Experimentalphysik III Experimentelle Grundlagen der Quantenphysik

Transkript

1 Experimentalphysik III Experimentelle Grundlagen der Quantenphysik Frank Cichos Vorlesung 8

2 1.3 Wellencharakter von Teilchen

3 Nachtrag C60 Beugung C60 molecule diffraction of C60 molecules on a grating Oven Collimation slits 100 nm diffraction grating 10 µ m 10 µ m Scanning photoionization stage Laser Ion detection unit Figure 1 Diagram of the experimental set-up (not to scale). Hot, neutral C 60 molecules leave the oven through a nozzle of 0:33 mm 1:3 mm 0:25 mm (width height depth), pass through two collimating slits of 0:01 mm 5 mm (width height) separated by 1.04 m, traverse a SiN x grating (period 100 nm) 0.1 m after the second slit, and are detected via thermal ionization by a laser 1.25 m behind the grating. The ions are then accelerated and directed towards a conversion electrode. The ejected electrons are subsequently counted by a Channeltron electron multiplier. The laser focus can be reproducibly scanned transversely to the beam with 1- m resolution. M. Arndt et al. Nature 401, 680 (1999). sometimes waves behave like particles (electromagnetic waves) sometimes particles behave like waves (electrons, C60) but how do predict wether the object behaves like a wave or particle?

4 Wellenfunktion und Wellenpakete ψ v g Momentaufnahme zur Zeit t = 0 v g = ω k x n x ψ = cos( ω t k x) + cos( ω t k 2 x) Abb a) x = 4 π / k x ψ

5 Gaußsches Wellenpaket ψ x = 8 ln2 k b) x

6 1.3.3 Unschärferelation

7 Heisenbergesche Unschärferelation 2 ψ( xt, 0 ) 2 ψ( xt, 0 ) x x = 1 k x x 0 x x 0 x Ck ( ) C( k) k k = 1 x a) k 0 k x b) k 0 Abb. 3.29a,b. k x

8 Größe des Atoms E [ev] 0.5 AS A FUNCTION OF a THE TOTAL ENERY LOOKS LIKE THIS a [Å] -13.6

9 Unschäfe und Beugung p x = 0 y b d d I( θ) θ θ p y θ p Lichtquelle α gestreutes Photon y Abb ϕ =2θ ϕ p x p = h/ λ Teilchen a) b) x D D= 2 1,2 y sinθ = 2 y λ / d Abb Erklärung der räumlichen Auflösungsgrenze eines

10 1.3.4 Atommodelle/Linienstrahlung

11 Absorptionsspektroskopie

12 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

13 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)

14 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

15 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)

16 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

17 Franck-Hertz Versuch

18 Bessere Auflösung

19 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

20 Bohr Sommerfeld Modell n Hauptquantenzahl l Drehimpulsquantenzahl