The Quantum Model

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The Quantum Model

• Energy as wave and particle

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C?f
It stands to reason that if energy is constant
then ? (wavelength) is inversely proportional to
f (frequency).
OR As wavelength increases frequency decreases
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Wave Comparison
Red Light
nm 1 x 10-9 m

• Low frequency
• Long wavelength

Violet Light

• High frequency
• Short wavelength

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C?f
Einstein gave us an understanding of energy and
matter in his equation Emc2. Basically, it told
us that matter and energy are the same thing.
Matter is simply frozen energy. From Einstein we
were able to come up with several more equations
to understand quantum mechanics.
E.g. yellow orange 580 nm 580 x 10-9 m 5.8
x 10-7 m
So as in the lab, using a spectroscope we can
determine the wavelength of the color of light
(?). We can solve for frequency (f)
mathematically.
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Max Planck
Max Planck mathematically found that a value now
called Plancks constant and represented by h
could be multiplied by f to solve for energy (E)
every time an electron gave off light as it fell.
(This simply means that all wavelengths are
proportional)
Thus E will tell us the relative distance apart
of each energy level in a given atom based upon
the spectral lines.
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The Electromagnetic Spectrum
V I B G Y O R
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De Broglie
De Broglie argued that as particles
(i.e.electrons) drop back to lower energies,
photons of energy are given off in packets or
specific amounts called quanta. His doctoral
board scoffed and was ready to deny his degree
but changed their minds when Einstein supported
him fully.
His model changed the Bohr model so that all
elements could be explained according to their
frequencies of energy.
Remember that energy is constant and that
standing waves are quantized as well (they only
increase by multiples of ½)
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De Broglie
Essentially the model went from
to
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Spectra
With the de Broglie Model, it became possible to
explain the spectral lines of all models. Each
wavelength would allow electrons to fall back to
lower energy levels emitting various energies
which translate to frequencies thus defining a
wavelength which corresponds to a color.
De Broglie Atom
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Spectra
Atoms are quantized, existing only in definite
energy states so an atom absorbs a specific
quanta of energy pushing electrons to higher
energy levels. An EXCITED electron jumps from
its ground state to a higher energy level. The
energy cannot be maintained so it falls back to
where it came from losing exactly the same amount
of energy that it absorbed. The QUANTA (or
packet of energy) is EMITTED in a specific
wavelength which we see as a color, or
a BRIGHT-LINE SPECTRA.
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Spectra
We can calculate the energy the electrons of a
hydrogen atom emit when they fall by using the
Balmer equation.
So if an electron falls from the 6th energy level
to the 2nd energy level then
Note energy levels are not actually distances
between electrons and the nucleus.
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Heisenberg Uncertainty Principle
An electrons location and speed cannot be
determined at the same time. If we cause change
to find one variable, we are no longer looking at
the actual e- situation. If we need to slow or
stop it to locate it or if we need to locate it
to find its speed, then we allow the chance of
change. So quantum mechanics can tell us the
probability that an electron is somewhere, but it
does not tell us how it got there.
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Nodal Surfaces
A nodal surface is a region that defines the
border of an orbital. This is where the
probability function equals zero. Electrons CAN
NOT exist in this area.
Nodal surfaces are spherical for the s
orbitals.
Nodal surfaces are NOT spherical for other
orbitals.
2p orbital
3s orbital
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Shapes of s and p orbitals
s
Nodal plane
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Shapes of d orbital
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Principle Quantum Numbers
The principle quantum numbers define the
characteristics of a particular electron. They
are essentially an address for the electron.
Because electrons repulse each other, no two
electrons can have the same address. This is the
Pauli Exclusion principle.
n - principle energy level 1, 2, 3, 4 . . .
l - orbitals the shape of the region of space
defined. (s, p, d, f)
m - sublevels, orientation axes of the magnetic
moment. E.g. the Px, Py and Pz sub levels.
s - spin. Can by 1/2 or 1/2 for electrons,
electrons in each sublevel must have opposite
spins
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Principle Energy Levels and their Sublevels
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Electron Diagrams
Pauli Exclusion Principle No two electrons can
have the same quantum numbers. Hunds Rule In a
given energy level, one e- per orbital until
filled, then double up.
Example Cr
3d
3p
4s
3s
2p
2s
1s
Cr 1s22s22p63s23p64s23d4
Cr Ar 4s23d4
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Aufbaus Process
4f 5f
3d 4d 5d 6d
2p 3p 4p 5p 6p 7p
1s 2s 3s 4s 5s 6s 7s
Ar 1s22s22p63s23p6 Ag 1s22s22p63s23p64s23d104p65s
24d105s1
Can start from noble gas.
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Mathematical Relationships of the Quantum Numbers
n is the principal energy level (1, 2, 3 . . .)
l 0 to (n-1), or n sublevels. The energy level
tells us the number of sublevels.
Ex. If n2, then l can be from 0 to (2-1). This
is 2 sublevels total.
l 0 known as s
l 1 known as p
l 2 known as d
l 3 known as f
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Mathematical Relationships of the Quantum Numbers
m can be from l to l or (2l 1) total
l 0 (s) m0 total 1 sublevels l 1
(p) m-1, 0, 1 total 3 sublevels l 2
(d) m-2, -1, 0, 1 ,2 total 5 sublevels Etc.

• Number of electrons in an orbital 2(2l 1)

• Number of electrons in an energy level 2n2