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Wave-particle duality

Wave-particle duality. Physics 123. Concepts . De Broigle waves Energy levels Quantum numbers Emission and absorption spectra. Wave – Particle duality. If light exhibits both wave and particle properties then particles (e.g. electrons) must also exhibit wave properties – e.g. interference.

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Wave-particle duality

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  1. Wave-particle duality Physics 123 Lecture XII

  2. Concepts • De Broigle waves • Energy levels • Quantum numbers • Emission and absorption spectra Lecture XII

  3. Wave – Particle duality • If light exhibits both wave and particle properties then particles (e.g. electrons) must also exhibit wave properties – e.g. interference. • Matter (de Broglie) waves l=h/p p=mv Lecture XII

  4. Interference of electrons • Send electron beam (a lot of electrons) on crystal structure • Interference pattern is determined by l=h/p • Double slits distance d~1nm • Interference pattern • Maxima (more e): d sinq = m l m=0,1,2,3,…. • Minima (no e): d sinq = (m+½ ) l Lecture XII

  5. Matter waves • Particle position in space cannot be predicted with infinite precision • Heisenberg uncertainty principle • (Wave function Y of matter wave)2dV=probability to find particle in volume dV. • But while probability is a real number, wave function is a complex number. It has a phase. • When two matter waves meet we add wave functions, not probabilities! Interference can be observed (phase is important Lecture XII

  6. Particle in a box • Infinite potential well • Particle mass m in a box length L  standing wave • Similar to guitar string • Wave function - string • We do not know with certainty where in the box the particle is • More chances to find the particle at a cress • No chance at a knot Lecture XII

  7. Particle in a box • Infinite potential well • Boundary condition: Y(0)=0; Y(L)=0; • Solve for wavelength: Wavelength is quantized! Lecture XII

  8. Particle in a box • Mass m • Length L • Possible wave lengths ln=2L/n • De Broigle waves pn=h/ln pn=hn/2L • Possible kinetic energy states Energy is quantized! Energy levels – spectrum. Lecture XII

  9. Electron in a box • Mass mec2=0.5MeV • Length L=0.62 nm Lecture XII

  10. Energy transitions e- • These are kinetic energy levels, PE=0 • What happens when e jumpsfrom n=4 to n=3 level? • KEe=16 eV  KEe=9 eV • Where did 7 eV of energy go? e- • 7 eV photon is emitted • This photon was not “sitting inside the electron”. • It is bornin this energy transition Lecture XII

  11. Energy transitions e- • What if e is on n=3 level and 7eV photon comes by? • e will gulp this photon and jump to n=4 level. • Photon is not hiding inside e, It is absorbed. • What if white light goes through this system? • Photons of 7 eV energy will be taken out • As will be photons of • 5 eV, 3 eV • 15, 12, 8 eV • Absorption spectrum – dark spectral lines • Note that 8.5 eV photon will pass by without any interaction! e- Lecture XII

  12. Hydrogen atom • Positively charged nucleus inside, negatively charged electrons around • Electron is attracted to nucleus • Electron is trapped in a potential well created by nucleus (“a box”) • Energy levels in atom Lecture XII

  13. Standing electron waves in Hydrogen atom • Standing waves: • 2prn=nl l=h/mv mvrn=nh/2p • Angular momentum L=mvrn is quantized L=nh/2p • n – orbital quantum number Lecture XII

  14. Hydrogen atom • Energy levels in H • Electron from level n goes to level n’ • Energy of emitted photon Lecture XII

  15. Absorption and emission spectra The first one to be discovered UV Visible light IR • Lyman series n’=1 • Balmer series n’=2 • Paschen series n’=3 • Rydberg constant R=1/91.2nm Lecture XII

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