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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_Effect

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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.gif

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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.jpg

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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.