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8/2/2019 7HC the Quantum Mechanical Model
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The Quantum
Mechanical Model
Mrs. CoyleHonors Chemistry
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Quantum Mechanical Model
1920s
Werner Heisenberg (Uncertainty Principle)
Louis de Broglie (electron has waveproperties)
Erwin Schrodinger (mathematical equationsusing probability, quantum numbers)
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Werner Heisenberg: Uncertainty Principle
We can not know both theposition and momentumof a particle at a given
time.
Dp Dx h
Dp uncertainty inmomentum (mDv)
Dx uncertainty in position
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Louis de Broglie, (France, 1892-1987)
Wave Properties of Matter (1923)Since light waves have aparticle behavior (as shown
by Einstein in thePhotoelectric Effect), thenparticles could have a wavebehavior.
de Broglie wavelength
l= hmv
http://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effecthttp://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effect8/2/2019 7HC the Quantum Mechanical Model
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Electron Motion Around Atom
Shown as a de Broglie Wave
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Davisson and Germer (USA, 1927)
confirmed de Broglies hypothesis
for electrons.
Electrons produced a diffractionpattern similar to x-rays.
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Example:
Determine the de Broglie wavelength for anelectron moving at a speed of 9. x 106m/s.
(me= 9.1 x 10 -31 kg)
Answer: 8.09 x 10 -11 m
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Erwin Schrodinger, 1925Quantum (wave) Mechanical Model
of the Atom
Four quantum
numbers are requiredto describe the state ofthe hydrogen atom.
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Four Quantum Numbers
1. Principal Quantum Number
2. Orbital Quantum Number
3. Magnetic Quantum Number
4. Spin Quantum Number
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Principal Quantum Number, n
Indicates main energy levels
n = 1, 2, 3, 4
Each main energy level has sub-levels
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Orbital Quantum Number, (Angular Momentum Quantum Number)
Indicates shape of orbital sublevels
= n-1
sublevel0 s
1 p2 d
3 f
4 g
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Atomic Orbital s
2s
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Degenerate Orbitals
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The 3 p orbitals
http://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif
http://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gifhttp://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gifhttp://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gifhttp://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif8/2/2019 7HC the Quantum Mechanical Model
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The d orbitals
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f orbitals
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Magnetic Quantum Number, ml
Indicates the orientation of the orbital in space.
Values of ml: integers -l to l
The number of values represents the number of
orbitals.
Example:
for l= 2, ml
= -2, -1, 0, +1, +2
Which sublevel does this represent?
Answer: d
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Electron Spin Quantum Number, (ms or s)
Indicates the spin of the electron
(clockwise or counterclockwise). Values of ms: +1/2, -1/2
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Example:
List the values of the four quantumnumbers for orbitals in the 3d sublevel.
Answer:
n=3
l = 2
ml= -2,-1, 0, +1, +2
ms = +1/2, -1/2 for each pair of electrons
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The Electron Cloud
http://www.chemeng.uiuc.edu/~alkgrp/mo/gk12/quantum/H_S_orbital.jpg
The higher theelectron density,the higher theprobability thatan electron may
be found in thatregion.
http://www.chemeng.uiuc.edu/~alkgrp/mo/gk12/quantum/H_S_orbital.jpghttp://www.chemeng.uiuc.edu/~alkgrp/mo/gk12/quantum/H_S_orbital.jpg8/2/2019 7HC the Quantum Mechanical Model
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The Electron Cloud for Hydrogen
90% probabilityof finding theelectron withinthis space
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Probability Curve for Hydrogen
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FYI: Schrodingers Equations!!!
y is called the wave function and indicatesthe probability of where an electron may
be found.
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