quantum mechanical model of the atom chapter 6 part iii
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Quantum Mechanical Model of the Atom
Chapter 6
Part III
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Bohr’s model was Imperfect
The model of an electron in a circular orbit around a nucleus worked only for Hydrogen, Lithium but by Boron, the model was ineffective.
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Electrons bound to the nucleus seemed similar to a standing wave.
See if video works
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De Broglie, Heisenberg and Schrödinger pioneered wave mechanics, aka Quantum Mechanics. http://www.colorado.edu/UCB/AcademicAffairs/
ArtsSciences/physics/PhysicsInitiative/Physics2000/quantumzone/debroglie.html
This site shows how a particle such as an electron can have wave-like functions.
http://www.chemtopics.com/lectures/unit04/lecture3/l3u4.htm
This site demonstrates wave like qualities of orbitals.
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Schrödinger & de Broglie
Both felt the electron acted like a standing wave. (see slinky)
Theorizing that the electron acts like a wave, and has a wave function That represents the x, y and z coordinates of the electron.
A specific wave function is often called an orbital.
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By treating the electron as a wave:
Schrödinger mathematically described a series of wave functions each having discrete energy levels.
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Heisenberg’s Uncertainty Principle
∆x * ∆ (mv) > h/4x= the uncertainty of the particle’s positionmv = the uncertainty of the particle’s
momentumh = Planck’s constant
Stating that we cannot know both the speed and position of an electron
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Heisenberg’s big idea
http://www.chemtopics.com/lectures/unit04/lecture3/l3u4.htm
This url demonstrates how the model of a circular orbit (Bohr) morphs into a model demonstrating the Uncertainty Principle.
Electron clouds as orbitals.
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Wave Functions
[(X1, Y1, Z1)]2 = N1
[(X2, Y2, Z2)]2 N2
N1/N2 gives the ratio of the probability of finding the electron at position 1 relative to position 2. If the number is 100, the electron is 100 times more likely to be in position 1 than 2.
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Probability Distribution
This square of the wave function is represented as a probability distribution.
AKA electron density map.
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When the electron density map is divided into equal spheres, the plot of finding the electron in each successive sphere gives the following curve
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The size of an atom
The definition of the size of a hydrogen atom 1s orbital is the radius of the sphere that encloses 90% of the total electron probability.
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Quantum numbers
When solving Schrödinger's equation for the hydrogen model we find wave functions / orbitals.
Each orbital is characterized by a series
of numbers called Quantum Numbers.
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Principle Quantum number
n has intergral values 1, 2, 3…
n is related to the size an energy level of the orbital.
Or n= energy level
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Angular quantum number
l has integral values of 0 to n-1 for each value of n.
Each value of l has a shape associated with it.
0= s1=p2=d3=f
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Magnetic quantum number
m is related to the orientation of the orbital and may equal any integral value between l and – l.This includes zero.
It relates to the orientation of the orbital in space relative to other orbitals in the atom.
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Spin
Each orbital may hold two electrons.
Quantum number are +1/2 and -1/2
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Nodes
See handout