10.7 The Hydrogen Orbitals

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10.7 The Hydrogen Orbitals

• In the Wave Mechanical model of the atom an
  orbital represents the space around the nucleus
  occupied by an electron.
• An orbital is the probability distribution for an
  electron where it can be found 90 of the time
  (see fig 10.20, 10.24, 10.25).

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• Hydrogen orbitals
• The discrete energy levels of hydrogen are
  called principal energy levels and are labeled
  with an integer (1, 2, 3, 4 )
• The principal levels have sublevels which
  contain spaces (orbitals) for electrons (fig
  10.22).
• Ex 1s, 2s, 2p, 3s, 3d, etc
• 1 energy level, s shape (sphere)
• 2 energy level, s shape (sphere)
• 2 energy level, p shape (lobed)
• 3 energy level, d shape (fig 10.28)

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• energy level 1 has one sublevel
• 1s has one orbital
• energy level 2 has two sublevels
• 2s has one orbital
• 2p has three orbitals (2px, 2py, 2pz)
• energy level 3 has three sublevels
• 3s has one orbital
• 3p has three orbitals (3px, 3py, 3pz)
• 3d has five orbitals (fig 10.28)
• energy level 4 has four sublevels
• 4s has one orbital
• 4p has three orbitals (4px, 4py, 4pz)
• 4d has five orbitals
• 4f has 7 orbitals

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• hydrogen also has energy levels above level 4
• an orbital is potential space for an electron
• energy can excite the electron in the 1s orbital
  (ground state) and move it to a higher energy
  level (2s, 2p, 3s, etc.) further from the nucleus
• when the excited electron returns to its lower
  energy orbital it gives off a photon of light
  with equal energy to the amount of energy it
  absorbed

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10.8 The Wave-Mechanical Model Further
Development

• Wave mechanics Matter as waves
• Light (photons) can be demonstrated to behave as
  either waves or particles.
• Similarly, matter can behave as waves.
• In 1923 Louis de Broglie proposed that a particle
  of mass can have wavelike properties. This meant
  that electrons can have a wave-particle duality,
  much like light does.
• In 1926 Erwin Schroedinger worked out the
  mathematics of depicting electrons as waves
• An electron could only exist in different regions
  around a nucleus, meaning its energy was
  quantized.
• The regions of stability were a complex interplay
  of the electrostatic field generated by charged
  electrons and atomic nuclei.

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• The wave mechanical model applies to all atoms,
  not just hydrogen.
• Electrons (in ground states, i.e., unexcited) are
  arranged in an atoms orbitals following specific
  rules.
• The Pauli exclusion principle no more than two
  electrons of opposite spin (designated by ? ? )
  can occupy an atomic orbital.
• The Aufbau principle electrons fill orbitals at
  the lowest possible energy level before filling
  higher levels (e.g., 1s before 2s, 2p before 3s,
  etc.)

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• Order of filling orbitals
• Hunds Rule electrons of the same spin are
  added to each orbital in a sublevel before a
  second electron of opposite spin is added

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• Principal Components of the Wave Mechanical Model
  
• (see pg 293)
• Atoms have a series of principal
• energy levels, n which can equal
• 1, 2, 3, 4, . . .
• 2. The energy of the level increases
• as n increases.
• 3. Each principal energy level
• contains one or more types of
• orbitals, called sublevels.

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• 4. The number of sublevels in a given
  principal energy level equals n.
• level 1 contains 1 sublevel
• level 2 contains 2 sublevels
• level 3 contains 3 sublevels
• and so on . . .
• 5. The n value is always followed with a letter
  indicating the shape of the orbital (s, p, d, f
  ).
• An orbital can be empty or contain one or two
  electrons with opposite spin.
• The shape of the orbital is a probability
  distribution for an electron in that orbital.

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10.9 Electron Arrangements in First Eighteen
Elements

• Electrons are placed in various orbitals starting
  with n 1, and continuing with n 2, n 3, and
  so on.
• The orbital closest to the nucleus is the 1s. As
  n increases, the orbital becomes larger and the
  electron occupies space further from the nucleus.
• Electron configurations show the electrons
  occupying orbitals in each energy level.
• Orbital diagrams (box diagrams) show orbitals as
  boxes grouped by sublevels with arrows showing
  electrons.

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• Valence electrons are the electrons in the
  outermost (highest) principal energy level of the
  atom.
• Example
• These electrons are involved in bonding between
  atoms
• Core electrons are the electrons not involved in
  bonding atoms to each other.
• Example

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10.10 Electron Configurations and the Periodic
Table

• The electron configuration of any element can be
  determined by understanding its position in the
  periodic table. See fig 10.31
• Some transition metals, however, do not follow
  the general pattern for placing electrons in
  orbitals (for reasons not discussed here).
• Summary of Wave-Mechanical Model and
  Valence-Electron Configurations.
• The W-M model pictures electrons in an atom
  arranged in orbitals, with each orbital holding
  two electrons.
• The same type of orbitals recur in going from one
  principal energy level to another.
• This means valence electron configurations recur
  periodically. See fig 10.34
• Elements in particular groups (such as the alkali
  metals, halogens, etc.) have the same valence
  electron arrangement and, therefore, share
  similar chemical properties.