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# Observations and Instrumentation 2 ASTR 3520

GPA 3.89

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This 61 page Class Notes was uploaded by Stephan Kuvalis on Thursday October 29, 2015. The Class Notes belongs to ASTR 3520 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/231963/astr-3520-university-of-colorado-at-boulder in Astronomy at University of Colorado at Boulder.

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Date Created: 10/29/15

Thursday September 13th Sommerfeld39s Refinements to the Bohr Model and Fine Structure Multielectron Atoms Permitted and Forbidden Line Emission Data Reduction Review amp Homework Questions Reduced Mass Correction Reduced Mass P quot395 1836153 me39mp 1 quot39memp3918238 u 54823x 10 4amu9 104589596X 10439 me u4793004302x10 319 Consequence for the Bohr Atom 2nzzze m 21r2124803 4793004302x1039 g nh2 166260755X103927ergs 6E00716eV A A4797A i1368x10 AA En Is fine structure important Fine structure is very small in general but significant for larger atoms with larger angular momenta szmEsz A EmEgB 9quot 57883817555x 10 S Zmecrr T I m3 3 3 gt E u E Lu lt 0 597 nm Sommerfeld39s Correction Semiclassical attempt to correct for small errors in the Bohr model treats electron orbits as ellipses The allowed eleetrenit erhits fer the feur main quantum numbers by the EehrSemmerfeld metiel Sommerfeld Quantization Instead of taking mvr nh which assumes a circular orbit use the path integral around the ellipse which is still angular momentum Ipdfnh 2 2 EUKZTepTmi 2 2 39 2 l3 m l l 7 rm 3 Since we39re looking an elliptical orbit Kepler39s 2nd law gives that angular momentum is conserved so L is a constant over the integral and therefore Ii d 2 if2lt 2 mwik i ie angular momentum is quantized l Him Em W 1 7 16151375 50 lam 1 1 73 we Lirecl 55 3531 amg KIgn 15 Wang Harvquot rk r 17555 MAJ M r fa ji WWW D f Hag same area 6W9 n h f Sommerfeld Correction to Energy There is no direct energy dependence on k but quotrelativistic effectsquot cause the orbits to precess Zze 1nilm221 3 T L o 7 7 i r quot 865171quot N k 4H Just as with the centerofmass correction we have a very small correction of order 45e5 eV or 1 angstroms Multielectron Atoms Energy calculated using approximations of Schrodinger equation called HartreeFock equanns centra potential of averaged nucleus and surrounding electrons quotexchange potentialquot effective repulsion from spin because of Pauli Exclusion principle Hund39s Rules strictly only for ground state larger spin gt lower energy in a given configuration and spin particles with the largest angular momentum havelowest energy Both result from electron repulsion spin from Pauli Exclusion angular momentum from electric repulsion Permitted Transitions Fine structure const 3dsz2 X 32 hC 312D32 Fine structure 5E E 14 5X10395 eV Spin orbit l s Hyperfine structure 5E 6x106 eV Selection Rules A1 0 1 Aj 0 1 even ltgt odd parity Ly 0c Forbidden Transitions Notation O 6300 Permitted Mg I 4571 Intercombination or Semiforbidden 0 II 7320 Forbidden Do Mn 5 no nu mm Retneve Data 7 Catalogue Lists Gel ALL Catalugue Cnlumns mienides check bnxes belmv M Shaw Snrt Cnlunul Variable UlnitlennnalEt I7 D 1d l7 Alternate ID alud l7 quot39 A 1 c DEC den 6 Slyma RA sxgaa mas 7 r Sjgma DEC slgdel mas r r Mean Epnch map years 4 Mu RA mura masyr 397 lquot mudec masyr l r Mu th mun nh m n r n Immediate Results USNO Archive Search Results for Field m57 Catalogge Info Image Info Center a 15 15 355 332012453 m57 Sue a 5 000040 a DD391D39DDD Equinox Epoch 120000 20000 o D a v y b a A a A O 0 v urns op a agmltm 3mgqu 012mm a U D 14gmltm 33vm o a Jegmqn 2mm aa uz gt21 m wroo x navy mnnmmm mun 171mm Slah n 2 25 The results you want to look at Catalogue and Finder Chart Results Star Chart w Flle Format Info Fleld Name 057 500mm 55059 12000 0 2000 00 Fleld enter 494951 19 9932750 7 33 0292500 huur5degreesl new sue 494951 01555557 x 0 1555557 degrees Pruuary Megnmae 92 Bnght and Famt Meg mus 000 10000 1 92 r 92 0e and Red Blur Lmlts r100 09 100 00 9roper Mutmn lens 0 00 10000 00 Immersseeyrl ataluques 0500791 L1s1 94 5505 Date furma l Juhan 555m wvwww ages Yes Image Database Information 55mm Plates Survey Fleld Plate Date Time 941919501 051 99 120001 051 Type F11t Exp 94 0510 Nlmg 90551 0335 257 19515095 05 20 4 994340 0525247 4900392 0525990 10395 992444 50 1 2 335 0001 90551 0335 257 1951 5095 0715 4 994340 0525247 4900392 0 525590 10390 None 12 275 su 336 0001 905511 0395 5504745 1992 5355 04 10 4 921925 0 510953 4 929591 0 511992 IIIaF 9051073 70 0 325 s10395 0002 905511 0395 5704093 1991 5332 05 93 4921954 0510952 4 929709 0511991 11191 50395 2 50 0 1E s0395 0002 905511 0395 51105957 1994 4527 0750 4 921759 0510950 47929513 0511979 1104 90979 50 1135 s00395 0004 905511 0455 5902415 19993374 0933 4 917523 0523594 4 925950 0 524593 IIIaF 9551073 100 2 275 stASS 00 1 905511 0459 5102497 1999 5072 05 27 4 917495 0 523590 4 925931 0 24590 11197 5539572 27E 510458 0002 905511 0459 5005300 1995 5524 04 90 4 917421 0 523579 4 925957 0 524597 1104 95979 95 1455 snu459 0004 NB n 111 mu 1 r 1 1 w 10 OFJJuuuute 01 909 M a A 1 a L web server The more p1xels that are requested the longer tins will take IRAF ReviewHelp I can help more with IRAF and computers than QM and physics I39ll leave that to Bally Onto demo of imexamine Homework 1 Analysis Orientation of the image to 1 degree precision The pixel scale on the sky in arcseconds per pixel Knowing that the pixel size is 68 micrometers calculate the effective focal length of the imaging system Estimate the magnitude of the faintest star that is reliably detected on the image Estimate the magnitude that corresponds to 1 count ADU on the image the photometric 0point I39m more concerned with how you choose to do these things than your actual answers please include an explanation if it39s a reasonable attempt but a wrong answer you39ll get more credit than a correct answer with no justification Tuesday September 11 Homework due Tuesday September 18th Outline Airmass Magnitudes Types of Spectra Blackbody Emission Line Photometry Basics Vega magnitudes m0 25 log F00 FVegak F0 Counts on source FVegaQ Counts on Vega Airmass z A sec 2 1 cosz Type of Spectra 0 Continuum Blackbody BVT freefree freebound Nonthermal Synchrotron radiation Compton scattering 0 Line amp Band E dipole B diplole E quadrupole fine structure hyperfine structure 0 O I n nnfrnn39l n francn1 nno Mi if T Stars A ABSORPTION SPECI39RA THE ELECTROMAGNETHC 5 P E CTRU M WEN Stars HELlur L 0t THESE WWI5 TRAVEL THROUGH THE ELECFRDF LBGNETIC HELD THEY WERE FORMERD GFRR39ED B me max1E2 w ICHMQS 155mm RE ampss law c1311 3 wqrr H 189 DUE TO BUDGET CUTS Opaque wwas m m quotgquot swwg gamma cagmmmms V L 8 18 L E 7 Gig La 3th w 85 quot C Il mm ro if r RawTr I CZ sianEl 39m I Half 600 quotQ mm SlNlSTER r s x 3 l VJ 39 39 39m w e m 1 lo 1039 mquot In mquot 1639 In coquot m mquot m mquot mquot 3925quot q u m quot mam Ian ye my n1 quot1 m c 1n 0 u cf w 1 a no 11 W 1 1 mm rho39 ro39 mquot rn mquot 40 m If mquot Ia mquot o39 5 laquot o39 m39 m n mquot vs 5 wquot mquot away WW Uh mu W In em mom in low naeIN 151 m mu m arm 59 DH mevs rsu Was m may a as 30 lw lv yP 4 6 I I In r I Ar 47 93947 2 W n n Emission line Ha 1e Planck Function Blackbody radiation Blackbody dlall0n 21113 1 52 LL 1 I11T erg S391 cm392 H2391 2 1 srl Vien BVIT 2 1 hv3 c2 e39hVkT 6 Wu 1 ayleighJeans PM 1 335 BvT 2kT72 MW e Planck Function Bla odyraliati n Jag 39mr ln ar an M Stella r WNWMM M h H kwv Spectra L w Blackbody WW continuum m M w Absorption Lines Wm WM Balmerjump ka m boundfree 3 transitions Hottest stars 0 AW stars have ionized W helium coolest stars have osv molecular 35mm 45mm 55mm EEDEI 75mm EEDEI Waveiengtn Angstrums transitions nization n to infinity hm E 136 3V 7 lt 912 Angstroms quot39 quotinm ransitions EhvEu El y Balmer mamma amnav v R 1nl2 111 2 R 3288 X 1015 Hz n 1I Elil Lohr model llowed orbits mvr nh 21 oulomh Force musmlaugweamgummmm Ze2 1 2 mV2r hus eliminate v r Ze2 mv2 n2h241tzle2 m nergy E 12 Ze2 r 2 11 Z2e4m n2h2 EmefuJm aghay Mm MW AELV 467 955mm 1 9 j im M4 em mM may me aw 5W7 M A r gt Lem enwgm 74 Jon M lfzkc flef39 Ionization Crosssection or hydrogen 136 eV 912 Angstrm 1011 Lyman line 5 v3 Balmer lines quot cur Crosssection l Wavelength 1 photon energy Atomic Structure 0 Refinements to Bohr Elliptical eorbits Integral of P in r and 6 lb 1 012 n1 Relativistic effects gt 1 makes small correction to Elevels Space quantization Orientation of orbits m Electron spin Atomic Structure Atomic quantum numbers completely specify 11 l m 5 state E n 1 2 3 4 shell M N max ne L 2 8 l O 1 2 3 4 s p d f g Atomic Structure Refinements to Bohr n Elliptical eorbits k Space quantization Orientation of orbits wrt magnetic eld m Electron spin s Pauli Ferminons No 2 e in same state nkms Shroedinger Wave function n gt principle quantum number radial 1 gt orbital angular momentum O 1 n m gt magnetic sublevels degenerate 2f 11 n Atomic Structure Multielectron atomsions Atomic quantum numbers completely specify nlms stateE n 1 2 3 4 shell L M N max 11e 2 8 1 O 1 2 3 4 s p d f 9 Al 1 Selection rules Orbitals Figure Iii12 F r39tlballlilitr densityplets nfseme hydrogen amnlie orbitals The uensitgr of the this represents the pr39nnbabilitr of nding the electron in that region 1933 U unremitjr Science Books quotQuantum Chemistryquot by Donald A McQuame 5 drogen energy levels showing allowed transitions A En e rm r EV DDU 4385 451 ydrogen energy levels showing fine structure 3d ZDSI2 3d 2Dsz Selection Rules A1 0 1 Aj 0 1 Ly 0c even ltgt odd H ground state um m 25 x 10 18 and A m 1095 1 Ionization amp Excitation o Radiation RT 0 Irad 039 cross section Collisions RC vgegalltw emalz my Aull Bu C 1 ll u Clu Tuesday September 11 Homework due Tuesday September 18th Outline Airmass Magnitudes Types of Spectra Blackbody Emission Line Photometry Basics Vega magnitudes m0 25 log Foo FVegaon F0 Counts on source FVegaO Counts 0n Vega Airm ass A sec z 1 c0sz Type of Spectra Continuum Blackbody BVT freefree freebound Nonthermal Synchrotron radiation Compton scattering Line amp Band E dipole B diplole E quadrupole ne structure hyper ne structure electronic transitions Vibrational transitions rotational transition Hot Opaque media Nebulae A til 5 El mti IZI H Li H E Stars fa ELECTROF LHGNETIC HEM E P E C T R U L ELECWNETIC F ELD THEY WERWORRR ED BYTHE I RED rawrm ramu can Bu mm 9 I WERE Ff Opaque Su E WAVES I 55mm IN 199 DUE TO BUDGET curs ABSORPTION spschA Stars m w medla A quot 39 quot 3 Emunail ammgufakms V L5 18 Lb HA W glw E29 Rpm vimo Ll GJWlT 94 MF 7 r PEFmTO 4 w CRITER ms w 39 gnu umEs V L amp 39 9 w WWW K 5 c3 1 39 U n 395 1 C a 3r o H TELEme RnDuo TV 1 xi 1 wquot m 5 rs A N DH W W 3 39n r vhWm39 39 m39 m laquot a n39 I n 00 mquot mo na w m mquot o mquot m m mquot wquot uquot lquotx wquot mu m cm mom JIIRI tom m 191 was am an a lu m mun gm u mm u an a m as 113 G 397 rr w w aquot r quot r 39 f fv a sea 1 394 39 Emission line Hon The Planck Function Blackbody radiation Blackbody radiation 21113 1 h 62 875 1 I11T erg s1 cm2 Hz1 2 1 srl Wien BVT 2 1 hv3 c1 9 w x pm 1 RayleighJeans BvT 2kTl2 mum x am The Planck F uncti Blackbody radiation E Infra en gulrmm Stellar Spectra Blackbody continuum Absorption Lines Balmerjump bound free transitions Hottest stars 0 stars Er have ionized helium coolest stars have molecular transitions 35mm 45mm 55mm BEDEI 75mm EEDEI Wavelength Angstrums Ionization n to in nity E 136 eV 7 lt 912 Angstroms Transitions E hv Eu El mamma amnav Ea m Balmer v R 1n12 1 muz R 3288 x 1015 Hz Lyman Bohr model Allowed orbits mvr nh 21I Coulomb Force Zez r2 var Thus eliminate v rZe1mv2 nzhz41I Ze2 m Energy 12 Zez r 2 12 Zze m nzh2 Construab aEaerV Thurs WW AELV 47 04mm jaunt mtquot exmz MM 904 In fweg Jaw EnsI77 M fgt sup mam 741 do M fzmjgzdh 7 C x p e Crosssection cmz oo Ionization crosssection or hydrogen v3 136 eV 912 Angstroms Lyman lines Balmer lines Wavelength 1 photon energy Atomic Structure Re nements to Bohr Elliptical eorbits Integral ofP in r and 9 lh l 012 n1 Relativistic effects gt 1 makes small correction to Elevels Space quantization Orientation of orbits m Electron spin Pauli No 2 e in same state Atomic Structure Atomic quantum numbers n l m s completely specify state E n 1 2 34 shell KL MN maxne 2 8 1 0 1 2 3 4 s p d f g Atomic Structure Re nements to Bohr n Elliptical e orbits k Space quantization Orientation of orbits Wrt magnetic eld m Electron spin s 0 Pauli F erminons No 2 e in same state nkms Shroedinger Wave function 11 gt principle quantum number radial 1 gt orbital angular momentum 0 1 n m gt magnetic sublevels degenerate if B0 s gt electron spid 12 Atomic Structure Multielectron atomsions Atomic quantum numbers n l m s completely specify state E n 1 2 3 4 shell K L M N max 116 2 8 1 0 1 2 3 4 s p d f g Selection rules A1 1 Orbitals a uvona Figure 612 Pruuhualluilitgr ensitypluts nfseme hydmgen amnlie orbitals The dB Sit f of the dais represents the prvoba39nlmilitr of nding the electron in that region 1933 U unremitjr Science Books quotQuantum Chen stryquot by Donald A McQuame Hydrogen energy levels showing allowed transitions 1 Energy EV DDU 4385 451 Hydrogen energy levels showing ne structure Zsle2 n1 1s 2812 V Selection Rules A 0 1 Aj 0 1 even ltgt odd Em Bm Absrom cn pl53 m J E 4 3 A 647r 11M 2 ul 3103 Mul H ground state um m 25 x 10 18 and A m 1095 1 Ionization amp Excitation Radlatlon Rr 039 Irad 039 cross section COHISIOHS Rc n 039 ltVtherWgt N 3 H 2 m12 ermal A1119 Bu C 111 B1 Clu ll

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