr bcaus Positiv charg distributd ovr siz of atom (10-10 m) M α >> M (lik movig truck hits a bicycl) prdict α-rays will pass thru array of atoms with littl scattr (~1 o ) Nd to tst this hypothsis Erst Ruthrford

3 Probig Withi a Atom with α Particls Most α particls pass thru gold foil with ary a dflctio SOME ( 10-4 ) scattr at LARGE agls Φ Ev fwr scattr almost backwards Why Ruthrford Scattrig discovrd by his PhD Studt (Marsd)

4 Ruthrford Discovrs Nuclus (Nobl Priz) Forc o α-particl du to havy Nuclus Outsid radius r =R, F Q/r Isid radius r < R, F q/r = Qr/R Maximum forc at radius r = R α particl trajctory is hyprbolic Scattrig agl is rlatd to impact par. kq Q θ = α Impact Paramtr b cot mv α α

5 Ruthrford Scattrig: Prdictio ad Exprimtal Rsult = 4 kzna 1 4 α α ϕ 4 R m v Si ( /) # scattrd Vs φ dpds o : = # of icidt alpha particls N = # of ucli/ara of foil Z = Nuclar charg K α of icidt alpha bam A= dtctor ara Ruthrford Scattrig & Siz of Nuclus distac of closst appoach r siz of uclus 1 Kitic rgy of α = K = mv α α β uclus uclus α particl will ptrat thru a radius r util all its kitic rgy is usd up to do work AGAINST th Coulomb pottial of th Nuclus: 1 mv MV= k K α = α β = 8 kz r = K For K =7.7.MV, Z = 13 α α kz r = K α Siz of Nuclus = 10 Siz of Atom = Al = m m ( Z)( ) r 15 m

6 Dimsio Mattrs! Siz of Nuclus = 10 Siz of Atom = m m how ar th lctros locatd isid a atom How ar thy hld i a stabl fashio cssary coditio for us to xist! All ths discovris will rquir w xprimts ad obsrvatios Ruthrford Atom & Classical Physics

7 Cotiuous & Discrt spctra of Elmts Visibl Spctrum of Su Through a Prism

8 Emissio & Absorptio Li Spctra of Elmts Kirchhoff Exprimt : D Lis i Na D lis dark oticably wh Sodium vapor itroducd Btw slit ad prism

9 Emissio & Absorptio Li Spctrum of Elmts Emissio li appar dark bcaus of photographic xposur Absorptio spctrum of Na Whil light passd thru Na vapor is absorbd at spcific λ Th Rapidly Vaishig Atom: A Classical Disastr! Not too hard to draw aalogy with dyamics udr aothr Ctral Forc Thik of th Gravitatioal Forc btw two objcts ad thir circular orbits. Prhaps th lctro rotats aroud th Nuclus ad is boud by thir lctrical charg MM 1 F= G k r QQ r 1 Laws of E&M dstroy this quivalt pictur : Why?

10 Bohr s Bold Modl of Atom: Smi Quatum/Classical - + r F Ur () = k r 1 KE = m v m V 1. Elctro i circular orbit aroud proto with vl=v. Oly statioary orbits allowd. Elctro dos ot radiat wh i ths stabl (statioary) orbits 3. Orbits quatizd: M vr = h/π (=1,,3 ) 4. Radiatio mittd wh lctro jumps from a stabl orbit of highr rgy stabl orbit of lowr rgy E f -E i = hf =hc/λ 5. Ergy chag quatizd f = frqucy of radiatio Gral Two body Motio udr a ctral forc Rducd Mass of -body systm + F - m V rducs to r m Both Nuclus & - rvolv aroud thir commo ctr of mass (CM) Such a systm is quivalt to sigl particl of rducd mass µ that rvolvs aroud positio of Nuclus at a distac of ( - -N) sparatio µ= (m M)/(m +M), wh M>>m, µ=m (Hydrog atom) Νot so wh calculatig Muo (m µ = 07 m ) or qual mass chargs rotatig aroud ach othr (similar to what you saw i gravitatio)

11 Allowd Ergy Lvls & Orbit Radii i Bohr Modl 1 E=KE+U = mv k r Forc Equality for Stabl Orbit Coulomb attractio = CP Forc k r mv KE = = k r Total Ergy E = KE+U= - k r Ngativ E Boud systm This much rgy must b addd to th systm to brak up th boud atom mv = r Radius of Elctro Orbit : mvr = v =, mr substitut i KE= mv = r r =, = 1,,... mk = 1 Bohr Radius a 1 10 a0 = = m mk I g r = a = 1 ral 0; 1,,... Quatizd orbits of rotatio 0 k Ergy Lvl Diagram ad Atomic Trasitios k E = K + U = r sic r = a, =quatum umbr 0 Itrstat trasitio: 0 k 13.6 E = = V, = 1,,3.. a E k 1 1 = a 0 i f = hf = E E f k 1 1 = ha 0 f i f k = = λ c hca i f i f i 1 1 = R f i f

12 Hydrog Spctrum: as xplaid by Bohr E k = a 0 Z Bohr s R sam as th Rydbrg Costat R drivd mprically from photographs of th spctral sris Aothr Look at th Ergy lvls E = k a 0 Z

13 Bohr s Atom: Emissio & Absorptio Spctra photo photo Som Nots About Bohr Lik Atoms Groud stat of Hydrog atom (=1) E 0 = V Mthod for calculatig rgy lvls tc applis to all Hydroglik atoms -1 aroud +Z Exampls : H +, Li ++ Ergy lvls would b diffrt if rplac lctro with Muos Bohr s mthod ca b applid i gral to all systms udr a ctral forc (.g. gravitatioal istad of Coulombic) QQ 1 M1M If chag Ur ( ) = k G r r Chags vry thig: E, r, f tc "Importac of costats i your lif"