Electronic Structure of Atoms

1
Electronic Structure of Atoms

• Chapter 7

2
The Dilemma of the Noncollapsing atom
3
Electromagnetic Radiation

• To understand the electronic structure of atoms,
  one must understand the nature of electromagnetic
  radiation.
• Electromagnetic radiation consists of
  electromagnetic waves are produced by the motion
  of electrically charged particles.
• They travel through empty space as well as
  through air and other substances.

4
Waves

• Electomagnetic radiation is described in terms of
  the waves.
• The distance between corresponding points on
  adjacent waves is the wavelength (?).

5
Waves

• The number of waves passing a given point per
  unit of time is the frequency (?).
• For waves traveling at the same velocity, the
  longer the wavelength, the smaller the frequency.

6
Electromagnetic Radiation

• All electromagnetic radiation travels at the same
  velocity the speed of light (c), 3.00 ? 108
  m/s.
• Therefore,
• c ??

7
Example 1

• A certain shade of green light has a wavelength
  of 550 nm. What is the frequency of this light?

8
Example 2

• An FM radio station broadcasts electromagnetic
  radition at a frequency of 104.3 MHz
  (megahertz). What is the wavelength of this
  radiation? (1 Hz 1 s-1)

9
The Nature of Energy

• The wave nature of light does not explain how an
  object can glow when its temperature increases.
• Max Planck explained it by assuming that energy
  comes in packets called quanta.

10
The Nature of Energy

• Einstein used this assumption to explain the
  photoelectric effect.
• He concluded that energy is proportional to
  frequency
• E h?
• where h is Plancks constant, 6.63 ? 10-34 J-s.

11
The Nature of Energy

• If one knows the wavelength of light, one can
  calculate the energy in one photon, or packet, of
  that light
• c ??
• E h?

12
Example 3

• Calculate the energy in joules of a photon of red
  light having a frequency of 4.0 x 1014 s-1

13
The Nature of Energy

• Another mystery involved the emission spectra
  observed from energy emitted by atoms and
  molecules.

14
The Nature of Energy

• One does not observe a continuous spectrum, as
  one gets from a white light source.
• Only a line spectrum of discrete wavelengths is
  observed.

15
The Nature of Energy

• Niels Bohr adopted Plancks assumption and
  explained these phenomena in this way
• Electrons in an atom can only occupy certain
  orbits (corresponding to certain energies).

16
The Nature of Energy

• Electrons in permitted orbits have specific,
  allowed energies these energies will not be
  radiated from the atom.
• Energy is only absorbed or emitted in such a way
  as to move an electron from one allowed energy
  state to another the energy is defined by
• E h?

17
The Nature of Energy

• The energy absorbed or emitted from the process
  of electron promotion or demotion can be
  calculated by the equation

where RH is the Rydberg constant, 2.18 ? 10-18 J,
and ni and nf are the initial and final energy
levels of the electron.
18
Bohrs Equation

• En -1312/n2
• E is measured in kilojoules per mole of electrons
  
• DE Efinal - Einitial

19
Bohr Atom

• Lyman n 1
• Ultraviolet
• Balmer n 2
• Visible
• Paschen n 3
• Infrared

20
Example 4

• Calculate the wavelength of light emitted when
  each of the following transitions occur in the
  hydrogen atom.
• n 3 ? n 2
• n 4 ? n 1

21
The Wave Nature of Matter

• Louis de Broglie proposed that if light can have
  material properties, matter should exhibit wave
  properties.
• He demonstrated that the relationship between
  mass and wavelength was

22
Example 5

• Calculate the deBroglie wavelength of an electron
  moving with a velocity that is 1.0 x 10-3 times
  the speed of light.

23
So

• If a subatomic particle can exhibit the
  properties of a wave, is it possible to say
  precisely just where the particle is located?

24
The Uncertainty Principle

• Heisenberg showed that the more precisely the
  momentum of a particle is known, the less
  precisely is its position known
• In many cases, our uncertainty of the whereabouts
  of an electron is greater than the size of the
  atom itself!

25
The Quantum-Mechanical Description of the Atom

• De Broglies hypothesis and Heisenbergs
  uncertainty principle set the stage for a new and
  more broadly applicable theory of atomic
  structure.
• In this new approach, any attempt to define
  precisely the instantaneous location and momentum
  of the electron is abandoned.

26
Wave Nature of the Electron

• The wave nature of the electron is recognized,
  and its behavior is described in terms
  appropriate to waves.

27
Quantum Mechanics

• Erwin Schrödinger developed a mathematical
  treatment into which both the wave and particle
  nature of matter could be incorporated.
• It is known as quantum mechanics.

28
Quantum Mechanics

• The wave equation is designated with a lower case
  Greek psi (?).
• The square of the wave equation, ?2, gives a
  probability density map of where an electron has
  a certain statistical likelihood of being at any
  given instant in time.

29
Quantum Numbers

• Solving the wave equation gives a set of wave
  functions, or orbitals, and their corresponding
  energies.
• Each orbital describes a spatial distribution of
  electron density.
• An orbital is described by a set of three quantum
  numbers.

30
Principal Quantum Number, n

• The principal quantum number, n, describes the
  energy level on which the orbital resides.
• The values of n are integers 0.

31
Azimuthal Quantum Number, l

• This quantum number defines the shape of the
  orbital.
• Allowed values of l are integers ranging from 0
  to n - 1.
• We use letter designations to communicate the
  different values of l and, therefore, the shapes
  and types of orbitals.

32
Azimuthal Quantum Number, l
Value of l 0 1 2 3
Type of orbital s p d f
33
Magnetic Quantum Number, ml

• Describes the three-dimensional orientation of
  the orbital.
• Values are integers ranging from -l to l
• -l ml l.
• Therefore, on any given energy level, there can
  be up to 1 s orbital, 3 p orbitals, 5 d orbitals,
  7 f orbitals, etc.

34
Magnetic Quantum Number, ml

• Orbitals with the same value of n form a shell.
• Different orbital types within a shell are
  subshells.

35
s Orbitals

• Value of l 0.
• Spherical in shape.
• Radius of sphere increases with increasing value
  of n.

36
s Orbitals

• Observing a graph of probabilities of finding an
  electron versus distance from the nucleus, we see
  that s orbitals possess n-1 nodes, or regions
  where there is 0 probability of finding an
  electron.

37
p Orbitals

• Value of l 1.
• Have two lobes with a node between them.

38
d Orbitals

• Value of l is 2.
• Four of the five orbitals have 4 lobes the other
  resembles a p orbital with a doughnut around the
  center.

39
F-Orbitals

• Value of l is 3

40
Energies of Orbitals

• For a one-electron hydrogen atom, orbitals on the
  same energy level have the same energy.
• That is, they are degenerate.

41
Energies of Orbitals

• As the number of electrons increases, though, so
  does the repulsion between them.
• Therefore, in many-electron atoms, orbitals on
  the same energy level are no longer degenerate
  (same energy).

42
Spin Quantum Number, ms

• In the 1920s, it was discovered that two
  electrons in the same orbital do not have exactly
  the same energy.
• The spin of an electron describes its magnetic
  field, which affects its energy.

43
Spin Quantum Number, ms

• This led to a fourth quantum number, the spin
  quantum number, ms.
• The spin quantum number has only 2 allowed
  values 1/2 and -1/2.

44
Pauli Exclusion Principle

• No two electrons in the same atom can have
  exactly the same energy.
• No two electrons in the same atom can have
  identical sets of quantum numbers.

45
Permissible Quantum States
46
Electron Configurations

• Distribution of all electrons in an atom.
• Consist of
• Number denoting the energy level.
• Letter denoting the type of orbital.
• Superscript denoting the number of electrons in
  those orbitals.

47
Guidelines for Order of Filling

• Three main guidelines govern the filling atomic
  orbitals within the energy levels. They are the
  Aufbau principle, the Pauli exclusion principle,
  and Hunds rule.

48
The Aufbau Principle

• Electrons enter orbitals of lowest energy first.
  The various orbitals within a sublevel of a
  principal energy level are always of equal
  energy. Yet the range of energy within a
  principal energy level can overlap the energy
  levels of a nearby principal energy level. As a
  result, the filling of orbitals does not follow a
  simple pattern beyond the second energy level.
  For example, the 4s orbital is lower in energy
  than the 3d.

49
The Pauli Exclusion Principle

• An atomic orbital may only hold two electrons. To
  occupy the same orbital, two electrons must have
  opposite spin.

50
Hunds Rule

• When electrons occupy orbitals of equal energy,
  orbitals must be singly occupied with electrons
  having parallel spins. Second electrons are then
  added to each orbital so that the two electrons
  in each orbital have opposite spins.

51
Diagonal Rule for Build-up Rule

• The periodic table can also be used to determine
  the electron configuration of an element.

52
Periodic Table and Electron Configurations

• Build-up order given by position on periodic
  table row by row.
• Elements in same column will have the same outer
  shell electron configuration.

53
Periodic Table

• Different blocks on the periodic table, then
  correspond to different types of orbitals.

54
Some Anomalies

• Some irregularities occur when there are enough
  electrons to half-fill s and d orbitals on a
  given row.

55
Some Anomalies

• For instance, the electron configuration for
  copper is
• Ar 4s1 3d5
• rather than the expected
• Ar 4s2 3d4.

56
Some Anomalies

• This occurs because the 4s and 3d orbitals are
  very close in energy.
• These anomalies occur in f-block atoms, as well.

57
Noble Gas Abbreviations

• The full electron configuration is referred to as
  the spectroscopic configuration. There is also a
  short hand method of indicating the configuration
  using the noble gases.

58
Example 6 Electron Configurations

• Spectroscopic
• Nobel Gas Abbreviation

59
Orbital Diagrams

• Each box represents one orbital.
• Half-arrows represent the electrons.
• The direction of the arrow represents the spin of
  the electron.

60
Hunds Rule

• For degenerate orbitals, the lowest energy is
  attained when the number of electrons with the
  same spin is maximized.

61
Example 7 Orbital Diagram
62
Electron Configuration of Ions

• Main group metals form cations by losing e? main
  group nonmetals become anions by gaining e?.
• Both adopt inert gas electron configuration.

63
Alkali Metals

• The alkali metals will lose a single electron to
  become M. The electron configuration is He,
  Ne, Ar, Kr, and Xe for Li, Na, K, Rb
  respectively.

64
Example 8 Halogen Ions
65
Transition Metal Ions

• Transition metals lose electrons to form positive
  ions from both the outer s sublevel as well as
  the d sublevel that was last filled.

66
Example 9 Transition Metal Ions
67
Post Transition Metals

• Post transition metals lose electrons from both
  the outer p and the outer s sublevel.

68
Example 10 Post-transition Metal Ions
69
Isoelectronic Substances

• Substances with the same number of electrons are
  isoelectronic ions.
• Isoelectronic ions (or molecules) ions (or
  molecules) with the same number of valence
  electrons.

70
Isoelectronic Substances

• Isoelectronic substances P3?, S2?, Cl?, Ar, K,
  Ca2.

71
Excited States

• The electron configuration of an element in an
  excited state will have an electron in a
  high-energy state
• Ar4s13d94p1 is an excited-state electron
  configuration for Cu.