(Lecture 5) The Atomic Models

Transcription

1 (Lctu 5) Th Atomic Modls. Ruthfod Scattig Expimt Ruthfod α- 입자산란실험 : E. Ruthfod, Gig, Masd 9 년경. (Expimtal aagmt) /, 의비율로 α- 입자들이 9 이상으로편향.. Thomso Modl of th Atom Thomso modl plum-puddig modl dispsiv positiv chag cloud + lcto plum Aalysis of Ruthfod scattig i Thomso modl + 전하가반경 R( 원자반경 ) 내에균일하게분포. Sufac pottial V ( R) R Ct pottial 3 V () 8πε R +z 의전하가 ct 를통과하는경 우의 pottial 높이 3 8πε z R Vc 5-

2 α-입자의경우 z, Au foil Z79, R Å - m V c 34 V E α 5 MV 5 6 V >>> V c 단일충돌에의해서는큰각도로의산란이불가능. 전자와의충돌? 전자질량 (/75)( α-입자질량 ) 다중산란 (multipl scattig) : 산란각의평균 θ, 산란각의분산 산란각 θ 에대한분포함수 θ σ Gaussia N( θ) N() θ / σ 산란각 θ에대한단위입체각당산란수 N() : 방향의단위입체각당산란수 5% 산란각도 θ p.6745σ.87 σ.3 주어진 σ에대해 θ 9 일때는 o N ( 9 ) N () N() (log.434) 3. Ruthfod Modl of th Atom Implicatio of lag agl scattig i th Ruthfod xpimt lag dflctio y a sigl cout vy its fild (foc) fom clos cout vy coctatd(small volum) chag (at th uclus) & lctos suoudig th uclus Aalysis of Ruthfod scattig α-paticl 의 impact paamt (ukow) iitial vlocity v fial vlocity v f lctostatic pottial z 표적핵의질량 >> α-입자의질량, 따라서표적핵의반동 (coil) 무시 표적핵은고정 ( 원점 ), 좌표계 (, φ), 산란각 θ 5-

3 총에너지보존법칙 E mv mv m( & + φ& f z ) + v f v : fial asymptotic vlocity iitial vlocity 각운동량보존법칙 ( 中心力작용 ) m mv mv f φ& ; v f 이므로 v Lt a paamt q ( 정면충돌시의최단접근거리 ) ( z ) / cost E / q & mv -: appoachig, +: cdig / dφ q m d dφ d &φ & istad of φ & (, φ ) appoachig poit A (solutio) φ cos + q q / cos + q q closst appoach : A, & A A A 5-3

4 φ A cos cos + q π cos + q symmtic tajctoy aout A : θ π φ A cos + q Lt θ q cos, th + q + q + q θ si. q cos si θ θ θ cot o q cot θ ( 와 θ 간의관계 ) impact paamt ag (, +d) aa dσ dflctio (θ, θ-dθ) dσ πd cot θ q dθ q d si ( θ / ) cos( θ / ) q dω d σ πd πq dθ ( dωπsiθdθ) 3 si ( θ / ) 4 si 4 ( θ / ) o dσ z d Ω 6E si 4 ( θ / ) : Ruthfod scattig coss sctio Ruthfod coss sctio : θ, (dσ/dω) R ( ) Ral situatio : lag, pottial (/) (/)xp(-/c) Du to th lcto scig of th ucla chag max ~ R (siz of th atom) > max, pottial ~ littl scattig 원자구조 핵 + 궤도전자 궤도전자의가속및에너지방출문제 표적의반동을고려하려면 CM 계에서위의과정을논의 결과식은동 일한형태이되 E E cm μv /, θ CM 계에서의산란각으로취급하면됨. 4. Th Hydog Spctum Light spctum Distiutio of itsity as a fuctio of wavlgth(o fqucy) 5-4

5 Optical spctomt light souc(a dischag lamp) + dispsig dvic(a pism o a gatig) + dtctio dvic(a simpl sc o a photogaphic plat oa PM tu) + fiig compots(slits ad ls tc.) Pism spctomt : Gatig spctomt : tasmissio gatig(fi goovs o a pla glass sufac) flctio gatig(fi goovs o a polishd mtal mio) Rflctio gatig quatio : d(si θi si θ) λ ( : itg) o-od flctio (mio flctio) θ i θ Typically, d ~ -4 cm, λ ~ -5 cm 5-5

6 Empiical fomulas : Balm fomula of hydog spctum λ(å) 4, 3,4, Rydg fomula fo havi lmts R ν A λ ( + α) ν : wav um /λ 또는 ducd wav um k/π R : Rydg costat m - A, α : adjustig costats to th paticula lmt, pat of th spctum o spctal sis Ritz fomula : R ν λ ( m + β) R ( + α) if αβ, m, this is ducd to th Balm fomula Pasch s hydog lis i th ifad gio : αβ, m3, 4,5,6, R m, m ν 5. Th Boh Modl Th accuat mpiical fomula fo hydog spctum ν R m 93 년, Daish physicist Nils Boh 일종의 platay modl 을수소원자에대해제안. 5-6

7 단일행성의태양계 단일전자의수소 중력 ( 만유인력 ) 에의한행성운동 전자기력에의한전자운동 F MM qq G F lliptic oit cicula oit( 가정 ) ct of th oit locatio(ct) of th uclus F o v mv ma m No futh limitatio o v ad i classical physics. Boh s postulat : agula momta (h/π) o ħ m v h, h h / π,,,3, L εh πm.59 ( A ) Z wh a Boh adius (adius of th fist oit i hydog) v h m h m ( Z m a o.59 - m v / h) A impotat costat fqutly mt i th quatum lctodyamics: Fi stuctu costat v α c h m ca Pottial gy (of lcto) Kitic gy Total gy E E k + E p E hc k 37.4 E p m v 8πε πm a Z 4 8πε 8πε ε h 8ε h a,,3, : picipal quatum um ( 주양자수主量子數 ) m Z 5-7

8 3.6 E E ( V ), -E : idig gy of th -th oit lcto O polm) 하전입자의가속 adiatio 발생 ( 고전전자기학 ) de q a Lamo s fomula :, a : acclatio 3 dt 6πε c oital gy loss y adiatio fall dow to th uclus Boh s scod postulat o adiatio : 궤도상의전자는 adiatio gy 를방출하지않음. Radiatio 은높은에너지준위에서낮은에너지준위로천이 (tasitio) 할때, 그에너지차이만큼이 adiatio quatum hν 로방출됨. Boh s fomula hν E E ) ( > 4 4 m ν Z mz o ν 3 3 8ε h λ c 8ε h c ν wh th cofficit is th Rydg costat, 4 m R m - R 3 (M ). 8ε h c Fiit ucla mass lcto ad uclus oit aoud th CM R CM 계에서의계산 R + ( m / M ) A slight vaiatio fom lmt to lmt 5-8

9 Idtificatio of vaious spctal sis : : Balm sis (884) visil light 3 : Pasch sis (98) ifad(ir) : Lyma sis (96) fa ultaviolt(uv) 4 : Backtt sis (9) ifad 5 : Pfud sis (94) ifad 6. Citicism ad lat dvlopmt M. Plack : quatizatio of adiatio(lctomagtic fild) gy xchag tw hatd ody ad th suoudig EM fild N. Boh : quatizatio of agula momtum ad quatizatio of gy lvls i atoms 5-9

10 ( 문제점 ). 수소원자의 fi spctum : 고분해능분광계로측정하면,3, 등의 li 들이분리되어있음 (doult) Sommfld s lliptic oit tatmt & lativistic coctio (, θ) 두개의운동자유도 adial ad azimuthal quatum ums, θ Old quatizatio uls p dq h q o θ q q, Uhlck ad Goudsmit : lcto spi 제의 (95) / 98, P. A. M. Diac 의전자상대양자론. O lcto modl : 두개이상의전자가존재할때 ctal foc 조건은충족불능. 파동역학 ( 量子力學 ) 의방법론. H 이상의원자번호에대해서는수학적으로여전히해석적해가난해. Hat-Fock appoach 3. Quatum Jump : 하나의에너지준위에서다른에너지준위로의 tasitio 이 quatum jump 로발생. Sommfld 의 old quatizatio coditio 으로 quatum jump 에 slctio ul 이존재함을발견하나설명은난이함. Wav mchaics ( 또는양자역학 Quatum Mchaics) 로서해결. Biliogaphy : (Basic). H.A. Eg, M.R. Wh, ad J.A. Richads, Itoductio to Atomic Physics, Radig, Addiso-Wsly Pulishig Compay, Ic., 97. F.A. Jkis ad H.E. Whit, Fudamtals of Optics, 4 th Ed., Tokyo, McGaw- Hill Kogakusha, Ltd., 957, 976 (Itmdiat) 3. F.K. Richtmy, E.H. Kad ad J.N. Coop, Itoductio to Mod Physics, Nw Yok, McGaw-Hill Ic., R. Eisg ad R. Rsick, Quatum Physics of Atoms, Molculs, Solids, Nucli ad Paticls, d Ed., Nw Yok, Joh Wily & Sos Ic., 974, H.E. Whit, Itoductio to Atomic Spcta, Sigapo, McGaw-Hill Itatioal Ic.,