--THE QUANTUM MECHANICAL MODEL · 2018. 9. 9. · The Quantum Mechanical Model Energy is quantized...
Transcript of --THE QUANTUM MECHANICAL MODEL · 2018. 9. 9. · The Quantum Mechanical Model Energy is quantized...
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--THE QUANTUM
MECHANICAL MODEL
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Bohr’s Energy Levels
Electrons reside in certain energy levels
Each level represents a certain amount of energy
Low Energy levels: closer to nucleus
High Energy levels: farther from nucleus
Ground State: Electron is in the lowest possible
energy level
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Excited Atoms
Excited Atom- has absorbed energy
Unstable
Atoms soon emit the same amount of energy they
absorbed
Energy seen as visible light (different colors)
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The Quantum Mechanical Model
Energy is quantized (comes in chunks)
A quanta is the amount of energy needed to
move from one energy level to another
Since the energy of an atom is never “in
between” there is a quantum leap in energy
Erwin Schrodinger derived an equation that
described the energy and position of electrons in
an atom
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Quantum Mechanical Model
1920s
Louis de Broglie (electron has wave properties)
Werner Heisenberg (Uncertainty Principle)
Erwin Schrodinger (mathematical equations
using probability, quantum numbers)
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Louis de Broglie, (France, 1892-1987)
Wave Properties of Matter (1923)
Since light waves have a particle
behavior (as shown by Einstein in the
Photoelectric Effect), then particles
could have a wave behavior.
Electrons act like waves confined
to a certain space around a nucleus
de Broglie wavelength
E=hv
Corresponds to quantized energies of
Bohr’s orbits
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Electron Motion Around Atom Shown as a
de Broglie Wave
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Werner Heisenberg: Uncertainty Principle
Things that are very small behave differently from things big enough to see
The Quantum mechanical model is a mathematical solution
Energy levels for electrons
Orbits are not circular
We can not know both the position and momentum of a particle at a given time.
Can only know the probability of finding an electron a certain distance from the nucleus
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Erwin Schrodinger, 1925
Quantum (wave) Mechanical Model of the Atom
The atom is found inside a
blurry “electron cloud”
An area where there is a
chance of finding an electron
Four quantum numbers are
required to describe the
state of the hydrogen atom.
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FYI: Schrodinger’s Equations!!!
y is called the wave function and indicates the probability of where an electron may be found.
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The Electron Cloud
http://www.chemeng.uiuc.edu/~alkgrp/mo/gk12/quantum/H_S_orbital.jpg
The higher the electron density, the higher the probability that an electron may be found in that region.
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Atomic Orbital:
A region in space in which there is high probability of finding an electron.
Within each energy level, Schrodinger’s equation describes several shapes
Shapes are called atomic orbitals (regions where there is a high probability of finding an electron)
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Four Quantum Numbers
Used to describe an electron in an atom.
1. Principal Quantum Number (n)
2. Orbital Quantum Number (l)
3. Magnetic Quantum Number (m)
4. Spin Quantum Number (s)
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Principal Quantum Number, n
Indicates main energy levels of electrons
n = 1, 2, 3, 4…
The maximum number of electrons in an
energy level is 2n2
Example: what is the maximum number of
electrons that can be in the 5th main
energy level?
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Orbital Quantum Number, ℓ(Angular Momentum Quantum Number)
Indicates shape of the orbital (sublevel) within an energy level
ℓ = n-1
ℓsublevel0 s
1 p
2 d
3 f
4 g
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Magnetic Quantum Number, ml
Indicates the orientation of the orbital in space.
S orbital is spherical and centered around nucleus, so
there is only 1 possible orientation (m=0)
P orbital can extend along x,y,or z axis so there are 3
p orbitals (m=-1 m= 0 m= 1)
There are 5 different d orbitals in each d sublevel
(m=-2 m=-1 m=0 m=1 m=2)
7 different f orbitals in each f sublevel
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Magnetic Quantum Number
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 quantum numbers 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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List the values of the four quantum numbers for
orbitals in the…….
2s
3p
3d
4s
4p
4f
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Atomic Orbital s
2s
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The 3 p orbitals
http://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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Comparing s, p, d, & f Orbitals
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The Electron Cloud for Hydrogen
90% probability
of finding the
electron within
this space