Experimentalphysik III Experimentelle Grundlagen der Quantenphysik

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1 Experimentalphysik III Experimentelle Grundlagen der Quantenphysik Frank Cichos Vorlesung 9

2 Linienspektren - Balmer Serie Emission spectrum of a hydrogen atom Balmer s formula " = 364.6nm m2 m 2 # 4 Brackett Pfund Paschen more common form: Rydberg - Ritz formula (1908) = Ry 1 1 m 2 n 2 Balmer n=1 Lyman n=2 Balmer n=3 Paschen n=4 Brackett wavelength excitation energy in ev n, m are principle numbers n defines the series Lyman

3 Bohrsches Atommodell Nils Bohr (1913) proton electron Coulomb centrifugal v electron is in circular orbit around positive charge r = Ze2 4 µv 2 in principle any radius is allowed Bohr s hypothesis angular momentum is quantized L = µrv = n orbits are stable, no radiation (we ll see later that this corresponds to the idea of a standing electron wave and to de Broglie s idea)

4 Bohrsches Atommodell summary of Bohrs model of the hydrogen atom electron moves on circles around the nucleus with quantized radii r n = n2 Z 2 a 0 a 0 = 0 h 2 with µe 2 radii increase quadratically with n possible values are inversely proportional to Ze, He+ is smaller than H each state has a well defined total energy (approaches 0 for r"!) energies are negative, since bound E n = Ry Z2 n 2 E pot = +2E n E kin = E n the energy E1 is needed to ionize the atom by absorption of h#, the atom can be excited from Ei to Ek

5 Bohrsches Atommodell - Schwächen weaknesses of Bohr s model accelerated charges do radiate light this means they lose energy and will finally crash into the positive charge, not compatible with classical electrodynamics lowest orbit has L =$ but experimentally one observes L =0 orbital momentum is actually L = l(l + 1) Zeeman effect, fine structure, hyperfine structure (but we do not know about this, yet)

6 Franck Hertz Versuch ( ) Franck-Hertz experiment electrons loose energy in collisions e (E kin ) + Hg Hg (E a ) + e (E kin E a ) atoms can acquire only discrete energy quanta the magnitude depends on the specific atom electron current as function of the acc. voltage for mercury vapor

7 Franck-Hertz Versuch

8 Bessere Auflösung

9 Linienspektren atomic spectra (1859/1885, Balmer, Kirchhoff, Bunsen) elements emit light of certain frequencies only each element has a characteristic emission and absorption spectrum spectral lines are not completely narrow emission spectrum of magnesium emission spectrum of silicon

10 Bohr Sommerfeld Modell n Hauptquantenzahl l Drehimpulsquantenzahl

11 2. Einführung in die Quantenmechanik

12 2.1. Die Schrödingergleichung

13 2.2. Anwendungen der Schrödingergleichung

14 Potentialstufe E E > E kin 0 A e ikx < E kin 0 E (x) p E 0 B e ikx D e ikx E = E p 0 I 0 II x

15 Potentialstufe E E 0 kin E e E kin A 0 B A = B 0 αx x λ π = 2 k π λ' = 2 k' v A 2 v' D 2 E > E 0 E 0 2 v B 0 x

16 Reflexion an einer Potentialstufe R 1 0,8 R 1,0 0,6 0,4 0,2 0, a) E 0/E b) 0 0,5 1 E 0/E 0

17 Tunneleffekt λ π = 2 k λ π = 2 k a E 0 Abb I II III 0 a x

18 Tunneln durch eine Potentialbarriere 1,0 T R und T 0,5 R E/E 0

19 Streuung an einer Potentialbarriere 1 T E E E E ( E E ) ,5 1 a/ λ' Abb Transmissionsvermögen T als Funktion des Ver-

20 G. Binnig H. Rohrer

21 Prinzipieller Aufbau eines STM (scanning tunneling microscope) [Interf. Phys. Group, Leiden Univ.] Energiebänder für Spitze und Probe ohne (links) und mit (rechts) angelegter Spannung [Interf. Phys. Group, Leiden Univ.]

22 STM erfordert eine genaue Positionierung der STM-Spitze (Å-Präzision). Zu diesem Zweck werden piezoelektische Elemente eingesetzt. Feedback-Loop im STM Piezoelektrika: Prinzip und 3D-Scanner [alle Bilder: Interf. Phys. Group, Leiden Univ.]

23 Scanning Tunnelin Microscopy (STM) Bilder Atomic Corral [IBM Gallery] Linescan und Bild von Graphit [Interf. Phys. Group, Leiden Univ.]

24 Tunneln beim α-zerfall E V Coulomb Tunneleffekt 0 V Kern V tot r r starke Kernkraft Atomkern Ladung Z e