Download CY 101- Chemistry Atomic Structure

CY 101- Chemistry
Atomic Structure
Dr. Priyabrat Dash
Email: [email protected]
Office: BM-406, Mob: 8895121141
Webpage: http://homepage.usask.ca/~prd822/
Dr. Priyabrat Dash
Email: [email protected]
Office: BM-406, Mob: 8895121141
Webpage: http://homepage.usask.ca/~prd822/
Dr. Priyabrat Dash
Email: [email protected]
Office: BM-406, Mob: 8895121141
Webpage: http://homepage.usask.ca/~prd822/
Atoms
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•
•
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The atom is mostly empty space.
Two regions.
Nucleus- protons and neutrons.
Electron cloud- region where you might
find an electron.
Subatomic particles
Name
Symbol
Charge
Relative
mass
Actual
mass (g)
Electron
e-
-1
1/1840
9.11 x 10-28
Proton
p+
+1
1
1.67 x 10-24
Neutron
n0
0
1
1.67 x 10-24
Bohr’s Model
Increasing energy
Fifth
Fourth
Nucleus
Orbit
Third
Second
First
Nucleus
Energy Levels Electron
Further away from the nucleus means more energy.
There is no “in between” energy
•Few difficulty Bohr model had
•The spectra of larger atoms. At best, it can make
some approximate predictions about the emission
spectra for atoms with a single outer-shell electron
•The relative intensities of spectral lines
•The existence of fine and hyperfine structure in
spectral lines.
•The Zeeman effect - changes in spectral lines due to
external magnetic fields
Bohr model: A semiclassical model
Wave-particle duality nature of light
Classical physics- A system can absorb or emit any
amount of energy.
Plank’ hypothesis- Energy absorbed or emitted by a
black body is restricted to the relation E = hν
Consequences:
1. Photoelectricity (Eistein, 1906)
2. Theories of atomic spectra (Bohr, 1913)
Photoelectric Effect
Emission of electrons from metals when exposed to
(ultraviolet) radiation.
Explanation (EINSTEIN 1905)
Threshold frequency 0 given by  = h0
For  > 0, the kinetic energy of the emitted electron
Ek = h   = h(  0).
Line Spectrum of Hydrogen atom
when subjected to higher temperature or a electric discharge emit
electromagnetic radiation
R = Rydberg Constant
109677.6 cm-1
Wave particle duality of material
particles
 Louis de Broglie (electron has wave properties)
 Werner Heisenberg (uncertainty Principle)
 Erwin Schrodinger (mathematical equations
using probability, quantum numbers)
de Broglie wavelength of electrons
λ= h/p
Consequence: Electrons produce diffraction
pattern when passed through thin
diffraction grating (Davison and Germer)
Electron Motion Around Atom
Shown as a de Broglie Wave
Schrödinger's equation, what is it ?
Newton’s law allows you to describe motion of mechanical systems and
mathematically predict the outcome of the system.
In quantum mechanics, the analogue of Newton's law is Schrödinger's
equation for a quantum system (usually atoms, molecules, and subatomic
particles whether free, bound, or localized).
It is a wave equation in terms of the wavefunction which predicts analytically
and precisely the probability of events or outcome.
The Schrodinger equation gives the quantized energies of the system and
gives the form of the wavefunction so that other properties may be
calculated.
The wave equation developed by Erwin Schrodinger in
1926
(one-dimensional form)
About the Wavefunction
The wavefunction is assumed to be a single-valued function of position and
time, which is sufficient to get a value of probability of finding the particle at a
particular position and time.
The wavefunction is a complex function, since it is its product with its
complex conjugate which specifies the real physical probability of finding the
particle in a particular state.
WAVEFUNCTION () (PSI)
Classically, the state of a system is described by its position
and momentum
In Quantum theory, the state of a system is described by its
wavefunction
WAVEFUNCTION () (PSI)
1. A wavefunction is a mathematical function (like sinx, ex).
Like any mathematical function it can have large value at
some place, small in other and zero elsewhere.
It can be real or complex
2. A wavefunction contains all information about the system
3. The wavefunction is a function of Cartesian coordinate
and time. ie.  (x, y, z, t)
4. If the wavefunction is large at a point in space, the particle
has a large probability at that point
5. The more rapidly a wavefunction changes from place to
place, higher the K.E. of the particle it describes
WAVEFUNCTION () (PSI)
A wavefunction describes the state of a system
How?
The state of a system is described by some measurable
quantities such as mass, volume, momentum, position,
Energy etc. These quantities are called observables
How to determine the observables from wavefunction ()
By performing a set of well defined mathematically
operations on . These mathematical operations are
called operators
Born interpretation
2

The state of a system (particle) is completely specified by its
wavefunction (x,y,z,t), which is a probability amplitude and
has the significance that
2 dV
(more generally 2dV since  may be complex)
represents the probability that the particle is located in the
infinitesimal element of volume dV about the given point, at
time t.
NORMALIZATION
As per Born interpretation, the probability of existence of
the particle in the entire space should be 1.
In mathematical term the wave function has to be normalized
For one dimension
N 2  2 dx  1
or
N 2   dx  1
Where N is the normalization constant
N
1
 dx
2
1
2
In 1913 Niels Bohr came up with a new atomic model in which
electrons are restricted to certain energy levels.
Schrödinger applied his equation to the hydrogen atom and found
that his solutions exactly reproduced the energy levels stipulated by
Bohr. The result was amazing and one of the first major achievement
of Schrödinger's equation and earned him the 1933 Nobel Prize in
physics.
Newton’s Law: Conservation of Energy ( Harmonic Oscillator example))
Time independent Schrodinger Equation
Quantum conservation of Energy Schrodinger Equation
H = E
In a wave equation, physical variables takes the form of “operators” (H),
Hamiltonian operator
In three dimensions,
ħ2/2m (2 ψ/x2 + 2 ψ/y2 + 2ψ/z2) + U(x,y,z)ψ(x,y,z) = Eψ(x,y,z)
Time dependent Schrodinger Equation
Eigen value equations
(operator) (function)= (constant factor) (function)
   
d ax
ax
e ae
dx
2
d
( Sin 4 x)  16( Sin 4 x)
2
dx
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How to proceed further?
•Let us test the Schrödinger equation for some simple physical
systems! Some model systems at first – easy to test ! Hopefully,
some quantum properties of matter will also be understood!
•If we can understand these ‘simple systems’ without doing any
approximation and can derive ‘exact solutions’, then we shall
proceed towards our major target – atoms and molecules
•Why we do not go right now to solve the Schrödinger equation
for atoms and molecules? Because the mathematical solution for
atoms and molecules is complicated.
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Characteristics of the wavefunctions
1. Wavelength = 2L/n
2. There are n-1 nodes (interior points where the wave
function passes through zero) in the wavefunction n
3. The energy increases with increasing number of nodes.
The ground state has no nodes.
4. The ground state energy is not 0, but h2/8mL2, the zero
point energy. This is a consequence of the uncertainty
principle.
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Applications of this model
1. Calculation of energy of -electrons of conjugated olefins
H2 C
C
H
C
H
CH2
2. Electrons in nano materials
3. Electrons present in cavities or color centers
4. Translational motion of ideal gas molecules
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