Electronic Structure of Atoms

1
Electronic Structure of Atoms
2
Daltons Atomic Model

• In 1804 Daltons Postulates described the
  existence of small indivisible particles called
  atoms that make up all matter.
• There are no electrons, protons, or neutrons in
  his atomic model.

3
Thomsons Cathode Ray Tube

• J. J. Thomson experimented with cathode ray
  tubes.
• Glass tubes are partially filled with gas.
• A high voltage produces a cathode ray in the tube
  (originates from negative cathode).
• Cathode rays cause certain materials to
  fluoresce.

4
(No Transcript)
5
1897 Cathode Ray Tube Experiment

• Rays are deflected by electric or magnetic
  fields.
• Ray travels in straight line in absence of
  electric or magnetic fields.
• Ray bends away from negative plate, towards
  positive plate.
• Metal plate exposed to rays gets a negative
  charge.
• Ray behavior stays the same regardless of cathode
  material.
• What did Thomson conclude from his experiment?

6
Thomsons Conclusion

• Cathode rays are streams of negatively charged
  particles with mass.
• Discovery of the electron!
• The ratio of an electrons charge to mass is 1.76
  x 108C/g.
• Thomson describes his Plum Pudding atomic model.

7
Millikans 1909 Oil Drop Experiment

• Millikan found the charge on an electron.
• Then using Thomsons charge-to-mass ratio, he
  found the electron mass to be 9 .1 x 10-28g.

8
Radioactivity

• Radioactivity spontaneous emission of
  high-energy radiation. (Henri Becquerel, Pierre
  Marie Curie, Ernest Rutherford)
• Three types of radiation
• Alpha (?) rays particles with 2 charge
• Beta (?) rays particles with 1- charge
• Gamma (?) rays no particles, no charge,
  high-energy radiation similar to X-rays.

9
Rutherfords 1910 Gold Foil Experiment

• Disproved Thomsons Plum Pudding model.
• Passed a beam of alpha particles through a piece
  of gold foil to a fluorescent screen.
• Most alpha particles passed directly through
  foil.
• A few particles deflected at large angles.

10
(No Transcript)
11
Rutherfords Conclusions

• Most of the atom must be empty space.
• There must be a small, dense region of positive
  charge.
• Rutherford discovered the nucleus!

12
Rutherfords New Atomic Model

• Rutherford discovers protons in 1919.
• New atomic model disproves Thomsons model.
• Chadwick discovers neutrons in 1932.

Daltons model
Thomsons Model
Rutherfords Model
13
The Wave Nature of Light

• Electromagnetic radiation (radiant energy)
  carries energy through space.
• All electromagnetic radiation travels through a
  vacuum at 3.00 x 108 m/s (speed of light).
• Wave characteristics of EM radiation are due to
  the periodic oscillations of the intensities of
  electronic and magnetic forces.

14
Parts of a Light Wave

• Wavelength (?) distance between two wave peaks
  (m)
• Frequency (?) number of wave cycles per unit of
  time. Units of Hertz (Hz) or reciprocal seconds
  (s-1).
• Amplitude half the distance from the wave peak
  to the trough.

15
What Is The Relationship Between Wavelength and
Frequency?
c ??
Where c speed of light 3.00 x
108 m/s ? wavelength (m)
? frequency (s-1)

Note ? nd ? are inversely proportional. As
wavelength gets shorter, the frequency gets
higher as wavelength gets longer, the frequency
gets lower.
16
Calculations With Wavelength and Frequency

• What is the wavelength of radiation with a
  frequency of 7.32 x 1019 s-1?
• 4.10 x 10-12 m
• What is the frequency of radiation having a
  wavelength of 754 nm?
• 3.98 x 1014 s-1

17
(No Transcript)
18
(No Transcript)
19
Phenomena Showing Interaction Between EM
Radiation and Atoms

• Black-body Radiation the emission of light from
  hot objects (heated metals)
• Photoelectric Effect the emission of electrons
  from metal surfaces on which light shines
• Emission Spectra the emission of light from
  electronically excited gas atoms

20
Planck and Black-body Radiation

• Max Planck studied black-body radiation to
  understand relationship between temperature and
  EM radiation.
• He assumed that energy can be emitted or absorbed
  by atoms only in discrete chunks of some
  minimum size.
• Quantum (fixed amount) is the smallest quantity
  of energy that can be absorbed or emitted as EM
  radiation.

21
Plancks Equation

• E h?

• Where
• E energy of a single quantum (J)
• h Plancks constant
• (6.626 x 10-34
  J-s)
• ? frequency (s-1)

22
Using the Energy Equation

• Calculate the energy of light with a frequency of
  6.00ee14 Hz.
• 3.98 x 10-19 J
• Calculate the wavelength of light having an
  energy of 2.54 x 10-20 J.
• 7.83 x 10-6 m

23
Plancks Quantum Theory

• Energy is always absorbed or emitted in whole
  number multiples of hv (hv, 2hv, 3hv, etc.)
• Allowed energies are quantized (restricted to
  certain values).
• Energy changes seem continuous in everyday life
  because the gain or loss of a single quantum goes
  unnoticed in large objects.
• Planck was awarded Nobel Prize in physics for
  quantum theory in 1918.

24
Albert Einstein and the Photoelectric Effect

• Albert Einstein discovered the photoelectric
  effect in 1905. For each metal, there is a
  minimum frequency of light below which no
  electrons are emitted from the metals surface.

There is a threshold energy!

• Einstein earned the Nobel Prize in
  physics for the photoelectric effect in 1921.

25
Einstein and Photons

• Radiant energy striking a metal surface is a
  stream of tiny energy packets called photons.
• Photons behave like particles.
• Each photon must have an energy proportional to
  the frequency of the light in which it travels.

Ephoton h? or Ephoton hc/?
Radiant energy is quantized!
26
How Does Einstein Explain the Photoelectric
Effect?

• When a photon strikes a metal, it may transfer
  its energy to an electron.
• An electron needs a certain amount of energy to
  hold it in the metal.
• If the photon has enough energy to meet the
  electrons energy requirement, the electron is
  emitted from the metal.
• Excess energy is used as kinetic energy for the
  electrons.

27
(No Transcript)
28
Radiant Energy and Spectra

• The radiant energy from a laser emits a single
  wavelength (monochromatic) but most common
  radiation sources such as light bulbs and stars
  emit many different wavelengths.

• A spectrum is produced when
  polychromatic radiation is separated into its
  different wavelengths.

A spectrum producing light of all colors is
called a continuous spectrum.
29
(No Transcript)
30
Line Spectra

• Not all radiation sources produce a continuous
  spectrum.
• When gases are placed in a tube under reduced
  pressure with high voltage, different colors of
  light are emitted.

• When light from such tubes are passed through a
  prism, only lines of a few wavelengths are seen.

• The colored lines are separated by black
  regions which correspond to absent wavelengths.

• These spectra are called line spectra.

31
(No Transcript)
32
Hydrogens Spectrum

• There are three groups of lines in hydrogens
  simple spectrum the Lyman series (UV), the
  Paschen series (IR) and the Balmer series
  (visible).
• Balmer made an equation (Rydberg Equation) to fit
  the hydrogen spectrum in the visible range

1/? RH (1/n21) - (1/n22)

• Where ? spectral wavelength
• n positive integers with n2 gt n1
  
• RH (Rydberg constant) 1.096776 x
  107m-1

33
Bohrs Atomic Model Based On Spectral Lines

• Here is Bohrs model of the hydrogen atom with
  electron movement corresponding to the spectral
  lines observed in the Lyman, Paschen, and Balmer
  series.

34
Bell Work

• Calculate the energy of a photon with a frequency
  of 2.72x1013 1/s.
• What wavelength of radiation has photons of
  energy 7.84x10-18 J?
• In what portion of the electron magnetic spectrum
  would this radiation be found?

1.80x10-20 J
2.53x10-8 m
UV
35
(No Transcript)
36
Niels Bohrs Atomic Model

• Bohr based his atomic model on the hydrogen atom
  with only one electron.
• He assumed that the electron moves in a circular
  orbit around the nucleus.
• According to classical physics, the electron
  should lose energy as it orbits and spiral into
  the nucleus.

• Since the electron does not spiral into the
  nucleus, the old laws of physics are
  inadequate to describe the atom.

37
Niels Bohrs Atomic Model
38
Bohrs Three Postulates

1. Only orbits of certain radii with certain
   definite energies are permitted for electrons in
   an atom.
2. An electron in a permitted orbit has a specific
   energy and is in an allowed energy state. It
   will not radiate energy and spiral into the
   nucleus.
3. Energy is only emitted or absorbed by an electron
   as it changes from one energy state to another.
   Energy is emitted or absorbed as a photon (E
   h?).

39
Bohrs Three Postulates
A
B
40
Energy States of the Hydrogen Atom

• Bohr equation E (-2.18 x 10-18 J) (1/n2)
• Integer n (values 1 to ?) is called the quantum
  number.
• Each n value corresponds to a different orbit.
• The radius of the orbit gets bigger as n
  increases.
• n 1 is closest to the nucleus succeeding ns
  get farther away.
• The spacing between the n levels are uneven the
  greatest spacing occurs between the nucleus and n
  1.
• Successive n levels are scrunched closer
  together.
• Lowest energy state is the ground state a higher
  energy state is an excited state.

41
(No Transcript)
42
Bohrs Equation for Hydrogen Changes in Energy
States

? ?E (-2.18 x 10-18 J) (1/n2f ) - (1/n2i )
Where ni and nf are the principal quantum numbers
of the initial and final states of the atom,
respectively.
Note If ?E is negative, the atom releases
energy. If ?E is positive, the atom
absorbs energy.
43
Bohrs Equation Calculations

• ?E (-2.18 x 10-18 J) (1/n2f ) - (1/n2i )

Calculate the wavelength of radiation detected
when an electron in the hydrogen atom moves from
n 6 to n 2. Is this wavelength visible?
Does the atom release or absorb energy for this
move? Why?
4.10x10-7 m
Yes
Release
44
Bohrs Equation Calculations

• ?E (-2.18 x 10-18 J) (1/n2f ) - (1/n2i )

Calculate the change in energy as an electron
moves from n3 to n1 level. What is its
wavelength? Can we see this wavelength?
?E -1.94x10-18 J
1.03x10-7 m
No
45
Significance of Bohr Model

• Bohrs model works best for hydrogen atom it
  does not work well with mutli-electron atoms.
• Bohrs model treats the electron as merely a
  small particle but it also has wave properties.

• Bohrs model introduces distinct energy levels
  described by quantum numbers.

• Bohrs model says that energy is needed to move
  an electron from one level to another.

• Bohr wins Nobel Prize in physics in 1922.

46
Is Radiation a Particle or a Wave?

• Depending on experiment, radiation has either
  wavelike or particle-like (photon) character.
• Given that wavelengths of radiation have
  particle-like character, can matter (made up of
  particles) have wavelike character?

47
Wave-Particle Duality

• Louis de Broglie theorizes that an electron in
  its movement about the nucleus does have a
  wavelength associated with it.

• De Broglie wins 1929 Nobel Prize in physics for
  wave-particle duality.

48
De Broglie Equation
? h/mv

• Where
• mv momentum
• m mass (kg)
• v velocity (m/s)
• h Plancks constant 6.626 x 10-34 kg m2/s
• Remember that 1 Joule 1 kg m2/s2

49
De Broglie Equation Practice

• What is the wavelength of an electron having a
  mass of 9.11 x 10-28 g and a velocity of 5.97 x
  106 m/s?

1.22x10-16 m
50
De Broglie Equation Practice

• What is the mass of an electron having a
  wavelength of 3.10x10-6 m and a velocity of
  7.01x107 m/s?

m 3.05x10-36 kg
51
Classical Physics and the Electron

• Using classical physics, we can easily calculate
  the position and speed of a ball rolling down a
  ramp at any point.
• Classical physics cannot adequately describe the
  location of an electron with wave properties.
• Physicist Werner Heisenberg concluded that the
  dual nature of matter puts a limitation on how
  precisely we can know both the location and
  momentum of matter with a very small mass.

52
Heisenbergs Equation

• Heisenberg makes an equation relating the
  uncertainty of an electrons position (?x) and
  the uncertainty in its momentum (?mv) to Plancks
  constant

?x ? ?mv ( h/4? )
This equation essentially tells us that if the
mass of an electron is known, its position will
be unknown.
53
Heisenbergs Uncertainty Principle

• It is impossible to know simultaneously both
  the exact momentum of an electron and its exact
  location.

Heisenbergs Uncertainty Principle leads to a new
atomic model in which the energy of an electron
is known but its location is described in terms
of mathematical probabilities.
Heisenberg receives the Nobel Prize in physics
for his uncertainty principle in 1932.
54
Heisenbergs Uncertainty Principle
Heisenberg is out for a drive when he's stopped
by a traffic cop. The cop says, "Do you know how
fast you were going? Heisenberg says, "No, but
I know where I am."
55
Bell Work

1. Calculate the wavelength of radiation detected
   when an electron in the hydrogen atom moves from
   n 3 to n 6.
2. Does the atom release or absorb energy for this
   move? Why?
3. Describe the Duality Principle.
4. Describe Heisenberg's Uncertainty Principle.

• ?E (-2.18 x 10-18 J) (1/n2f ) - (1/n2i )

56
Quantum (Wave) Mechanics

• Erwin Schrödinger uses an equation to incorporate
  the wavelike and particle-like qualities of
  electrons.
• This became the basis for the quantum mechanical
  (wave mechanical) model.
• Schrödinger incorporates series of mathematical
  functions (wave functions) that describe the
  electrons matter wave.
• Schrödingers work deals with probabilities.

57
Quantum (Wave) Mechanics
The electron cloud of an atom can be compared to.
58
Wave Functions

• Wave functions (?) describe a matter wave.
• Probability density (?2) represents the
  probability that an electron will be found at a
  given location.
• ?2 0 denotes a location where there is no
  probability of finding an electron.
• Electron density is a region where there is a
  high probability of finding an electron 90 of
  the time.
• Wave functions are called orbitals.

59
Electron Density and Orbital Shape
60
The s-orbitals

• All s-orbitals are spherical.
• As n increases, the s-orbitals get larger.
• As n increases, the number of nodes increase.
• A node is a region in space where the probability
  of finding an electron is zero.
• At a node, ?2 0
• For an s-orbital, the number of nodes is (n - 1).

61
Relative Sizes of s-orbitals
62
Nodes of s-orbitals
63
p-orbitals

• There are three p-orbitals px, py, and pz.
• The three p-orbitals lie along the x-, y- and z-
  axes of a Cartesian system.
• The orbitals are dumbbell shaped.
• As n increases, the p-orbitals get larger.
• All p-orbitals have a node at the nucleus.

64
Representations of p-orbitals
65
How Do s-orbitals and p-orbitals Fit Together?
66
Orbital Hotel

• Vocab check
• Shell Level
• Subshell Sublevel
• Within a subshell there are orbitals

67
d-orbitals and f-orbitals

• There are five d and seven f-orbitals.
• Three of the d-orbitals lie in a plane bisecting
  the x-, y- and z-axes.
• Two of the d-orbitals lie in a plane aligned
  along the x-, y- and z-axes.
• Four of the d-orbitals have four lobes each
  (cloverleaf).
• One d-orbital has two lobes and a collar (double
  baby binky).

68
(No Transcript)
69
f-orbitals
70
Orbitals and Quantum Numbers

• Any electron has a series of 4 quantum numbers
• Principal Quantum Number (n). Same as Bohrs n.
  Designates particular energy level and controls
  size of orbital. The higher the number for n, the
  higher the associated energy. Uses n 1, 2, 3,
• Orbital Angular Momentum Quantum Number
  (Azimuthal Quantum Number) (l). Controls shape of
  orbital. Depends on the value of n. Uses
  l 0 (s-orbital) l 1 (p-orbital) l 2
  (d-orbital) l 3 (f-orbital).

71
Orbitals and Quantum Numbers Continued

• 3. Magnetic Quantum Number (ml). Designates a
  specific orbital, gives 3D orientation of each
  orbital. Has integral values between -l and l.
  For instance, if l 2, ml can be -2, -1, 0,
  1, or 2.
• 4. Spin Magnetic Quantum Number (ms). Indicates
  spin of electron in the orbital. Uses 1/2.

72
Orbitals and Quantum Numbers
73
Orbitals and Their Energies

• In a many-electron atom, the energy increases in
  this order slt p lt d lt f
• The exact spacing of energy levels and energy
  differ from one atom to another.
• All orbitals of a given subshell have the same
  energy and are called degenerate.

74
Bell Work

1. All orbitals of a given subshell have the same
   energy and are called __________.
2. The principle quantum number designates
   ___________.
3. The azimuthal number designates ___________.
4. The magnetic quantum number designates
   ___________.
5. The spin magnetic quantum number designates
   ___________.

75
Electron Configurations

• Electron configurations tell us which orbitals
  are assigned for each electron in an atom.
• There are three rules to guide configurations.
• Pauli Exclusion Principle
• Aufbau Diagram
• Hunds Rule

76
Pauli Principle and Electron Spin

• Line spectra of many electron atoms show each
  line as a closely spaced pair of lines.
• A beam of atoms was passed through a slit and
  into a magnetic field and the atoms were then
  detected.
• Two spots were found one with the electrons
  spinning in one direction and one with the
  electrons spinning in the opposite direction.

77
Electron Spin
One electron spins clockwise, the other
counter-clockwise.
78
Paulis Exclusion Principle

• At most, there can be two electrons in a given
  orbital and they must have opposite spin.
• One spins clockwise, the other counter-clockwise.
  
• In block diagrams, we show this as ? and ?

79
Aufbau Diagram

• Using an Aufbau Diagram, electrons fill in the
  following order from bottom to top (lower energy
  to higher energy)
• 7s 7p
• 6s 6p 6d 6f
• 5s 5p 5d 5f
• 4s 4p 4d 4f
• 3s 3p 3d
• 2s 2p
• 1s

80
Aufbau Diagram

1. Write the electron configuration for nitrogen.
2. Write the electron configuration for iron.

81
Aufbau Diagram
82
Energy and Atomic Orbitals
Remember, as n increases, energy also increases.
Orbitals of increasing energy begin to overlap
because the space between the energy levels
decreases with increasing n. Recall that the 4s
orbital fills before the 3d orbital.
83
Aufbau Diagram

• Write the electron configuration for lead.

84
Hunds Rule

• Hunds Rule For degenerate orbitals, the lowest
  energy is obtained when the number of electrons
  with the same spin is maximized.
• Therefore, we fill each degenerate orbital with a
  single electron spinning in one direction before
  we add each orbitals second electron spinning in
  the opposite direction.

85
Hunds Rule

• Practice Hunds Rule by writing electron
  configurations and box diagrams for the following
  elements
• Nitrogen
• Sulfur
• Cobalt

86
Reading Electron Configurations from the Periodic
Table
87
Coloring Time!
88
Condensed Electron Configurations

• Neon completes the 2p subshell.
• Sodium marks the beginning of a new row.
• So, we write the condensed electron configuration
  for sodium as
• Na Ne 3s1
• Ne represents the electron configuration of
  neon.

89
Core and Valence Electrons

• Core electrons Electrons in closed shells.
  Usually in the brackets in condensed e-
  configs.
• Valence electrons Electrons in the outermost
  principal quantum level and unfilled lower
  quantum numbers of an atom. (Electrons in d
  sublevel are often not counted as valence
  electrons.) Valence electrons participate in
  chemical rxns and are responsible for some
  physical properties. Write electron
  configurations in order of increasing n to see
  valence electrons more clearly.
• Ar3d84s2 Core Valence
• Ar3d104s24p1 Core Valence

90
Unusual Electron Configurations

• Elements Ce - Lu have the 4f orbitals filled and
  are called lanthanides or rare earth elements.
• Elements Th - Lr have the 5f orbitals filled and
  are called actinides. Most actinides are not
  found in nature.
• The first three lanthanides and actinides have
  unusual electron configurations.
• La Xe6s25d1 Ce Xe6s25d14f1 Pr
  Xe6s24f3

91
Anomalous Electron Configurations

• Some common transition elements do not follow the
  usual pattern for electron filling.

Element Actual Expected
Cr Ar3d54s1 Ar3d44s2
Cu Ar3d104s1 Ar3d94s2
Ag Kr4d105s1 Kr4d95s2
92
Bell Work
93
Electronic Structure of AtomsHoopla Game

• Blue Cloodle (Without talking or using numbers
  or letters, try to get the other players to guess
  what youre drawing.)
• Yellow Tongue-Tied (Use words other than listed
  on the slip to get the other players to guess the
  topic.)
• Green Soundstage (Act out your topic using
  appropriate gestures and sound effects.)
• Red Tweener (Use clues like Its bigger than
  ______ but smaller than ________. to describe
  your topic.)
• Purple Wild (Your choice!)