Atomic Structure

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Atomic Structure

• Edward A. Mottel
• Department of Chemistry
• Rose-Hulman Institute of Technology

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Cathode Ray Tube
Heated cathodes emitted cathode "rays"
Deflected by either magnetic or electric fields
J.J. Thomson, 1897
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J. J. THOMSON (1897)British Physicist
The "beam" carried a negative charge.
How did he know that?
The ratio of charge to mass (e/m) was independent
of the cathode material.
Why does this indicate that cathode rays
(electrons) are an integral part of each element?
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Photoelectric Effect
Albert Einstein (1905)German Physicist Interprete
d the Photoelectric Effect
Confirmed that light is corpuscular (possess
particle-like properties)
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Gold Foil Experiment(10-4 cm thick)
Kotz Purcell (1987)
Rutherford, 1911
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Ernest Rutherford (1911)British Chemist
Most of the alpha particles (a, 4He2) passed
straight through, but a few were deflected
or reflected straight backwards.
Since alpha particles were known to have a
positive charge, this indicated that the nucleus
of an atom contained most of the mass, and that
it was positive in charge
Diagram source unknown
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The Atom Before 1913

• Smallest unit of matter which maintains the
  physical and chemical properties of the element.

• Combines with other atoms to form molecules, but
  it itself is not destroyed.
• Consists of a positive nucleus of very small size
  containing most of the mass of the atom.
• Exhibits a volume much larger than the nucleus
  due to the presence of electrons.

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Other physical properties had to be accounted for
All the mass of the atom cannot be accounted
for by only protons and electrons.
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Dark and Bright Line Spectra
hydrogen
prism
white light source
If the gas is heated until it glowed, the same
wavelengths of light are emitted by the gas.
If white light is passed through a sample of
hydrogen gas, certain selected wavelengths of
light are absorbed by the gas.
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A Possible Solution

• A unified theory explaining these facts was
  proposed by Niels Bohr in 1913.

• An atom consists of a positive nucleus surrounded
  by electrons moving in spherical orbits.
• planetary model of the atom

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The Bohr Model of the AtomA Break From Classical
Mechanics
The electrons continuously circle the
nucleus without losing energy.
This represents a break from classical
physics since any acceleration (including
centripetal) is expected to require some energy.
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The Bohr Model of the Atom
Radiation (light) is emitted when an electron in
a higher energy orbit moves to a lower energy
orbit
If energy is absorbed the electron moves from
a lower to a higher energy orbit.
energy difference energy absorbed or emitted
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Other Things To Consider
If white light is passed through a sample of
hydrogen gas, certain selected wavelengths of
light are absorbed by the gas.
The spectral lines of hydrogen can be
explained by the Rydberg equation. (1899)
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Bohr Theory (1913)Accounted for two important
developments
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Bohr Theory (1913)
only certain energy changes are allowed within
the atom.
Because only certain frequencies are absorbed or
emitted
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Bohr Model of the Hydrogen AtomPlanetary Model
integer principal quantum number (1, 2, 3,..., )
Only integral multiples of h/2p are allowed
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Bohr Model of the Hydrogen AtomPlanetary Model
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Bohr Model of the Hydrogen AtomPlanetary Model
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Emission and Absorption are Opposite Processes
Emission
Absorption
Absorption
The energy difference between levels corresponds
to the observed lines in the hydrogen spectrum
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Emission and Absorption are Opposite Processes
Big absorption
What happens if an electron moves to an
orbit infinitely distant from the nucleus?
IONIZATION
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Horsehead Nebula in Orion48 inch Schmidt
Telescope - Hale Observatories
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Visible Solar Spectrum13-foot Heliospectrograph,
Mt. Wilson Observatory
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A Caveat(Note of Caution)

• The Bohr Atom calculations and the Rydberg
  equation for electronic transitions only work for
  hydrogen-like species.
• One electron species H, He, Li2, ...

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Niels Bohr (1913)(Danish Physicist)

• Postulated that electrons spin around the nucleus
  in an orbit.

The energy differences between these orbits can
be used to explain the various colors of
light emitted and absorbed by gaseous elements.
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Erwin Schrodinger (1926)(Austrian Physicist)

• Developed the modern view of the atom, treating
  electrons as mathematical functions.
• sine and cosine wave functions.

Louis de Broglie (1926)(French Physicist)

• Proposed that matter has both wave and particle
  properties.

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Standing Wave(General Equation - One Dimension)

• l wavelength
• y amplitude
• c displacement of the wave from origin

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Schrödinger Equation(One Dimension)
Y is a wave function which describes the particle
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Schrödinger Wave Equation(Three Dimensions)
To solve this equation in three dimensions for
hydrogen, the energy (E) of the electron must
take on certain (quantized) values related by
integers.
These integers are known as QUANTUM NUMBERS.
Quantum numbers need not be assumed (as was done
by Bohr), but are required by the mathematics of
the system.
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Wave Functionsare composed on sine and cosine
terms
y2 is the probability of finding an electron at a
specific location
The wave function (y) has no physical significance
What is the probability of finding an electron at
a node?
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A Mathematical Model of the Atom

• These wave equations give a "mathematical model"
  for the electron.
• the electron can be at many different places

• The likelihood (probability) of "finding" the
  electron at any point depends on
• Radial function (distance)
• Angular function (direction)

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Orbitals

• The region around a nucleus in which an electron
  has a probability of being located is called an
  orbital.
• Orbitals can vary in
• distance from the nucleus (radial function)
• direction (angular function)

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Wave Function
The shape of the orbital and the energy of the
electron is related to the wave function (y).
The electron is mathematically described by the
wave function,
The wave function is composed of radial and
angular functions (in three dimensions).
the Schrödinger Equation is used to calculate the
energy of that electron.
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Orbitals WithNo Angular Dependence
1s
isotropic orbitals
2s
s orbitals have a spherical shape
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Orbitals WithAngular Dependence
Anisotropic orbitals
p orbitals have a propeller shape
the angular probability function is not the same
in all directions
How can you distinguish px from py or pz?
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Higher Energy Orbitals

• Higher energy levels correspond to higher wave
  functions including 3s, 3px, 3py, 3pz and d
  orbitals.

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d Orbitals
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Quantum Numbers

• Each electron in the orbital of the atom can be
  described by an unique combination of values
  known as quantum numbers.

• There are four different quantum numbers

n , l , ml , ms
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Principal Quantum Number
range n 1, 2, 3, ,
n1
n2
Larger values of n refer to higher
energy orbitals (further from the nucleus)
n3
n4
n5
n6
n7
The principal quantum number is related to the
rows of the periodic table.
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Angular Quantum Number
range l 0, , n-1
l 0
l 1
l 2
l 3
s orbital
p orbital
d orbital
f orbital
(no angular dependence)
Is it possible to have a 3p orbital?
Is it possible to have a 2f orbital?
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Magnetic Quantum Number
ml -l , , 0, , l
p-1
p0
p1
In a magnetic field aligned along the z-axis, an
electron in the 2pz orbital will behave
differently than an electron in the 2px or 2py
orbitals.
Differentiates between orbitals with the same n
and l quantum numbers
What would be the names of these orbitals?
How many f-orbitals are there in an f-orbital set?
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Spin Quantum Number
ms -1/2, 1/2
Each orbital can contain up to two electrons
one aligned with an external field
one aligned against an external field
Which electron has lower energy?
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Quantum Numbersand the Periodic Table
p
s
d
f
Identify the regions of the periodic table
that correspond to the s, p, d and f orbitals
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Four Quantum Numbers

• Each electron in an atom can be described
  uniquely by the four quantum numbers.

• Three rules involving quantum numbers
• Pauli Exclusion Principle
• Aufbau Principle
• Hund's Rule

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Pauli Exclusion Principle

• Only one electron in an atom may have the same
  four quantum numbers.

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Aufbau Principle

• In the ground state, electrons fill in the lowest
  available energy state (orbital) first

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Hund's Rule

• If more than one electron occupies a degenerate
  set of orbitals (orbitals of the same energy),
  then the electrons will fill in such a way as to
  maximize the number of orbitals filled.

• It is more stable for the spin of the electrons
  to be aligned in the same direction.

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