PowerPoint Presentation Quantum Theory

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General Wave Theory
Definitions
A wave transmits energy without transmitting
matter.
A mechanical wave is a disturbance in a medium
Examples Waves on a rope water waves
An electromagnetic wave does not need a medium.
Examples Heat, light, x-rays
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A Transverse Wave
Frequency The number of waves per unit of time
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The Wave Equation
Wavelength has the symbol l units of meters/wave
Frequency has the symbol n units of waves/sec
A frequency of 1 wave/sec is called 1 Hertz (Hz)
n
wave velocity
l

m
m
waves


wave
s
s
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The Electromagnetic Spectrum
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Using the Wave Equation
n
c
l

What is the frequency of a light wave that has a
wavelength of 400 nm?
400 nm 400 x 10-9 m 4.00 x 10-7 m

n

(4.00 x 10-7 m )
3.0 x 108 m/s

3.0 x 108 m/s
n

7.5 x 1014 Hz
4.00 x 10-7 m
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A Very Brief History of Quantum Mechanics
1900 Max Planck introduces the idea of
quantization of energy without experimental
verification.
1905 Einstein uses Plancks ideas to explain the
photoelectric effect.
1913 Neils Bohr develops a quantized model of the
atom that can, for the first time, explain the
hydrogen spectrum.
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Plancks Quantization of Energy (1900)
Energy a frequency
Energy is quantized according to
E n (hn)
Where h (Plancks constant) 6.63 x 10-34 J. s
and n must be an integer.
(hn) represents a packet of energy also called
a quantum of energy or a photon
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Using Plancks Equation
E n (hn)
What is the energy of a photon of light that has
a frequency of 7.5 x 1014 Hz?
h 6.63 x 10-34 J. s
n is usually equal to 1

E
(6.63 x 10-34 J. s)
7.5 x 1014 1/s

E
4.97 x 10-19 J
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Three Types of Spectra
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The emission spectrum of hydrogen
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J.J. Balmer and J.R. Rydberg and A. Einstein
1885 J.J. Balmer finds that the spectrum of
hydrogen follows a precise mathematical relation
1890 J.R. Rydberg extends Balmers formula to
include hydrogen spectral lines at other
wavelengths and some other elements.
1905 Einstein uses Plancks equation to solve an
urelated problem the photoelectric effect.
This showed that Plancks ideas were correct.
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1913 Niels Bohr
Three Part Theory
1. Classical planetary picture of the atom.
2. Quantum Assumption The electron can only be
in certain orbits (energy levels) around the
nucleus
3. Transitions between energy levels An electron
in an atom absorbs or emits energy by undergoing
a transition from one energy level to another.
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The Bohr Equation
Bohr derived the following formula for the energy
levels of the electron in the hydrogen atom
-RH

En
n2
RH is a constant with a value of 2.18 x 10-18 J.
(for H only)
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Transitions in the Bohr Atom
When an electron falls from n 3 to n 2 energy
level, a photon of red light (l 685 nm) is
emitted
When red light of this same wavelength shines on
a hydrogen atom in the n 2 level, the energy is
gained by the electron that undergoes a
transition to n 3.
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Transitions in the Hydrogen Atom
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A Very Brief History of Quantum Mechanics
1923 Louis de Broglie suggests the wave/particle
dual nature for the electron.
1926 Schroedinger combines the approaches of Bohr
and de Broglie to produce the wave mechanical
model for the atom.
1926 Werner Heisenberg publishes his atomic
model based on matrix mechanics which does not
use Schrodingers wave approach but gives the
same results.
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History of Quantum Summary

• 1913 N. Bohr develops first quantum atomic
  model. It works only for one-electron systems.
• 1923 L. de Broglie suggests wave/particle
  duality.
• 1926 W. Heisenberg develops matrix mechanics
  treating the electron as a particle.
• 1926 E. Schrodinger develops wave mechanics
  treating the electron as a wave.

Wave mechanics and matrix mechanics both lead to
the same result. Wave mechanics is easier to
work with.
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Standing Waves
L
n Vw/2 L
n 2Vw/ 2L
n 3Vw/ 2L
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de Broglie Waves
I thus arrived at the overall concept which
guided my studies for both matter and
radiations, light in particular, it is necessary
to introduce the corpuscle concept and the wave
concept at the same time. - Louis de Broglie,
1929
E mc2
E hc/l
hc/l mc2
Louis de Broglie (1892-1987)
l h/mc
In his thesis in 1923, Prince Louis V. de Broglie
suggested that particles should have wave
properties similar to electromagnetic radiation.
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Bohrs Quantization Condition revisited

• One of Bohrs assumptions in his hydrogen atom
  model was that the angular momentum of the
  electron in a stationary state is quantized.
• This turns out to be equivalent to saying that
  the electrons orbit consists of an integral
  number of electron de Broglie wavelengths

2 p r n l
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Wave Mechanics

• Based on the Schrodinger equation
• Sets of numbers that satisfy the Schrodinger
  equation are called quantum numbers.
• Each quantum number describes a property of the
  electron
• Three quantum numbers are needed to describe an
  electrons location.
• Four quantum numbers are needed to completely
  describe an electron.

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The Quantum Numbers

• The Principal Quantum Number (n).
• Values n 1,2,3... practical max. 7
• Describes the energy level the electron can be
  found on.
• n specifies the energy of the electron according
  to En - RH/n2.
• n also describes the distance from the nucleus

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The Quantum Numbers

• The Secondary (Angular Momentum) Quantum Number
  (l)

Values l 0....(n-1) (integral values
only)
practical max 3

• Describes the shape of the orbital.

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Definition of an Orbital
Orbital the wave function (y) of an electron
in an atom.
The square of the wave function (y2) describes
the probability of locating the electron in a
given region of space.
A three-dimensional representation of the
probability of finding the electron in a given
region of space.
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What is an orbital?

• An orbital is a 3D description of the probability
  of finding an electron in a given region of space
• 90 of the time the electron will be found within
  a fairly easily defined region of space quite
  close to the nucleus. Such a region of space is
  called an orbital. You can think of an orbital as
  being the region of space in which the electron
  lives..

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p Orbitals

• At the first energy level, the only orbital
  available is the 1s orbital, but at the second
  level, as well as a 2s orbital, there are also
  orbitals called 2p orbitals.
• A p orbital is rather like 2 identical balloons
  tied together at the nucleus. The diagram on the
  left is a cross-section through that
  3-dimensional region of space. The orbital shows
  where there is a 90 chance of finding a
  particular electron.
• Unlike an s orbital, a p orbital points in a
  particular direction - the one drawn points up
  and down the page.

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The Quantum Numbers
3. Magnetic Quantum Number (ml)
Values ml -l....0....l
Each value of ml describes an allowed
orientation for the orbital in space.
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The s and p atomic orbitals
n 2 l 0 ml 0
n 2 l 1
There are three allowed orientations each one
corresponding to a value of ml -1, 0, 1
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The d atomic orbitals
n 3 l 2 ml -2, -1, 0, 1, 2
There are five allowed orientations each one
corresponding to a value of ml
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The Quantum Numbers
4. Spin Quantum Number (ms)
Values ms 1/2, -1/2
Describes the magnetic spin energy of the
electron.
The spin quantum number is not a result of the
solution to the Schrodinger equation.
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Table of Orbitals
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Hydrogenic Orbitals
The orbital energy levels for the hydrogen atom
The energy of the orbital depends on the n
quantum number only
The energy of any orbital on a given level n is
given by
En - RH/n2
All the orbitals on the same energy level are
degenerate that is they have the same energy.
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Hydrogenic Orbitals
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The Aufbau Principle
Also called the building-up principle
The ground state electron configurations for
many-electron atoms can be approximated using the
excited states of the hydrogen atom.
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Aufbau Order
For all atoms with more than one electron, the
presence of electron-electron interactions
changes the energy of the hydrogenic orbitals.
They are no longer degenerate.
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Writing the Order of Filling
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
4f 14 5d106p6 7s2 5f14 6d10 7p6
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Electron Configurations
1s1
1H
1s2
2He
1s2 2s2 2p6 3s1
11Na
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p3
33As
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p4
52Te
Kr 5s2 4d10 5p4
Xe 6s2 4f14 5d7
77Ir
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Rules for Electron Distribution

• The Pauli Exculsion Principle
• No two electrons in the same atom can have
  the same four quantum numbers.

• Hunds Rule
• The most stable arrangement of electrons is
  the one with the greatest number of parallel
  spins.

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Electron Configurations
Electron configurations of main group elements
follow the Aufbau order.
7N
1s22s22p3
2px
2py
2pz
2s
1s
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Electron Configurations
Electron configurations of main group elements
follow the Aufbau order.
9F
1s22s22p5
2px
2py
2pz
2s
1s
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Regions of The Periodic Table
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Classification by sublevels
s
p
H
He
Li
Be
B
Ne
F
O
N
C
d
Si
Na
Mg
Al
Ar
Cl
S
P
K
Ca
Zn
Cu
Sc
Ni
Co
Fe
Mn
Cr
V
Ga
Kr
Br
Se
As
Ge
Ag
Sb
Rb
Sr
Cd
Y
Pd
Rh
Ru
Tc
Mo
Nb
In
Xe
I
Te
Sn
Cs
Tl
Hg
Au
Lu
Ba
Pt
Ir
Os
Re
W
Ta
Rn
At
Po
Bi
Pb
Fr
Lr
Ra
Gd
Tb
Sm
Eu
Nd
Pm
Ce
Pr
Yb
La
Er
Tm
Dy
Ho
f
Cm
Bk
Pu
Am
U
Np
Th
Pa
No
Ac
Fm
Md
Cf
Es
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p6
s1
1
s2
p1
p5
2
d1
d9
3
3s1
3p5
4
4p6
5
5p2
6s2
6
7
4f
5f