Quantum Theory and the Electronic Structure of Atoms

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Quantum Theory and the Electronic Structure of
Atoms
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Properties of Waves
Wavelength (l) is the distance between identical
points on successive waves. Frequency (n) is the
number of waves that pass through a particular
point in 1 second (Hz 1 cycle/s). Speed (u) of
the wave l x n Amplitude is the vertical
distance from the midline of a wave to the peak
or trough.
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l x n c
l c/n
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Bohrs Model of the Atom (1913)

• e- can only have specific (quantized) energy
  values
• light is emitted as e- moves from one energy
  level to a lower energy level

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QUANTUM NUMBERS

• The shape, size, and energy of each orbital is a
  function of 3 quantum numbers which describe the
  location of an electron within an atom or ion
• n (principal) ---gt energy level
• l (orbital) ---gt shape of orbital
• ml (magnetic) ---gt designates a particular
  suborbital
• The fourth quantum number is not derived from the
  wave function
• s (spin) ---gt spin of the electron
  (clockwise or counterclockwise ½ or ½)

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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
principal quantum number n
n 1, 2, 3, 4, .
distance of e- from the nucleus
n3
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Types of Orbitals (l)
s orbital
p orbital
d orbital
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p Orbitals

• this is a p sublevel with 3 orbitals
• These are called x, y, and z

3py orbital
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p Orbitals

• The three p orbitals lie 90o apart in space

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f Orbitals

• For l 3, f sublevel with 7 orbitals

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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
magnetic quantum number ml
for a given value of l ml -l, ., 0, . l
if l 1 (p orbital), ml -1, 0, or 1 if l 2
(d orbital), ml -2, -1, 0, 1, or 2
orientation of the orbital in space
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ml -1
ml 0
ml 1
ml -2
ml -1
ml 0
ml 1
ml 2
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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
spin quantum number ms
ms ½ or -½
ms -½
ms ½
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Energy of orbitals in a single electron atom
Energy only depends on principal quantum number n
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Energy of orbitals in a multi-electron atom
Energy depends on n and l
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Fill up electrons in lowest energy orbitals
(Aufbau principle)
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The most stable arrangement of electrons in
subshells is the one with the greatest number of
parallel spins (Hunds rule).
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Order of orbitals (filling) in multi-electron atom
1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt
5p lt 6s
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Why are d and f orbitals always in lower energy
levels?

• d and f orbitals require LARGE amounts of energy
• Its better (lower in energy) to skip a sublevel
  that requires a large amount of energy (d and f
  orbtials) for one in a higher level but lower
  energy
• This is the reason for the diagonal rule! BE SURE
  TO FOLLOW THE ARROWS IN ORDER!

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Electron configuration is how the electrons are
distributed among the various atomic orbitals in
an atom.
1s1
Orbital diagram
H
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What is the electron configuration of Mg?
Mg
What are the possible quantum numbers for the
last (outermost) electron in Cl?
Cl
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Outermost subshell being filled with electrons
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Paramagnetic
Diamagnetic
unpaired electrons
all electrons paired
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Exceptions to the Aufbau Principle

• Remember d and f orbitals require LARGE amounts
  of energy
• If we cant fill these sublevels, then the next
  best thing is to be HALF full (one electron in
  each orbital in the sublevel)
• There are many exceptions, but the most common
  ones are
• d4 and d9
• For the purposes of this class, we are going to
  assume that ALL atoms (or ions) that end in d4 or
  d9 are exceptions to the rule. This may or may
  not be true, it just depends on the atom.

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Exceptions to the Aufbau Principle

• d4 is one electron short of being HALF full
• In order to become more stable (require less
  energy), one of the closest s electrons will
  actually go into the d, making it d5 instead of
  d4.
• For example Cr would be Ar 4s2 3d4, but since
  this ends exactly with a d4 it is an exception to
  the rule. Thus, Cr should be Ar 4s1 3d5.
• Procedure Find the closest s orbital. Steal one
  electron from it, and add it to the d.

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Try These!

• Write the shorthand notation for
• Cu
• Ag
• Cu

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Keep an Eye On Those Ions!

• Electrons are lost or gained like they always are
  with ions negative ions have gained electrons,
  positive ions have lost electrons
• The electrons that are lost or gained should be
  added/removed from the highest energy level (not
  the highest orbital in energy!)

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Keep an Eye On Those Ions!

• Tin
• Atom
• Sn2 ion
• Sn4 ion
• Note that the electrons typically came out of the
  highest energy level, not the highest energy
  orbital!