Rutherford Scattering & Size of Nucleus

Transcription

1 Bria Wcht, th TA is back! Pl. giv all rgrad rqusts to him Quiz 4 is This Friday : Chaptr 3 Emphasis will b O th Ruthrord Scattrig & Th Bohr Atom Ruthrord Scattrig & Siz o Nuclus distac o closst appoach r siz o uclus 1 Kitic rgy o 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 o 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 o Nuclus = 1 Siz o Atom = Al = m m ( Z)( ) r 15 m

2 Spctral Obsrvatios : sris o lis with a pattr Empirical obsrvatio (by trial & rror) All ths sris ca b summarizd i a simpl ormula = R, > i, i = 1,,3,4.. λ i Fittig to spctral li sris data Rydbrg Costat R= How dos o xplai this? m 7 1 Bohr s Bold Modl o 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 rom a stabl orbit o highr rgy stabl orbit o lowr rgy E -E i = h =hc/λ 5. Ergy chag quatizd = rqucy o radiatio

3 Gral Two body Motio udr a ctral orc Rducd Mass o -body systm + F - m V rducs to r m Both Nuclus & - rvolv aroud thir commo ctr o mass (CM) Such a systm is quivalt to sigl particl o rducd mass µ that rvolvs aroud positio o Nuclus at a distac o ( - -N) sparatio µ= (m M)/(m +M), wh M>>m, µ=m (Hydrog atom) Νot so wh calculatig Muo (m µ = 7 m ) or qual mass chargs rotatig aroud ach othr (similar to what you saw i gravitatio) Allowd Ergy Lvls & Orbit Radii i Bohr Modl 1 E=KE+U = mv k r Forc Equality or 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 o Elctro Orbit : mvr = v =, mr substitut i KE= mv = r r =, = 1,,... mk = 1 Bohr Radius a 1 1 a = =.59 1 m mk I g r = a = 1 ral ; 1,,... Quatizd orbits o rotatio k

4 Ergy Lvl Diagram ad Atomic Trasitios k E = K + U = r sic r = a, =quatum umbr Itrstat trasitio: k 13.6 E = = V, = 1,,3.. a E k 1 1 = a i = h = E E k 1 1 = ha i k = = λ c hca i i i 1 1 = R i Hydrog Spctrum: as xplaid by Bohr E k = a Z Bohr s R sam as th Rydbrg Costat R drivd mprically rom photographs o th spctral sris

5 Aothr Look at th Ergy lvls E = k a Z Rydbrg Costat Bohr s Atom: Emissio & Absorptio Spctra photo photo

6 Som Nots About Bohr Lik Atoms Groud stat o Hydrog atom (=1) E = V Mthod or calculatig rgy lvls tc applis to all Hydroglik atoms -1 aroud +Z Exampls : H +, Li ++ Ergy lvls would b dirt i rplac lctro with Muos Bohr s mthod ca b applid i gral to all systms udr a ctral orc (.g. gravitatioal istad o Coulombic) QQ 1 M1M I chag Ur ( ) = k G r r Chags vry thig: E, r, tc "Importac o costats i your li" Bohr s Corrspodc Pricipl It ow appars that thr ar two dirt worlds with dirt laws o physics govrig thm Th macroscopic world Th microscopic world How dos o trascd rom o world to th othr? Bohr s corrspodc Pricipl prdictios o quatum thory must corrspod to prdictios o th classical physics i th rgim o sizs whr classical physics is kow to hold. wh [Quatum Physics] = [Classical Physics]

7 Atomic Excitatio by Elctros: Frack-Hrtz Expt Othr ways o Ergy xchag ar also quatizd! Exampl: Trasr rgy to atom by collidig lctros o it Acclrat lctros, collid with Hg atoms, masur rgy trasr i ilastic collisio (rtardig voltag) Atomic Excitatio by Elctros: Frack-Hrtz Expt Plot # o lctros/tim (currt) ovrcomig th rtardig pottial (V) Equally spacd Maxima ad miima i I-V curv E E Atoms accpt oly discrt amout o Ergy, o mattr th ashio i which rgy is trasrd

8 Bohr s Explaatio o Hydrog lik atoms Bohr s Smiclassical thory xplaid som spctroscopic data Nobl Priz : 19 Th hotch-potch o clasical & quatum attributs lt may (Eisti) ucovicd appard to m to b a miracl ad appars to m to b a miracl today... O ought to b ashamd o th succsss o th thory Problms with Bohr s thory: Faild to prdict INTENSITY o spctral lis Limitd succss i prdictig spctra o Multi-lctro atoms (H) Faild to provid tim volutio o systm rom som iitial stat Ovrmphasizd Particl atur o mattr-could ot xplai th wavparticl duality o light No gral schm applicabl to o-priodic motio i subatomic systms Codmd as a o trick poy! Without udamtal isight raisd th qustio : Why was Bohr succssul? Pric Louis d Brogli Ky to Bohr atom was Agular momtum quatizatio Why Quatizatio mvr = L = h/π? Ivokig symmtry i atur th Pric dbrogli postulatd Bcaus photos hav wav ad particl lik atur particls must hav wav lik proprtis Elctros hav accompayig pilot wav (ot EM) which guid particls thru spactim. Mattr Wav : Pilot wav o Wavlgth λ= h / p = h / (γmv) rqucy = E / h I mattr has wav lik proprtis th thr would b itrrc (dstructiv & costructiv) Us aalogy o stadig wavs o a pluckd strig to xplai th quatizatio coditio o Bohr orbits