Quantum Mechanical Model of the Atom

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Quantum Mechanical Model of the Atom
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• Many scientists contributed to the development of
  the quantum mechanical model of the atom.
• Bohr
• Planck
• DeBroglie
• Heisenberg
• Schrodinger
• Pauli

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What was already known..

• Early 1900sbelieved that
• Energy is quantized
• Electrons have both wave and matter properties
• Electrons can be at a variety of specific energy
  levels in an atom
• Energy levels are called orbits (Bohr model)
• Proposed that electron had both wave and matter
  properties

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Next round of research

• Goal was to describe electrons in atoms
• Ultimately describe for each electron
• Energy level size of the region it occupies (n)
  
• 3-D shape of the region it occupies (l)
• Orientation of the region/orbital (ml)
• Spin on the electron (ms)

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Schrodinger deBroglie

• S deB pictured the electron bound to the atom
  in a standing wave
• Standing vs. traveling waves
• See page 301

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Schrodinger

• Sch.. Proposed that electrons move around the
  nucleus in standing waves
• Each orbit represents some whole number multiple
  of a wavelength
• Schrodinger analyzed the hydrogen data based on
  the assumption that the electrons behaved as
  standing waves.

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Schrodinger

• Schrodingers equation takes into account
• The position of the electron in 3D space (its
  x,y,z coordinates)
• Potential energy of the atom due to the
  attraction between electrons and protons
• Kinetic energy of the electron

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Schrodinger

• Schrodingers equation has many solutions
• Each solution is called a wave function (y) and
  is correlated to a specific amount of energy
• Each wave function is more commonly called an
  orbital.

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Orbitals

• Each solution to Schrodingers equation describes
  a specific wave function (y) /orbital
• The square of a wave function, (y)2, generates a
  probability distribution for an electron in that
  orbital
• Also called an electron density map for a given
  orbital
• (y)2 describes the shape, size, and orientation
  of the orbital

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Orbitals

• Orbitals are regions in space where an electron
  is likely to be found
• 90 of the time the electron is within the
  boundaries described by the electron density map
• Can describe its energy, shape, and orientation
• The exact path of an electron in a given orbital
  is not known!

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Heisenberg

• Heisenberg uncertainty principle states that we
  cannot know both the position and the momentum of
  an electron at the same time.
• Therefore, we do not know the exact path of the
  electron in an orbital.

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Orbitals

• The lowest energy solution to Sch..s equation
  for an electron in a hydrogen atom describes what
  is known as the 1s orbital.
• See pages 306/307

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Describing Orbitals

• Use quantum numbers to describe orbitals. A
  given orbital can be described by a set of 3
  quantum numbers
• Principal quantum number (n)
• Angular momentum quantum number (l)
• Magnetic quantum number (ml)

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Principal Quantum Number (n)

• (n) describes the size and energy of the oribital
• Possible values whole number integer
• 1, 2, 3,
• As n increases so does the size and energy of
  the orbital

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Angular momentum quantum number (l)

• (l) is related to the shape of the orbital
• Possible values (l) is an integer between 0 and
  n-1
• Each (l) value is also assigned a letter
  designation

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Angular momentum quantum number (l)
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Magnetic quantum number (ml)

• (ml) is related to the orientation of the orbital
  in 3-D space
• Possible values - l to l

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Magnetic quantum number (ml)

• Consider the p orbitalit has an l value of 1 and
  thus the possible ml values are -1, 0, 1
• These 3 ml values correspond to the 3 possible
  orientations of the p orbital

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Ml and Orbitals
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Quantum Number Summary

• See page 304 and board.
• A set of 3 quantum numbers describes a specific
  orbital
• Energy and size - n
• Shape - l
• Orientation ml

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4th Quantum Number!

• A 4th quantum number was added to describe the
  spin on a given electron.
• Called the electron spin quantum number - ms
• Possible values 1/2 and -1/2

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More on electron spin.

• Each orbital can hold a maximum of 2 electrons of
  opposite spin.
• Pauli exclusion principle states that no two
  electrons in an atom can have the same set of 4
  quantum numbers

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Summary

• Three quantum numbers describe a specific orbital
• Energy and size, shape, and orientation
• Four quantum numbers describe a specific electron
  in an atom

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7.9 Polyelectronic atoms

• The Schrodinger model was based on H and works in
  principle for atoms with more than one electron.
• The shapes and possible orientations of the
  hydrogen based orbitals holds true for
  polyelectronic atoms.
• However, the size and energy of the orbitals in
  polyelectronic atoms differ from those calculated
  for hydrogen.

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Polyelectronic Atoms

• In general, find that in a given principal
  quantum number (n)
• S is lower energy than p, which is lower energy
  than d..
• s lt p lt d lt f
• Already know that 1s lt 2s lt 3s and 2p lt 3p lt
  4p. (in terms of size and energy)

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7.11 The Aufbau Principle

• Putting electrons in to orbitals
• Aufbau means building up in German
• Electrons always enter the lowest energy orbital
  with room

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Hunds Rule

• The orbitals of a given sublevel (e.g. p, or d,
  or f) are degenerate (of the same energy).
• The lowest energy state occurs with the maximum
  number of unpaired electrons.
• Meaning..electrons enter an empty orbital of a
  given sublevel before pairing up.

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Goals

• To be able to write for any atom
• Electron configuration
• Box/energy diagram
• Lewis dot symbol
• State the quantum numbers for each electron in an
  atom.
• To relate the electron configuration of an atom
  to its location on the periodic table and its
  properties.

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Goals Elaborated

• Electron configuration shows the number of
  electrons in each sublevel
• Format 1s22s22p4 or He 2s22p4
• Box/energy diagram shows electrons as arrows
  and each orbital as a box. Electrons of opposite
  spin are indicated by up and down arrows.
• Format

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Goals Elaborated

• Lewis Dot Symbol shows valence electrons as
  dots around the symbol for the atom
• Maximum of 2 electrons per side of the symbol
• Valence electrons are all of the electrons in the
  highest occupied principle quantum level (n)
• Format

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1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s