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Hydrogen Atom: Wave Function
Bohr Model
Hydrogen Atom: more quantum numbers
Quantum Physics
According to Bohr’s Model, the energy levels of an
electron in a Hydrogen atom:
En = −
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n = 1, 2, 3,....
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Pauli Exclusion Principle
Quantum Numbers for Allowed Electron States in an Atom
No two electrons in an atom can be in
the same quantum state (n, l, ml, ms)
n = Principal Quantum Number (1,2,3,...)
*Determines energy (Bohr)
2π 2 me k 2 e4
n2h2
2π 2 me k 2 e4
En = −
n2h2
l = Orbital Quantum Number (0,1,2,...n-1)
h
L = l(l + 1)
*Determines angular momentum
2π
* l < n always true!
ml = Magnetic Quantum Number (-l,...,-1,0,1,...l)
*Component of l along some z axis
Lz = ml
h
2π
1 1
ms = Spin Quantum Number (− , + )
2 2
*”Spin Up” or “Spin Down”
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Nomenclature
Probability Functions for a few states of H
Example: 1 electron in the ground state of Hydrogen
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Example
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Periodic Table & Pauli Exclusion Principle
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Filling Energy Levels
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Filling Energy Levels
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Periodic Table & Pauli Exclusion
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Periodic Table & Pauli Exclusion
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Photons & Matter
Laser (Light Amplification by stimulated emission
http://www.youtube.com/watch?v=5uAMTcaKLpI
Ruby is an aluminum oxide crystal in which some Al atoms
have been replaced with chromium. Chromium atoms absorb
green and blue light and emit or reflect only red light.
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Laser (Light Amplification by stimulated emission)
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Laser (Light Amplification by stimulated emission)
1. High-voltage electricity causes
the quartz flash tube to emit an
intense burst of light, exciting
some of the atoms in the ruby
crystal to higher energy levels.
3. Mirrors at each end reflect
the photons back and forth,
continuing this process of
stimulated emission and
amplification.
2. At a specific energy level, some
atoms emit photons. At first,
photons are emitted in all
directions. Photons from one
atom stimulate emission of
photons from other atoms and
the light intensity is amplified.
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4. The photons leave through
the partially silvered mirror at
one end. This is laser light.
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Ruby Laser Energy Levels
Helium-Neon Laser Energy Levels
Key to the
laser:
population
inversion
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Helium-Neon Laser
15% helium, 85% neon
λ = 632.8 nm (E = 1.96 eV)
Characteristics of laser beams: coherent (photons
have the same frequency in phase, and the same
direction of propagation), very small angular
divergence, intense.
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