1. Wave-particle duality
Physics 123
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2. Concepts De Broigle waves Energy levels Quantum numbers
Emission and absorption spectra
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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
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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
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5. Matter waves
Particle position in space cannot be predicted with infinite precision
Heisenberg uncertainty principle
(Wave function Y of matter wave)2 dV=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
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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
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7. Particle in a box Wavelength is quantized! Infinite potential well
Boundary condition:
Y(0)=0;
Y(L)=0;
Solve for wavelength:
Wavelength is quantized!
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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.
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9. Electron in a box Mass mec2=0.5MeV Length L=0.62 nm 11/15/2018
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10. Energy transitions These are kinetic energy levels, PE=0
What happens when e jumps from n=4 to n=3 level?
KEe=16 eV  KEe=9 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
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11. Energy transitions 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- e-
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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
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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
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14. Hydrogen atom Energy levels in H
Electron from level n goes to level n’
Energy of emitted photon
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15. Absorption and emission spectraUV
Visible light IR
Lyman series n’=1
Balmer series n’=2
Paschen series n’=3
Rydberg constant R=1/91.2nm
The first one to be discovered
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