PHYS 450 Spring semester Lecture 08: Optical Spectroscopy and Spectral Lines. Ron Reifenberger Birck Nanotechnology Center Purdue University

Transcription

1 /4/01 PHYS 450 Spring semester 01 Lecture 08: Optical Spectroscopy and Spectral Lines Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 08 1 Roadmap: Where We ve Been and Where We re Going Overview & History: Concept of OPL Mirrors Lenses Refraction Prism; Dispersion Gratings OPL: Interference (-slits) Fresnel Diffraction Interferometers Fourier Optics Optical Instruments Spectroscopy Polarization 1

2 /4/01 Light from Gas Discharge Tube - Discrete Wavelengths (Ångström 1853, Sweden) Glass tube, evacuated and back-filled to low pressure with a gas like hydrogen, helium, neon, etc Glass prism light is dispersed Eventually, the prism was replaced by diffraction grating 3 3 Spectral Lines for Common Gases Check out Wavelengths accurately measured Why are there so many DISCRETE lines? 4

3 /4/01 Focus on visible light emitted from Hydrogen discharge tube Balmer s empirical formula (1884) explains the observed visible wavelengths from hydrogen with high accuracy n= n=6 n=5 n=4 n=3 Balmer s Series = RH - ; n =3, 4,5 λ n or 1 A = B ; n =3, 4,5 λ n Why does this work? 5 Finding the Series Limit: n 1/ (nm 1 ) B=R H /4 Balmer Series H Series Limit A=R H slope A0011 nm11010 m B nm nm 1 00 n 304 hc E n 335 ev /n 6 3

4 /4/01 The H Spectrum Series Limit Series Limit = R H - 1 ; n =,3, 4 λ n = R H - ; n =3,4,5 λ n = R H - ; n = 4,5,6 λ 3 n clicks Finding the Series Limit: n 1/ (nm 1 ) Series Limit Paschen Series - Hydrogen A0011 nm11010 m B nm nm n 833 hc E n 149 ev /n 8 4

5 /4/01 Schrödinger s wave equation for the H atom (196) m where U(r) r E r e -, m e ( x, yz, ) Uxyz (,, ) ( xyz,, ) E ( xyz,, ) x y z U( x, y, z) U( r) 1 qq 1 e 4 r 4 r r sin r,, m e r r r r sin r sin Ur ( ),,,, (, r, ) R() r ( ) () o o d m d ( ) ( ) 0 1 d d m sin ( ) ( 1) ( ) 0 sin d d sin d dr m ( 1) () () () 0 m r e rr r U r E rr r e where ( +1) and m are separation constants ev E mec n nlm,, nl, lm, n e 1 n 1,, 4 c (, r, ) R () r Y (, ) o 9 Comparing Bohr to Schrödinger Energy levels for H (1 e - ) Note: Energy levels are schematic, not to scale n=5 n=4 n=3 5s 5p 5d 5f 5g 4s 4p 4d 4f 3s 3p 3d n= s p n=1 Bohr (1913) Schrödinger (196) 1s 10 5

6 /4/01 Schrödinger s map of the energy spectrum n= Influence on atomic spectra? allowed n,l,m l plus m s Paschen series limit n=3 E=-151 ev (3,0,0); (3,1,-1); (3,1,0); (3,1,1); (3,,-); (3,,-1); (3,,0); (3,,1); (3,,) (all degenerate) Balmer series limit n= E=-340 ev (,0,0); (,1,1); (,1,0);(,1,-1) (all degenerate) n=1 E=-136 ev (1,0,0) - ground state 11 Term Diagram for H Electron orbital angular momentum l

7 /4/01 The Spin Flip Transition in Atomic H (the famous 1 cm line) The two possible orientations of the electron spin causes a slight energy splitting in the ground state of H State: 1s Orbital motion Spin up Higher a energy p e o orbital, z State: 1s Lower energy Orbital motion p Spin down e 1s hyperfine splitting 1s E= 58x10 6 ev Since H is ubiquitous, the heavens are filled with radiation from this spin-flip transition The start of radio astronomy 1s orbital, z = cm (f= GHz; ΔE = 58x10-6 ev) predicted by van de Hulst in 1944, first measured in 1951 by Ewen and Purcell ; Cost: $500; Purcell BSEE from Purdue What happens to the energy spectra from atoms with multiple electrons? (degeneracy of H energy levels is lifted) Energy levels for H (1 e - ) Note: Energy levels are schematic, not to scale 5s 5p 5d 5f 5g n=5 n=4 4s 4p 4d 4f 3s 3p 3d n=3 n= s p Energy levels for multi-electron atoms: (Pretend that each electron has its own wavefunction) 4d 5s 4p 3d 4s 3p 3s p s n=1 Bohr(1913) 1s Schrödinger(196) 1s 14

8 /4/01 He is simplest element with multiple electrons 1s orbital 15 Emission spectra for He is complicated Energy levels for H (1 e - ) Note: Energy levels are schematic, not to scale 5s 5p 5d 5f 5g n=5 n=4 4s 4p 4d 4f 3s 3p 3d n=3 n= s p Energy levels for multi-electron atoms: (Pretend that each electron has its own wavefunction)? nd electron??? 4d 5s 4p 3d 4s 3p 3s p s n=1 Bohr 1s Schrödinger 1 st electron 1s 8

9 /4/01 Some Physical Intuition 8x10-18 J to remove nd electron Ground state 39x10-18 J to remove 1 st electron Importance of shielding effects Ground state Maybe transitions are close to those found in H? excited state Two Possibilities a) OrthoHelium (Triplet, S=1) b) ParaHelium (Singlet, S=0) excited state excited state Ground state Ground state 1 Visible Lines in He Spectrum Look carefully for this line Appendix Q 18 9

10 /4/01 Search for the signature of a well-defined series of lines similar to H? 30 ev Hydrogen Photons 6 5 Helium Photons 30 ev Example Shifted Helium Photons Photon Energy 5 ev 0 ev 15 ev 0 ev 4 3 Balmer series in H Shift and search for series alignment E 5 ev 0 ev 15 ev 0 ev Evidence for H-like series! 19 Implications Similar to H Singlet Helium Triplet n=5 n=4 n=3 Hydrogen 0 ev -1 ev - ev E E singlet E triplet n= -3 ev -4 ev -46 ev ground state ground state ground state -5 ev -136 ev 0 10

11 /4/01 Series Limit Plots for He 0003 Helium - final state P Triplet Series Limit 0003 Helium - final state P Singlet Series Limit 1/ (nm 1 ) / (nm 1 ) /n /n A00106 nm10610 m B nm nm n 3448 hc E n 360 ev A00111 nm11110 m B nm nm 1 00 n 304 hc E n 335 ev 1 Term Diagram for He 335 ev 360 ev Series Limit Energies Parahelium (S=0) Orthohelium (S=1) Electron orbital angular momentum l 11

12 /4/01 The Noise Problem Signal (au) Helium 6 5 S i 4 3 Signal or 1 Noise? Wavelength (nm) Background For low level signals, perform a dark experiment 1 1 N B Bi s B B N i1 N 1 i1 N i 95% of background signal should be within B s if B s S B s, there is 95% chance it is background i 3 Are the discharge tubes contaminated? Spectrum of nitrogen Spectrum of oxygen 4 1

13 /4/01 Next element? 5 Term Diagram for Na (Low Resolution) Energy levels for Na (ev) 00 ev -10 ev -0 ev -30 ev s 6s 5s 4s S P D F Hydrogen n= p 5f n=5 5p 6p 6d 6f 5d 4d 4f n=4 4p 3d n=3-40 ev 5888 and 5894 nm -50 ev 3s 3p n= Electron orbital angular momentum l 6 13

14 /4/01 Predicting Transitions for Na R Na R m n fin n fin init ini t Na Quantum defects for the various spectral series in Na Spectral Series Transition n init n fin δ init δ fin Comment S n init s 3p 4,5,6, Visible lines P n init p 3s 3,4,5, UV lines D n init d 3p 3,4,5, Visible lines F n init f 3d 4,5,6, IR lines Do these predictions match any lines that you measure? Up Next Coherent Light and Young s Double Slit 8 14