The world of Atoms

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The world of Atoms
2
Quantum Mechanics
Theory that describes the physical properties of
smallest particles (atoms, protons, electrons,
photons)
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The hydrogen atom

• electron orbits around the nucleus like a wave

• orbit is described by wavefunction

• wavefunction is discrete solution of wave
  equation

• only certain orbits are allowed

• orbits correspond to energy levels of atom

4
The hydrogen atom
In the Bohr model of the atom, the hydrogen atom
is like a planetary system with the electron in
certain allowed circular orbits.
The Bohr model does not work for more complicated
systems!
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Quantum numbers
Each orbital is characterized by a set of quantum
numbers.
Principal quantum number (n) integral values
(1,2,3). Related to the size and energy of the
orbital.
Angular momentum quantum number (l) integral
values from 0 to (n-1) for each value of n.
Magnetic quantum number (ml) integral values
from - l to l for each value of n.
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Quantum numbers
How many orbitals are there for each principle
quantum number n 2 and n 3?
For each n, there are n different l-levels and
(2l1) different ml levels for each l.
n2
n 2
different l-levels
l 0, 1
(2l1) 2 x 0 1
1 ml-levels for l 0
(2l1) 2 x 1 1
3 ml-levels for l 1
Total 1 3 4 levels
for n 2
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Quantum numbers
How many orbitals are there for each principle
quantum number n 2 and n 3?
For each n, there are n different l-levels and
(2l1) different ml levels for each l.
n3
n 3
different l-levels
l 0, 1,2
(2l1) 2 x 0 1
1 ml-levels for l 0
(2l1) 2 x 1 1
3 ml-levels for l 1
(2l1) 2 x 2 1
5 ml-levels for l 2
Total 1 3 5 9 levels for n 3
The total number of levels for each n is n2
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Quantum numbers
Names of atomic orbitals are derived from value
of l
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Quantum numbers
Quantum numbers for the first four levels in the
hydrogen atom.
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What is the meaning of ?
Wavefunction itself is not an observable!
Square of wavefunction is proportional to
probability density
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Wavefunction and probability
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Quantum numbers
A subshell is a set of orbitals with the same
value of l. They have a number for n and a
letter indicating the value of l.
l 0 (s)
l 1 (p)
l 2 (d)
l 3 (f)
l 4 (g)
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Orbital Shapes
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Heisenberg uncertainty principle
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Heisenberg uncertainty principle
It is not possible to know both the position and
momentum of an electron at the same time with
infinite precision.
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Heisenberg
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The s orbitals in hydrogen
probability distributions
The higher energy orbitals have nodes, or regions
of zero electron density.
s-orbitals have n-1 nodes.
The 1s orbital is the ground state for hydrogen.
orbital surfaces
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Pauli exclusion principle
How many electrons fit into 1 orbital?
Only 2 electrons fit into 1 orbital
1 spin up
1 spin down
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Pauli exclusion principle
Electrons are fermions. There are also bosons
As the temperature is lowered, bosons pack much
closer together, while fermions remain spread
out.
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Energy Levels
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Energy Transitions
For the energy change when moving from one level
to another
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Lines and Colors
Change in energy corresponds to a photon of a
certain wavelength
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Lines and Colors
What is the wavelength of the photon that is
emitted when the hydrogen atom falls from n3
into n2?
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Light out of Molecules
hydrogen
Fluorescence
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Degeneracy
Orbital energy levels for the hydrogen atom.
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Beyond hydrogen
Hydrogen is the simplest element of the periodic
table.
Exact solutions to the wave equations for other
elements do not exist!
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Polyelectric Atoms
What do the orbitals of non-hydrogen atoms look
like?
Multiple electrons electron correlation
Due to electron correlation, the orbitals in
non-hydrogen atoms have slightly different
energies
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Polyelectric Atoms
Screening due to electron repulsion, electrons
in different orbits feel a different attractive
force from the nucleus
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Screening changes the energy of the electron
orbital the electron is less tightly bound.
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Polyelectric Atoms
Penetration within a subshell (n), the orbital
with the lower quantum number l will have higher
probability closer to the nucleus
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Polyelectric Atoms
Hydrogen
Polyelectric atom
Orbitals with the same quantum number n are
degenerate
Degeneracy is gone Ens lt Enp lt End lt Enf
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Spectra of Polyelectric Atoms
Due to lifting of degeneracy, many more lines are
possible in the spectra of polyelectric atoms