Electronic Structure of Atoms

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Electronic Structure of Atoms Wave nature of
matter In 1925 Louis de Broglie proposed that
matter has wave properties mv is mass x
velocity momentum Examples what is the
wavelength of an electron with velocity 5x106
m/s? What is the wavelength of a baseball
(0.1415 kg) with velocity 1500 m/s? In 1927,
Davisson and Germer showed that high speed
electrons are diffracted by crystals just like
x-rays The electron microscope is a application
of the wave nature of high speed electrons used
to image matter with great magnification.
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• Electron Structure of Atoms
• Heisenberg Uncertainty Principle states that it
  is impossible to know exactly both the position
  and momentum of an object.
• The uncertainty principle implies a probabilistic
  view of nature and has important consequences
  regarding our viewpoint of how the electron
  behaves in the atom.
• If one knows exactly the velocity of the electron
  one cannot know its position
• Velocity refers both to speed - Dx/Dt - and
  direction of travel
• Schrödingers Wave Mechanics views the electron
  as a standing wave inside an atom
• There are two important results from this picture
  of how the electron behaves in the atom
• Wave mechanics gives the energies of the electron
  waves
• Wave mechanics gives the three dimensional shapes
  of the electron waves in a probability density
  picture.

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• Electron Structure of Atoms
• The results of wave mechanics are expressed in
  the form of a wave function, Y. Y characterizes
  the electron as a matter wave
• The behavior of the electron in an atom is best
  described as a standing wave where only certain
  wave functions are possible
• Each wave function corresponds to an allowed
  energy value for the electron
• A natural consequence of the wave mechanics is
  the energy of an electron is quantized
• Y2 gives information on the probability density
  - the probability of finding the electron within
  a given region of space
• This is often referred to as the electron density
  in a given region of space
• Each of the Ys are called orbitals
• Each orbital is described in terms of 3 quantum
  numbers

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• Electronic Structure of Atoms
• Quantum numbers
• n is called the principal quantum number and has
  integer value 1, 2, 3,
• The greater n, the greater the average distance
  or most probable distance for finding the
  electron wave from the nucleus.
• The energy of an electron with a particular n
  value is the same as calculated from the Bohr
  model En -Rhc/n2
• Each n value represents an electron shell. A
  shell may contain more than 1 e.
• l is called the angular momentum or azimuthal
  quantum number and has integer values of
• 0, 1, 2, , n-1.
• The value of this quantum number is associated
  with the shape of the orbital
• lower case letters are applied to these quantum
  numbers
• 0s 1p 2d 3f 4g
• ml is called the magnetic quantum number and it
  describes the orientation of the orbital in
  space and has values
• - l , - l 1, , 0, 1, 2, , l

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• Electron Structure of Atoms
• Quantum Numbers and Orbitals
• A shell is the collection of orbitals with the
  same n value
• A subshell is the collection of orbitals having
  the same n and l value
• The restriction of the values of the quantum
  numbers indicates how many orbitals are in each
  shell or subshell.
• Each shell with a value of n consists of n
  subshells
• There are n values of l for n1, there is only
  one value of l 0 for n2 there are 2 values for
  l0,1 for n3, there are 3 values of l0,1,2.
• Each subshell has 2 l1 orbitals corresponding to
  the 2 l1 values of ml
• An s subshell (l 0) has one orbital there is
  only one value for ml .
• A p subshell (l 1) has 3 orbitals there are 3
  values for ml .
• There are n2 orbitals in a shell. This is
  important in explaining the organization of the
  periodic table into rows of various lengths.

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• Electronic Structure of Atoms
• H Atom Orbital shapes see Kotz Treichel, p
  319-323.
• Three Dimensional Shapes of Orbitals
• s oritals are spherically symmetric
• As n gets larger, the electron probability
  increases at larger distances from the nucleus.
• There are n- l -1 nodes for s orbitals these are
  radial nodes.
• p orbitals have two lobes separated by a planar
  node
• There are n- l -1 radial nodes and l 1 planar
  nodes
• d orbitals have four lobes separated by two
  planar nodes
• There are n- l -1 radial nodes and l 2 nodal
  planes
• Often a contour representation is more than
  adequate to show the shape of an orbital
• This shows an outer boundary inside which is
  found the major probability of finding the
  electron

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Boundary surface diagrams for electron densities
of 1s, 2s, 3s, 2p, 3p, and 3d orbitals. Note s
orbitals have no nodal planes, p orbitals have 1
nodal plane and d orbitals have 2 nodal planes
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Nodal planes for p and d orbitals
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Plots of y2 vs. distance from the nucleus for 1s,
2s, and 3s orbitals of the H atom. Points where
y2 0 define the radii of spherical nodes
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Plot of Y vs. distance from the nucleus of a 2p
orbital for an H atom along the axis of maximum
electron density.
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• Electronic Structure of Atoms
• Magnetism is a phenomenon associated with the
  motion of electric charge in matter
• It is most often associated with the interaction
  of compass needles with the earths magnetic
  field or the attraction of iron containing
  objects by bar magnets
• If electric charge moves in matter, the matter
  will have magnet properties
• Most matter is diamagnetic and is repelled by a
  magnet
• Some substances are attracted to a magnet and are
  paramagnetic or ferromagnetic
• Paramagnetism and ferromagnetism result from a
  property of the electron called electron spin

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• Electronic Structure of Atoms
• Electron Spin
• The electron behaves like a spinning charge and
  has an associated magnetic moment that causes
  it to act like a bar magnet
• Electron spin is quantized and has quantum number
  ms 1 or -1
• An atom like H with one electron is
  paramagnetic, whereas He is diamagnetic
• It appears that the one electron in Hs 1s
  orbital confers the paramagnetism
• The second electron in Hes 1s orbital must be
  of opposite spin and the net result is a
  cancellation of the magnetism of each electron
• The electrons are said to be paired or spin paired

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• Electronic Structure of Atoms
• The Pauli Exclusion Principle states that no two
  electrons in an atom may have the same values
  for all four quantum numbers.
• The n, l and ml values define the orbitals in
  an atoms and since there are only two values for
  ms, each orbital can have only 2 electrons in it.
• Orbital box diagrams make use of a box
  representing each orbital
• Electrons are represented as either an
  up-pointing arrow (ms ) or down-pointing
  arrow (ms - )
• For H atom

N1, 0, ml0, ms
1s or
N1, 0, ml0, ms -
1s
N1, 0, ml0, ms

• For He atom

N1, 0, ml0, ms -
1s
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Number of electrons accommodated in by shell and
subshell with n 1 to 6