Download 2. Atomic Structure 2.1 Historical Development of Atomic Theory

2. Atomic Structure
2.1 Historical Development
of Atomic Theory
Remember!? Dmitri I. Mendeleev’s Periodic Table (17 Feb. 1869 )
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2.1.1 The Periodic Table
of the Elements
2.1.2 Discovery of Subatomic
Particles & the Bohr Atom
Each element emits light
of specific energies when
excited by electric discharge
or heat. For the H-atom
(Balmer, 1885):
n= 6
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4
3
2
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2.1.2 Discovery of Subatomic
Particles & the Bohr Atom
The Hydrogen Spectrum:
Johann Jacob Balmer
(Physicist, 1825 – 1899)
2.1.2 Discovery of Subatomic
Particles & the Bohr Atom
Bohr Model (1913 ~ 1923) of the Hydrogen Atom:
Note, Rydberg’s
“constant” is f(mn)
Niels Bohr
(1885 - 1962)
principle
quantum
numbers!
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2.1.2 Discovery of Subatomic
Particles & the Bohr Atom
Theodore Lyman
(1874 - 1954)
Friedrich Paschen
(1865-1940)
Energy levels only
valid for hydrogen!
2.1.2 Discovery of Subatomic
Particles & the Bohr Atom
All Moving Particles have Wave Properties (de Broglie , 1920):
Energy of spectral lines (electron)
can be measured with great precision
(Δpx is small) -> Uncertainty in
location of the electron is large.
No exact orbits but orbitals with
probability to find the electron
Louis de Broglie
(1892-1987 )
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2.1.2 Discovery of Subatomic
Particles & the Bohr Atom
Uncertainties in the Location and Momentum
of a Moving Particle (Heisenberg , 1927):
“The more precisely the position is determined,
the less precisely the momentum is known
in this instant, and vice versa.”
(Heisenberg, 1927)
Δt ΔE >= h/4π
Not quite correct…there is no operator
in presenting Δt (time)
Werner Heisenberg
(1901-1976 )
2. 2 The Schrödinger
Equation
Wave Properties of an Electron in Terms of Position, Mass
Total Energy, and Potential Energy:
Wave function, Ψ,
describes electron wave in space.
Hamiltonian operator, H,
includes derivatives that operate on Ψ
Each orbital, characterized by its own Ψ,
has a characteristic energy
Erwin Schrödinger
(1887-1961)
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The “Solvay Congress”
in Copenhagen 1927
Bohr in intense discussion
with Heisenberg and Pauli
(L to R) in Copenhagen
Heisenberg, standing
front left, next to P.A.M.
Dirac, in front of A.H.
Compton.
Univ. of Chicago, 1929.
The “Solvay Congress”
in Copenhagen 1927
…but don’t forget good old “Al”!
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The “Solvay Congress”
in Copenhagen 1927
2. 2 The Schrödinger
Equation
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2. 2 The Schrödinger
Equation
Unlimited solutions…but for a physically realistic solution
for Ψ:
Each Ψ describes the wave properties of a given electron
in a particular orbital . The probability of finding an
electron at a given point in space is proportional to Ψ2
2.2.1 Particle in a Box
Particle in a Box
n=3
n=2
n=1
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2.2.2 Quantum Numbers
& Atomic Wave Functions
*
* lines in alkali metal spectra are doubled
beam of alkali metal atoms splits into two if it passess through H
2.2.2 Quantum Numbers
& Atomic Wave Functions
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2.2.2 Quantum Numbers
& Atomic Wave Functions
2.2.2 Quantum Numbers
& Atomic Wave Functions
R(r): Radial Function “R”: Electron
Density @ Different Distances from
the Nucleus. Determined by n and l
The Radial Probability Function 4πr2R2 describes the
probability of finding the electron at a given distance
from the nucleus, summed over all angles
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2.2.2 Quantum Numbers
& Atomic Wave Functions
The Angular Functions:
How does the probability
change from point to point
at a given distance?
Angular Functions “ΘΦ” Y: Describe the
Shape of the Orbital and its Orientation
in space: Y(θφ) -> s, p, d Orbitals
Determined by l and ml
2.2.2 Quantum Numbers
& Atomic Wave Functions
The Nodal Surfaces:
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2.2.2 Quantum Numbers
& Atomic Wave Functions
2.2.2 Quantum Numbers
& Atomic Wave Functions
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2.2.2 Quantum Numbers
& Atomic Wave Functions
note the
difference
taken from Harvey & Potter
“Introduction to Physical
Inorganic Chemistry”
Wesley 1963
2.2.2 Quantum Numbers
& Atomic Wave Functions
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2.2.2 Quantum Numbers
& Atomic Wave Functions
2.2.2 Quantum Numbers
& Atomic Wave Functions
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2.2.2 Quantum Numbers
& Atomic Wave Functions
The s and p-orbitals…that’s the way we like them most!
2.2.2 Quantum Numbers
& Atomic Wave Functions
The s and p-orbitals…that’s the way we like them most!
electron density
on the axes!
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2.2.2 Quantum Numbers
& Atomic Wave Functions
The five d-orbitals…my favorite ones!
2.2.2 Quantum Numbers
& Atomic Wave Functions
The five d-orbitals…my favorite ones!
electron density
on the axes!
electron density in between the axes!
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