Physics 123

1
Wave-particle duality

• Physics 123

2
Concepts

• De Broigle waves
• Energy levels
• Quantum numbers
• Emission and absorption spectra

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
• lh/p pmv

4
Interference of electrons

• Send electron beam (a lot of electrons) on
  crystal structure
• Interference pattern is determined by lh/p
• Double slits distance d1nm
• Interference pattern
• Maxima (more e) d sinq m l
  m0,1,2,3,.
• Minima (no e) d sinq (m½ ) l

5
Matter waves

• Particle position in space cannot be predicted
  with infinite precision
• Heisenberg uncertainty principle
• (Wave function Y of matter wave)2 dVprobability
  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

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

7
Particle in a box

• Infinite potential well
• Boundary condition
• Y(0)0
• Y(L)0
• Solve for wavelength

Wavelength is quantized!
8
Particle in a box

• Mass m
• Length L
• Possible wave lengths
• ln2L/n
• De Broigle waves
• pnh/ln pnhn/2L
• Possible kinetic energy states

Energy is quantized! Energy levels spectrum.
9
Electron in a box

• Mass mec20.5MeV
• Length L0.62 nm

10
Energy transitions

• These are kinetic energy levels, PE0
• What happens when e jumps from n4 to n3 level?
• KEe16 eV ? KEe9 eV
• Where did 7 eV of energy go?

e-
e-

• 7 eV photon is emitted
• This photon was not sitting inside the
  electron.
• It is born in this energy transition

11
Energy transitions

• What if e is on n3 level and 7eV photon comes
  by?
• e will gulp this photon and jump to n4 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-
e-
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

13
Standing electron waves in Hydrogen atom

• Standing waves
• 2prnnl lh/mv mvrnnh/2p
• Angular momentum Lmvrn is quantized
• Lnh/2p
• n orbital quantum number

14
Hydrogen atom

• Energy levels in H

• Electron from level n goes to level n
• Energy of emitted photon

15
Absorption and emission spectra
Visible light
UV
IR

• Lyman series n1
• Balmer series n2
• Paschen series n3
• Rydberg constant R1/91.2nm