Quantum Theory and the Atom

1
Quantum Theory and the Atom

• Chapter 5
• Section 2

2
Bohr Model of the Atom

• Observed hydrogen only emits certain
  frequencies of light
• Niels Bohr (Danish) proposed a quantum model for
  the atom
• Lowest energy level allowed for an electron is
  its ground state
• When atom gains energy, electron goes to a higher
  level, an excited state.
• The electron can have many excited states

3
Bohr Model (Cont.)

• Each energy level corresponds to one quanta of
  energy
• Bohr model correctly predicted the emission
  spectra for hydrogen.

4
Bohr Atomic Model
5
Explaining the Hydrogen Line Spectrum

• When energy is added, electron moves to a
  higher-energy orbit (from n 1 to n 2)
• When atom moves back to lower-energy orbit, a
  photon of energy is released
• Energy release is equal to the frequency of the
  light spectrum.
• Because only certain atomic energies are possible
  (certain orbits), only specific frequencies are
  emitted.

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Energy and Atoms

• Higher Energy Orbit Lower Energy Orbit
• Specific distance
• Specific amount of energy (quanta)
• Specific frequency
• Specific frequency specific color

7
Bohr Atomic Model

• Bohr model failed to explain the spectra of any
  other element
• It was later determined that the Bohr model was
  fundamentally correct.

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Quantum Mechanical Model

• 1920s DeBroglie (French) Experiments
• Electron orbits behaved like waves, could they
  have multiple frequencies?
• Could particles, including electrons, behave like
  waves?
• If an electron has a wavelike motion AND is
  restricted to circular orbits of fixed radius,
  the electron is allowed only certain wavelengths

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Multiples of Wavelengths
10
Wavelengths in Orbits
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Quantum Mechanical Model

• DeBroglie Equation
• ? h/mv
• Predicts that ALL moving particles have wave
  characteristics
• Auto moving at 25 m/s, with mass 910kg has a
  wavelength of 2.9x10-38 (way too small to be
  detected)
• Electron at same speed has a wavelength of
  2.9x10-5 (easily measured)

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DeBroglies Findings

• Notice also that this means the electron does not
  exist at one single spot in its orbit, it has a
  wave nature and exists at all places in the
  allowed orbit. And the Bohr atom really looks
  like the following diagram

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Heisenberg Uncertainty Principle

• It is impossible to make any measurement on an
  object without disturbing the object at least a
  little
• States
• That is is fundamentally impossible to know
  precisely both the velocity and the position of a
  particle at the same time.

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Heisenberg Uncertainty Principle
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Schrödinger Wave Equation

• 1926 Erwin Schrödinger (Austria) furthered the
  theory.
• Created an equation that treated the hydrogen
  atoms electron like a wave
• New model applied equally well to other atoms
• This body of knowledge became the quantum
  mechanical model of the atom

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Just For Reference
The Schrödinger equation is the fundamental
equation of physics for describing quantum
mechanical behavior. It is also often called the
Schrödinger wave equation, and is a partial
differential equation that describes how the
wavefunction of a physical system evolves over
time. Viewing quantum mechanical systems as
solutions to the Schrödinger equation is
sometimes known as the Schrödinger picture, as
distinguished from the matrix mechanical
viewpoint, sometimes known as the Heisenberg
picture. The time-dependent one-dimensional
Schrödinger equation is given by
where i is the imaginary unit,          is
the time-dependent wavefunction,     is h-bar,
V(x) is the potential, and       is the
Hamiltonian operator. However, the equation can
be separated into temporal and spatial parts
using separation of variables     to write
thus obtaining
Setting each part equal to a constant then gives
And so on and so on..
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What does this mean about electron orbits?

• Atomic orbits are 3-dimensional regions around
  the nucleus (like a fuzzy cloud).
• Principal quantum numbers are assigned to
  indicate relative size and energy of orbitals
• As n increases, orbital gets larger, has more
  energy
• Up to 7 energy levels have been detected for
  hydrogen

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What does this mean about electron orbits?

• Each principal energy level can have sublevels
• Principal energy level one has only one sublevel
• Principal energy level 2 has 2 sublevels
• Principal energy level 3 has 3 sublevels
• And so on..

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What does this mean about electron orbits?

• Sublevels are labeled s, p, d, or f according to
  their shape
• s sublevels are spherical
• p sublevels are dumbell shaped
• d sublevels and f sublevels are not all shaped
  the same.
• Each orbital can have at most 2 electrons

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What does this mean about electron orbits?

• Principal level one has only ONE sublevel
• Designated as 1s (spherical)
• 2 total electrons (2 elements in 1st row)
• Principal level 2 has 2 sublevels
• Designated as 2s and 2p
• 2s is spherical (like 1s) but larger
• 2p has three dumbbell shaped orbitals on each of
  three axis
• Total 8 electrons (8 elements)

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What does this mean about electron orbits?
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What does this mean about electron orbits?
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What does this mean about electron orbits?
Note alignment along the axes
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What does this mean about electron orbits?

• Third principal energy level has 3 sublevels
• 3s, 3p, and 3d
• d-orbitals have 5 orbitals of equal energy
• 4 of the d-orbitals have identical shapes but
  different orientations
• 5th d-orbital has a different shape and
  orientation than the others

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What does this mean about electron orbits?