1. Chapter 7 Atomic Structure and Periodicity

2. Topics Electromagnetic radiation The nature of matter
The atomic spectrum of hydrogen
The Bohr model
The quantum mechanical model of the atom
Quantum numbers
Orbital shapes and energies
Electron spin and Pauli exclusion principle
Polyelectronic atoms
The history of the periodic Table
The aufbau principle and Periodic Table
Periodic trends in atomic properties

3. The Wave-like Electron
The electron propagates through space as an energy wave. To understand the atom, one must understand the behavior of electromagnetic waves.
Louis deBroglie

4. 7.1 Electromagnetic Radiation
form of energy that acts as a wave as it travels
includes: X rays, Ultraviolet, visible light, infrared light, microwaves, and radio waves
travel at a speed of x 108 m/s in a vacuum
All forms of EMR are combined to form electromagnetic spectrum

5. Low Frequency High Frequency Short Wavelength Long Wavelength
Low Energy
High Energy
Electromagnetic Spectrum
The whole range of frequencies
is called “Spectrum”
Radiowaves
Microwaves
Infrared .
Ultra-violet
X-Rays
Gamma Rays
Low Frequency
High Frequency
Short Wavelength
Long Wavelength
Visible Light
R O Y G B I V”

6. Parts of a wave
Crest
Wavelength
Amplitude
Origin
Trough

7. Wavelength λ = Greek letter lambda
distance between points on adjacent waves (consicutive peaks or troughs)
Units used are in nm (109nm = 1m)
Frequency
 = Greek letter nu
number of wave cycles that passes a point in a second. 108 cycles/s= 108 s-1
=108 Hertz = 108 Hz
in 1/second (Hertz = Hz)

8. Electromagnetic radiation propagates through space as a wave moving at the speed of light.
Equation:
c = speed of light, a constant (2.998 x 108 m/s)
 (lambda) = wavelength, in meters
 (nu) = frequency, in units of hertz (hz or sec-1)

9. matter energy particles mass position wave massless delocalized
7.2 Nature of Matter
Before 1900, scientists thought that matter and energy were totally different
matter
energy
particles
mass
position
wave
massless
delocalized

10. In 1900
According to the old views, matter could absorb or emit any quantity (frequency) of energy.
Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave.
Max Planck studied the radiation emitted by solid bodies heated to incandescence.
Max Planck postulated that energy can be gained or lost only in whole number multiples of the quantity
h =Planck’s constant= 6.626x10-34 J.s
That is change in energy of a system, E is
n is an integer;  is the frequency of EMR
emitted or absorbed

11. Nature of Matter
Mack’s Planck suggested that an object emits energy in the form of small packets of energy called quanta. That is the energy is quantized
Quantum- the minimum amount of energy that can be gained or lost by an atom (energy in each packet)
Thus energy seems to have particulate properties

12. also showed that energy has mass
Nature of Matter
Einstein proposed that radiation itself is really a stream of particles called photons
Energy of each photon is :
also showed that energy
has mass

13. Nature of Matter
shows that anything with both mass and velocity has a corresponding wavelength

14. Calculate the energy of red light vs. blue light. red light: 700 nm
blue light: 400 nm
red:
blue:
E = 2.85 x J
E = 4.96 x J

15. What is light?  = h/mv (from Louis de Broglie)
Light has certain characteristics of particulate matter
Light is a wave - we can measure its wavelength and it behaves as a wave
If we combine E=mc2 , c=, E = 1/2 mv2 and E = h, then we can get:
 = h/mv (from Louis de Broglie)
called de Broglie’s equation
This equation allows calculation of the wavelength of a particle.

16. Wave-Particle Duality
J.J. Thomson won the Nobel prize for describing the electron as a particle.
His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron.
The electron is a particle!
The electron is an energy wave!

17. 7.3 The Atomic Spectrum of Hydrogen
Main experiments led to the information related to atom:
Thompson discovery of electron
Rutherford discovery of nucleus
Study of emission of light by excited hydrogen atom
When H2 molecules absorb energy, some H-H bonds are broken and excited H-atoms will be produced
The excited H-atoms release energy by emitting light at various wavelengths that is known as emission spectrum of H-atoms

18. Spectroscopic analysis of the visible spectrum
White light
When sunlight is dispersed by rain drops the rainbow is
Produced; that is a continuous spectrum is
produced.
continuous spectrum contains all colors; that is all
wavelengths of the visible light

19. The Continuous Spectrum
The different colors of light correspond to different wavelengths and frequencies
l ~ 650 nm
~ 575 nm
l ~ 500 nm
l ~ 480 nm
l ~ 450 nm

20. Spectroscopic analysis of the hydrogen spectrum…
H receives a high energy
spark
H-H bonds
Are broken and H atoms are excited
Hydrogen emission spectrum is called “line spectrum”

21. Line spectrum
Unique to each element, like fingerprints!
Very useful for identifying elements

22. Significance of the line spectrum of H-atom
Only certain energies are allowed for the electron in the hydrogen atom
That is, the energy of an electron in a hydrogen atom is quantized.
Changes in energy between discrete energy levels in hydrogen will produce only certain wavelengths of emitted light.
The discrete line spectrum of hydrogen shows that only certain energies are possible.
The electron energy levels are quantized. If all energy levels are allowed the spectrum would be continuous

23. 7.4 The Bohr Model Niels Bohr (Danish physicist) 1885-1962
Developed a quantum model
for H atom that explained the emission line spectrum
Electron moves around the nucleus only in certain allowed circular orbits, in which it has a certain amount of energy
The electrons were attracted to the nucleus because of opposite charges.
But electron does not fall in to the nucleus because it is moving around.

24. The Bohr Atom
He didn’t know why but only certain energies were allowed.
He called these allowed energies energy levels.
Putting Energy into the atom moved the electron away from the nucleus.
From ground state to excited state.
When it returns to ground state it gives off light of a certain energy.

25. The Model: Summary
Space around nucleus is divided into spherical (circualr) paths (orbits) each has a number called “Principal Quantum number”
The electron can exist only in one of these orbitals but not in between
Orbits possess fixed size and energy, therefore electron has a definite energy characteristic of its orbit

26. An electron can pass only from one orbit to another
An electron can pass only from one orbit to another. Absorption or emission will occur
Energy of the outermost orbit is zero

27. The Bohr Atom
n = 4
n = 3
n = 2
n = 1

28. Bohr Model
equation can be used twice to find the ∆E when an electron moves energy levels

29. Bohr Model Wavelength of photon released can be calculated by using
E=0 is set at an distance of ∞ away from the nucleus and becomes more negative as the electron comes closer to the nucleus

30. Example 1
Calculate the energy required to move the hydrogen electron from n=1 to n=2. Find the wavelength of radiation that had to be absorbed by the electron.

31. Example 2
Calculate the energy required to remove the electron from the hydrogen atom in its ground state.
Energy was absorbed by the electron so the value of ∆E value is positive.

32. Bohr Model problems: did not work for other atoms
did not explain chemical behavior of atoms

33. Heisenberg’s Uncertainty Principle
According to de Broglie: Electron behaves like a wave
Is it possible to specify the position of a wave at a particular instant?
Energy, wavelength and amplitude can be determined
But exact position is impossible to be determined
The electron cannot be imagined as :
moving particle
In a path of the same radius (well defined orbits)
Thus, location, direction and speed of motion of a particle cannot be determined
Then Bohr Model had to be “Abandoned

34. Heissenberg Uncertainty Principle
“It is impossible to determine both the position and momentum of a subatomic particle (such as the electron) with arbitrarily high accuracy”
The effect of this principle is to convert the laws of physics into statements about relative, instead of absolute, certainties.

35. Heisenberg Uncertainty Principle
we cannot know the exact position and momentum (motion) of the electron
as more is known about position, less is known about momentum
uncertainties are inversely proportional
where
∆x: uncertainty in position
∆m : uncertainty in mometum
minimum uncertainty is h/4

36. 7.5 The Quantum Mechanical Model
Exact position of electron can not be defined
Exact bath of electron about nucleus can not be defined
Werner Heisenberg, Louis de Broglie and Erwin Schrodinger made the approach called “Quantum Mechanics”
They assumed that the electron is a standing wave

37. The Quantum Mechanical Model
Waves are associated with electrons
Information about energies of electrons and their positions are obtained from studying the associated waves
Description of electron is based upon
“ Probability of finding a particle within a given region of space” “ but not on the exact position”

38. Schrödinger Equation Wave equation describing electron as being a wave
The amplitudes (height), , of electron wave at various points of space are calculated
 commonly called “wave function”
 provides information about the allowable energies for an electron in H atom.
 corresponds to a certain energy and describes a region around nucleus “Orbital” where the electron having that energy may be found

39. Orbital: Region around the nucleus where the electron can be expected to be found
The Function 2
2 describes the probability of the position of the electron at a particular point
2  Probability of finding a particle in a given region of space
2  Electric charge density at a given region of space

40. Thus,
The charge can be assumed to be spread out as a charge cloud by rapid motion of electron
The cloud is denser in some regions than others
The probability of finding electron in a given region in space is proportional to the density of the cloud

41. Meaning of Wave Function
the wave function itself does not have concrete meaning
the square of the wave function represents the probability of finding an electron at a certain point
easily represented as probability distribution where the deepness of color indicates the probability

42. Meaning of Wave Function
(a) electron density map
probability of finding an electron is highest at short distances from nucleus
(b) calculated probability of finding an electron at certain distances from nucleus in the 1s orbital

44. 7.6 Quantum Numbers
There are many solutions to Schroedinger’s equation for H atom
Each solution is a wave function called Orbital.
Each orbital can be described with quantum numbers that describe properties of the orbital

45. 4th describes state of electron
Quantum numbers specify the properties of atomic orbitals and of electrons in orbitals
the first three quantum numbers come from the Schrödinger equation and describe:
main energy level
shape
orientation
4th describes state of electron

46. Principal Quantum Number, n
Main energy level occupied by electron. They are called atomic orbitals
regions where there is a high probability of finding an electron.
n is related to the size and energy of the orbital
values are all positive integers >0 (1,2,3,…)
As n increases
size of orbital is larger and electron is less tightly bound to nucleus
The electron spends more time further from nucleus
electron has higher energy
the electron’s average distance from the nucleus increases

47. Principal Quantum Number
Maximum number of electrons that can fit in an energy level:
2n2

48. Angular Momentum Quantum Number: l
It indicates the shape of the orbital
The number of possible shapes (or l values) for an energy level is equal to n
The possible values of l are 0 and all positive integers less than or equal to
n - 1

49. l has integer values from 0 to n-1
l = 0 is called s
l = 1 is called p
l =2 is called d
l =3 is called f
l =4 is called g

50. Magnetic Quantum Number, ml
ml indicates the orientation of the orbital in space relative to the other orbitals in the atom
ml has integer values from + l  - l including 0
each orbital holds maximum of 2 electrons
total number of orbitals is equal to n2 for an energy level
number of possible ml values for a certain subshell is equal to 2l + 1

51. Quantum Numbers for the first four levels of orbitals in the hydrogen atom

52. 7.7 Orbital shapes and Energies
s orbitals: 1: s
spherical
l value of 0

53. Representations of the Hydrogen 1s, 2s, and 3s Orbitals
A. The Electron Probability Distribution
B. The surface contains 90% of the total electron
probability

54. p-orbitals l value = 1 - + - + + - p orbitals: 3 2px, 2py, 2pz
dumbbell-shaped
l value = 1
No 1p orbitals
1st occur at n=2
for n>2, shape is same but size increases - + - + + -

55. d- orbitals l value of 2 - + -
d orbitals: 5: 3dxz, 3dyz, 3dxy, 3dx2-y2, dz2
mostly cloverleaf
l value of 2
1st occur at n=3; no d-orbitals for n=1 or n=2
for n>3, same shape but larger size

56. f-orbitals l value of 3 f orbitals: 7 types various shapes
begin in n=4

57. Other shapes can exist in energy levels as long as they follow the rules
g (l =4) starts in 5 with 9 orbitals
h (l =5) starts in 6 with 11 orbitals, etc
but no known elements have electrons in them at ground state
Remember that all orbitals of the same n has the same energy; they are called “degenerate”

58. 7.8 Electron spin and the Pauli Principle Spin Quantum Number: ms
Electron has a magnetic moment with two possible orientations when the atom is placed in an external magnetic field
The electron could have two spin states
only 2 possible directions
ms can have two possible values: +½ and -½
paired electrons must
have opposite spins

59. Pauli Exclusion Principle:
In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml , ms )
An orbital can hold only two electrons and they must have opposite spins.

60. 7.9 Polyelectronic Atoms Three energy contributions must be considered
in the description of polyelectronic atom:
Kinetic energy of electrons - as the electrons move around the nucleus
Potential energy - from attraction between electrons and nucleus
Potential energy of repulsion between two electrons

61. Electron Correlation Problem
can’t find the exact location of electrons
can’t find the specific repulsions between electrons
so we must treat each electron as if it has an average amount of attraction to nucleus and repulsion to other electrons

62. Electron Shielding
occurs when an electron is not attracted to the nucleus
because of electrons in lower energy levels repelling it.

63. Penetration Effect
all orbitals in the same energy level do NOT have the same amount of energy ( are not degenerate) same as the case in H-atom
Ens < Enp < End < Enf
the amount of energy in each sublevel is determined by its average distance from the nucleus
For example, in He atom, 2p orbital has its maximum probability closer to the nucleus than 2s orbital, thus we would predict 2p would have less energy than 2s.
However, 2s electron spends more time closer to nucleus and usually has less energy.
That is 2s electron penetrates to the nucleus more than an electron in a 2p orbital

64. 7.10 The history of the Periodic Table
Developed independently by German Julius Lothar Meyer and Russian Dmitri Mendeleev (1870’s).
They didn’t know much about atom.
Elements were arranged in columns by similar properties.
Properties of missing elements were predicted.

65. Mendeleev's Early Periodic Table, Published in 1872

66. 7.11 The aufbau Principle and Periodic Table Electron Arrangement in Atoms
The way electrons are arranged in various orbitals around the nuclei of atoms.
Aufbau is a German word means “Building up”
Aufbau principle - electrons enter the lowest energy first.
Orbitals of different energies overlap

67. Electron Configurations
Electron configuration describes the distribution of
electrons among the various orbitals in the atom
The spdf notation uses numbers to designate a principal shell and the letters to identify a subshell; a superscript number indicates the number of electrons in a designated subshell

68. Orbital Diagram
An orbital diagram uses boxes to represent orbitals within subshells and arrows to represent electrons:
EOS
Each box has arrows representing electron spins; opposing spins are paired together

69. Rules for Electron Configurations
Electrons occupy the lowest available energy orbitals
Pauli exclusion principle – no two electrons in the same atom may have the same four quantum numbers
Orbitals hold a maximum of two electrons
with opposed spins

70. Rules for Electron Configurations
For orbitals of identical energy, electrons enter empty orbitals whenever possible – Hund’s rule
When electrons occupy orbitals of equal energy,
they don’t pair up until they have to.
Electrons in half-filled orbitals have parallel spins
EOS

71. Rules for Electron Configurations
Capacities of shells (n) and subshells (l)
EOS

72. Rules for Electron Configurations
Subshell filling order :
Each subshell must be filled before moving to the next level

73. Electron Configurations
Let’s write the electron configuration for Phosphorus
We need to account for all 15 electrons in phosphorus

74. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 15P 3d 4s 3p 3s
The first two electrons go into the 1s orbital
Notice the opposite direction of the spins
only 13 more to go

75. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
The next electrons go into the 2s orbital
only 11 more

76. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
The next electrons go into the 2p orbital
only 5 more

77. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
The next electrons go into the 3s orbital
only 3 more

78. Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p
The last three electrons go into the 3p orbitals.
They each go into separate orbitas (Hund’s)
3 unpaired electrons
= 1s22s22p63s23p3

79. The Aufbau Principle
A hypothetical building up of an atom from the one that precedes it in atomic number
(Z = 1) H 1s1
(Z = 2) He 1s2
(Z = 3) Li 1s22s1
EOS
(Z = 3) Li 1s22s1  [He]2s1
Abbreviated electron configuration

80. The Aufbau Principle
[He]2p2
[He]2p3
[He]2p4
[He]2p5
EOS
[He]2p6

81. Orbital Diagram for A Nitrogen Atom
1s 2s p s     

82. Orbital Diagram for A Fluorine Atom
1s 2s p s     

83. Orbital Diagram for A Magnesium Atom
12Mg
1s 2s p s      

84. 8O
1s 2s p s     

85. Write the orbital diagram for the electrons in an iron atom 26Fe
1s 2s p s p 3d              

86. Orbitals fill in an order
Lowest energy to higher energy.
Adding electrons can change the energy of the orbital. Full orbitals are the absolute best situation.
However, half filled orbitals have a lower energy, and are next best
Makes them more stable.
Changes the filling order

87. Write the electron configurations for these elements:
Titanium - 22 electrons
1s22s22p63s23p64s23d2
Vanadium - 23 electrons
1s22s22p63s23p64s23d3
Chromium - 24 electrons
1s22s22p63s23p64s23d4 (expected)
But this is not what happens!!

88. Chromium is actually: 1s22s22p63s23p64s13d5 Why?
This gives us two half filled orbitals (the others are all still full)
Half full is slightly lower in energy.
The same principal applies to copper.

89. Copper’s electron configuration
Copper has 29 electrons so we expect: 1s22s22p63s23p64s23d9
But the actual configuration is:
1s22s22p63s23p64s13d10
This change gives one more filled orbital and one that is half filled.
Remember these exceptions: d4, d9

90. Irregular configurations of Cr and Cu
Chromium steals a 4s electron to make its 3d sublevel HALF FULL
Copper steals a 4s electron to FILL its 3d sublevel

91. Electron Configurations of Ions
Cations: lose e– to attain a complete valence shell
Example:
(Z = 11) Na
(Z = 11) Na+

92. Details of the Periodic Table
Elements in the same column have the same electron configuration.
Elements in columns have similar properties.
Noble gases have filled energy levels.
Transition metals are filling the d orbitals

93. Valence electrons- the electrons in the outermost energy levels (not d).
Core electrons- the inner electrons.
C 1s2 2s2 2p2

94. Valence Electrons and Core Electrons
Valence electrons are those with the highest principal quantum number
The electrons in the outermost energy
levels (not d).
Sulfur has six valence electrons

95. Valence Electrons and Core Electrons
Electrons in inner shells are called core electrons
EOS
Sulfur has 10 core electrons

96. Periodic Relationships
We can deduce the general form of electron configurations directly from the periodic table

97. The Periodic Table

98. More exceptions Lanthanum La: [Xe] 6s2 5d1 Cerium Ce: [Xe] 6s2 4f1 5d1
Promethium Pr: [Xe] 6s2 4f3 5d0
Gadolinium Gd: [Xe] 6s2 4f7 5d1
Lutetium Pr: [Xe] 6s2 4f14 5d1
We’ll just pretend that all except Cu and Cr follow the rules.

99. Main Group (Representative) and Transition Elements
Elements in which the orbitals being filled in the aufbau process are either s or p orbitals of the outermost shell are called main group (Representative) elements
“A” group designation on the periodic table
The first 20 elements are all main group elements

100. Lanthanides: electrons fill 4f subleve
Transition Elements
In transition elements, the sublevel (shell) being filled in the aufbau process is in an inner principal shell (d or f)
d-Block transition elements: Electrons enter the
d-sublevels.
f-Block transition elements: d sublevels are completely filled. Electrons enter f-sublevels
Lanthanides: electrons fill 4f subleve
Actinides: electrons fill 5f sublevels

101. The Periodic Table

102. Periodic Relationships

103. 7.12 Periodic Trends in Atomic Properties

104. Ionization Energy A (g) + energy  A+ (g) + e-
Ionization energy the energy required to remove an electron completely form a ground state atom in the gaseous phase
A (g) + energy  A+ (g) + e-
Highest energy electron removed first.
First ionization energy (I1) is that required to remove the first electron.
Second ionization energy (I2) - the second electron, etc.

105. Successive ionization Energies
for Mg
I1 = 735 kJ/mole
I2 = 1445 kJ/mole
I3 = 7730 kJ/mole
The effective nuclear charge increases as electrons are removed
It takes much more energy to remove a core electron than a valence electron because there is less shielding.

106. Successive ionization Energies
Continual removal of electrons increases ionization energy greatly
B  B+ + e– I = 801 kJ mol–1
B+  B+2 + e– I = 2427 kJ mol–1
B+2  B+3 + e– I = 3660 kJ mol–1
Core electron
B+3  B+4 + e– I = 25,025 kJ mol–1
B+4  B+5 + e– I = 32,822 kJ mol–1

107. Ionization Energy

108. First ionization energies across Periods and Groups

109. The Values of First Ionization Energy for the Elements in the First Six Periods
E for O < E for N due to extra electron repulsion in the doubly occupied O 2p orbitals
For B electrons in 2s provide some shielding
From nucleus charge

110. Ionization Energy

111. Ionization Energy

112. Electron Affinity
Electron Affinity – the energy change when an electron is added to a gaseous neutral atom
A + e-  A- + energy
Cl(g) + e-  Cl-(g) E = -349 kJ/mol
Electron affinities are expressed as negative because the process is exothermic

113. Electron affinity values

114. Electron Affinity

115. Electron Affinity Across Period: Down Group:
releases more energy so number increases (gets more negative)
because electrons added in the same energy level do not shield electrons from nuclear charge
Down Group:
releases less energy so number decreases (gets less negative)
because the electrons being added are farther away from the attracting protons

116. Atomic Radii
Size of orbitals can not be specified exactly, neither can the size of atom
Atomic Radii – half the distance between the nuclei of identical atoms that are bonded together

117. Atomic Radii atoms get larger increases
Across Period:
atoms get smaller
because of the increased number of protons attracting the electrons
the electrons added in the same energy level do not shield electrons from nuclear charge
Down Group:
atoms get larger
increases
because the energy levels being added to the atom

118. Atomic Radii Properties

121. Summary of Periodic Trends