Atomic structure and properties. (Chapter 3)

Сентябрь 9, 2022

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Atomic structure and properties. (Chapter 3)

Содержание

2. Picture of the Atom Electromagnetic radiation and Atomic Spectra The Nature of Electron and Atomic Orbitals
3. 3.1.1 Atomic concept, 3.1.2 Subatomic particles, 3.1.3 Atomic structure: first ideas Part I
4. Dalton Atomic Theory Elements are made of tiny particles called atoms 2. The atoms of a
5. J.J. Thomson’s Cathode Tube Charge-to-mass ratio
6. The Atom : J. J. Thomson (1856-1940) e/m = -1.76 x 108 C/g Experiment date 1898-1903
7. The Atom based on Thomson’s experiment A ray of particles is produced between two metallic electrodes.
8. Mass of electron Mass of a single electron e= -1.6x10-19 C m = 9.11 x 10-31
9. Rutherford Experiment Ernest Rutherford – 1911 With Thomson Model : a particles should travel through the
10. Rutherford Experiment
11. The Nucleus Ernest Rutherford – 1911 Conclusion : Dense positive center with electrons far from the
12. Modern View
13. 3.2. Electromagnetic Radiation and Quantization 3.2.1: Electromagnetic Radiation 3.2.2: Quantization 3.2.3: The Atomic Spectrum of Hydrogen
14. Spectrum
15. Electromagnetic radiation Light X-ray MRI Microwave Travel like a wave Travel with the speed of light
16. Electromagnetic Radiation Electromagnetic Radiation = a way for energy to travel. 2 oscillating fields (H and
17. ELECTROMAGNETIC RADIATION
18. Electromagnetic Radiation - Characteristics λ = wavelength = distance between two peaks or two troughs in
19. Radio in the 909kHz. What wavelength does it correspond to? λ = c/ν = 330 m
20. Nature of Matter At the end of the 19th century : Matter ≠ Energy Matter =
21. Photoelectric effect When UV radiation hits a metal surface, electrons are ejected – photoelectric effect. (in
22. E = h x ν E = 6.63 x 10-34 (J•s) x 3.00 x 10 8
23. Dual Nature of Light Energy – Mass relationship : A particle but also a wave :
24. De Broglie 1924 λ = h/mν λ Proportional to h/mν H :Planck Constant M : masse
25. Diffraction What is the wavelength for an electron? Me = 9.11x10-31 kg Ve = 1.0x107 m/s
26. How to test the wave properties of an electron?
27. How to test the wave properties of an electron?
28. Diffraction When X-rays are scattered by ordered atoms ? Diffraction pattern.
29. Conclusion All matter exhibits both particulate and wave properties. Large particles : mainly particle Small particles
30. Atomic Spectrum of Hydrogen When a high energy discharge is passed through H2 ? H-H breaks
31. Table 3.4. The atomic spectrum of hydrogen
33. Atomic Spectrum of Hydrogen Why do we have a line spectrum for H ? Only certain
34. 3.3.2: The Bohr Model
35. The Bohr Model General Idea : The electron in a hydrogen atom moves around the nucleus
36. The Bohr Model Example : Energy emitted from n=6 to ground state : The negative sign
37. Wave Function and Atomic Orbitals 3.5.1 Wave properties of matter, Heisenberg uncertainty principle 3.5.2 Wave-functions and
38. De Broglie All moving particles have wave properties λ= h mu = Wavelength h = Planck
39. 2.2 SCHRONDINGER EQUATION Enter
40. Quantum Mechanical Description of the Atom Heisenberg – de Broglie – Schrödinger Only certain circular orbits
41. The Schrödinger equation The probability distributions and allowed energy levels for electrons in atoms and molecules
42. Schrodinger Wave Equation
43. Kinetic Energy of the Electron Motion Potential Energy of the Electron. The result of electrostatic attraction
44. Kinetic Energy Potential Energy
45. Cartesian and Spherical Coordinate
46. The wavefunction Atomic wavefunctions are usually expressed in spherical polar coordinates – give value of Ψ
47. Homework-2 Please solve problems ; Chapter 3 6, 9, 10, 12, 14, 16 and 17 Due
48. Wave Equation for the Hydrogen Atom – R(r) is radial part of wavefunction Describes electrons density
49. Quantum numbers : Quantum numbers : n = principal quantum number : size and energy of
50. Radial and Angular Wave Function for 1s derived from Schrodinger Equation
51. Plot of Radial Wave Function = f(r)
52. s orbitals Size : 1s Energy : 1s Surface of 0 probability = nodal surface /
53. Physical Meaning of Orbitals The wave function has no easy physical meaning. The square of the
54. a1 = 52.9pm radius at n =1 for hydrogen
55. a1 = 52.9pm radius at n =1 for hydrogen
56. p orbitals Two lobes separated by a node. Sine function : + and - ? same
57. d orbitals 2 different shapes : dxz,dyz,dxy, dx2-y2 and dz2
58. f orbitals Very complex shapes
59. Schrödinger Equation Each solution ψ of the Schrödinger equation has a specific value for E. A
60. Heisenberg uncertainty principle There is a fundamental limitation to just how precisely we can know both
61. The Hydrogen Atom : summary The quantum mechanical model : electron = wave Series of wave
62. Polyelectronic Model Schrödinger equation can be solved exactly only for hydrogen. Schrödinger equation cannot be solved
63. Self-Consistent Field Method http://www.youtube.com/watch?v=UVkTuOwfOh0
64. https://www.youtube.com/watch?v=A6DiVspoZ1E Review this link at home
65. Many Electron Atoms Electron spin, Aufbau principle, Anomalies in electronic configuration, Structure of Periodic table Part
66. Electron Spin and Pauli Principle A 4th quantum number describe the electron : ms : electron
67. History of the Periodic Table Dmitri Mendeleev : ми́трий Менделе́ев One of first to arrange known
68. The Aufbau Principle Principle to populate orbitals.
69. Valence electrons Valence electrons = electrons from the outermost principal quantum level of an atom. Group
70. Rules
71. Rules After 4s2, we fill 3d. Mn : [Ar]4s23d5 – Fe [Ar]4s23d6 Additional Rules: The (n+1)
72. Rules Element above 118 are generally unstable G contain 9 orbitals l = n-1 = 4
73. Rules
74. Hund’s Rule The lowest energy configuration for an atom is the one having the maximum number
75. Pauli Exclusion Principle Pauli Exclusion principle ; no two electrons in an atom can have the
76. Penetration Effect Why do we fill s, p and then d?. Core electrons : 1s, 2s
77. Penetration Effect The penetration effect also explains why 4s is filled before 3d. Potassium : 1S22S22P63S23P64S1
78. 4s 5g 5s 3p 3s 2p 2s Slater rules provide an approximate Guide explain why certain
79. https://en.wikipedia.org/wiki/Effective_nuclear_charge
80. Slater’s Rules The rules were devised semi-empirically by John C. Slater and published in 1930 Identify
81. Slater’s Rules The rules were devised semi-empirically by John C. Slater and published in 1930 Rules
82. Slater’s Rules for determining S for a specific electron The shielding constant (S) ns and np
83. Slater’s Rules for determining S for a specific electron Rule -3b: Each electron in n-1 group
84. Z* for Na = Z – S = 11 – 8.8 = 2.2
85. Slater’s Rules for determining S for a specific electron Rule -4a: Each electron in nd and
86. Nickel Use slater rules to calculate the shielding constant S and effective nuclear charge of 3d
87. Solution Rule-1 : the electron configuration is written using slater’s groupings: (1s2)(2s2, 2p6)(3s2, 3p6)(3d8)(4s2) To calculate
88. Solution Rule-1 : the electron configuration is written using slater’s groupings: (1s2)(2s2, 2p6)(3s2, 3p6)(3d8) (4s2) To
89. Comparison of The effective nuclear charge 3d electrons The effective nuclear charge Z*=28-20.45=7.55 4s electrons Z*=28-23.95=4.05
90. Periodic Properties of Atoms : Ionization Energy Ionization Energy : Energy required to remove an electron
91. Trend in Atomic Properties : Ionization Energy IE core electrons >> IE >> from left to
94. Trend in Atomic Properties : Ionization Energy Li: 1s22s1 (3 electrons) Be: 1s22s2 (3 electrons) Expected
95. Trend in Atomic Properties : Ionization Energy IE goes down along a group. The removed electron
96. Trend in Atomic Properties : Atomic Radius Atomic Radius: half the distance between the nuclei in
97. END END
98. Alkali Metals – 1A Low melting point Lose easily an electron Strong reducer Li > K
99. ρsinφ Δρ Angle = Arc Length radius of the circle
102. Скачать презентацию

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Picture of the Atom
Electromagnetic radiation and Atomic Spectra
The Nature of

Electron and Atomic Orbitals
Many-electron atoms
Atomic properties and Periodicity
Nuclear chemistry

Chapter 3

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3.1.1 Atomic concept,
3.1.2 Subatomic particles,
3.1.3 Atomic structure: first ideas
Part

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Dalton Atomic Theory
Elements are made of tiny particles called atoms
2.

The atoms of a given elements are identical
3. Chemical compounds are formed when atoms combine with one another. A given compound has the same relative numbers and types of atoms
4. Chemical reaction involve reorganization of the atoms. The atom themselves are not changed.

The classical picture of the atom

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J.J. Thomson’s Cathode Tube
Charge-to-mass ratio

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The Atom : J. J. Thomson (1856-1940)
e/m = -1.76 x 108

C/g

Experiment date 1898-1903

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The Atom based on Thomson’s experiment
A ray of particles is produced
between

two metallic electrodes.
These particles are negatively charged
Since electrons could be produced from electrodes made of various types of metals, all atoms must contain electrons
e/m = -1.76 x 108 C/g
Atoms = neutral! Positive charges are located somewhere.

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Mass of electron
Mass of a single electron
e= -1.6x10-19 C m =

9.11 x 10-31 kg (Millikan)

http://www.youtube.com/watch?v=XMfYHag7Liw

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Rutherford Experiment
Ernest Rutherford – 1911
With Thomson Model : a particles should

travel through the atom without deflection.

http://sun.menloschool.org/~dspence/chemistry/atomic/ruth_expt.html

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Rutherford Experiment

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The Nucleus
Ernest Rutherford – 1911
Conclusion : Dense positive center with electrons

far from the nucleus

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Modern View

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3.2. Electromagnetic Radiation and Quantization
3.2.1: Electromagnetic Radiation
3.2.2: Quantization
3.2.3: The Atomic Spectrum

of Hydrogen

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Spectrum

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Electromagnetic radiation
Light
X-ray
MRI
Microwave
Travel like a wave
Travel with the speed of light

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Electromagnetic Radiation
Electromagnetic Radiation = a way for energy to travel.
2 oscillating

fields (H and E)

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ELECTROMAGNETIC RADIATION

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Electromagnetic Radiation - Characteristics
λ = wavelength = distance between two peaks

or two troughs in a wave. (m)
= frequency = number of waves / s at a specific point of space. (s-1 or Hz)
Because speed = c
= 3x108 m/s

The radiation with the shortest wavelength has the highest frequency

λ ∞ 1/ν

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Radio in the 909kHz. What wavelength does it correspond to?
λ =

c/ν = 330 m

C = 2.998 108 ms-1
ν = 909. 103 s-1

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Nature of Matter
At the end of the 19th century :
Matter

≠ Energy
Matter = particles and Energy = electromagnetic radiations
Max Planck and the black body radiation :

Classic : matter can absorb or emit any quantity of energy ? no maximum ? infinite intensity at very low wavelength.
Quantum : Energy could only be gained or emitted in whole number multiples of hν. h = Plank’s constant = 6.626x10-34Js

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Photoelectric effect
When UV radiation hits a metal surface, electrons are ejected

– photoelectric effect. (in 1905 explained by Albert Einstein using a quantum approach)
hν = Φ + EKE
Φ - work function – minimum energy required to remove the electron
EKE – kinetic energy of the ejected electron

Albert Einstein Theory :
Energy itself is quantified and radiation could be seen as a stream of particles (photons)!

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E = h x ν
E = 6.63 x 10-34 (J•s) x

3.00 x 10 8 (m/s) / 0.154 x 10-9 (m)

E = 1.29 x 10 -15 J

E = h x c / λ

When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm.

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Dual Nature of Light
Energy – Mass relationship :
A particle but also

a wave :
Summary :
- Energy is quantized
- Only discrete units of energy (quanta) could be transferred
- Dual nature of light

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De Broglie 1924
λ = h/mν
λ Proportional to h/mν
H :Planck Constant
M :

masse
ν : velocity

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$Diffraction What is the wavelength for an electron? Me = 9.11x10-31$

Diffraction
What is the wavelength for an electron?
Me = 9.11x10-31 kg
Ve

= 1.0x107 m/s
1 J = 1 kg.m2/s2
6.626x10-34Js

The electron has a WL similar to the spacing of atoms in a crystal.
Confirmed for Ni crystal.
Diffraction : result of light scattered from a regular array of points or lines.

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How to test the wave properties of an electron?

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How to test the wave properties of an electron?

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$Diffraction When X-rays are scattered by ordered atoms ? Diffraction pattern.$

Diffraction
When X-rays are scattered by ordered atoms ? Diffraction pattern.

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Conclusion
All matter exhibits both particulate and wave properties.
Large particles : mainly

particle
Small particles : mainly wave
Intermediate particles (electron) : both

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Atomic Spectrum of Hydrogen
When a high energy discharge is passed through

H2 ? H-H breaks ? excited H atoms.
Release of energy ? Emission spectrum.

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Table 3.4. The atomic spectrum of hydrogen

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Atomic Spectrum of Hydrogen
Why do we have a line spectrum for

H ?
Only certain energies are allowed for the electron in the hydrogen atom.
Energy is quantized!

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3.3.2: The Bohr Model

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The Bohr Model
General Idea :
The electron in a hydrogen atom moves

around the nucleus only in certain allowed circular obits.
Bohr used classical physics to calculate the radii of these orbits.
At an infinite distance E=0 (n=∞)

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The Bohr Model
Example : Energy emitted from n=6 to ground state

:
The negative sign means that the electron is more tightly bound when
n=1 than when n=6

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Wave Function and Atomic Orbitals
3.5.1 Wave properties of matter, Heisenberg uncertainty

principle
3.5.2 Wave-functions and Schrödinger equation
3.5.3 Shapes of atomic orbitals

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De Broglie
All moving particles have wave properties
λ=
h
mu
= Wavelength
h = Planck

Constant
m = Mass
u = Velocity of the particle

The electron bound to the nucleus is similar to a standing wave.
The waves do not travel.
Node = no displacement of the wave = each end.
? Always a whole number of half-WL.

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2.2 SCHRONDINGER EQUATION
Enter

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Quantum Mechanical Description of the Atom
Heisenberg – de Broglie – Schrödinger
Only

certain circular orbits have a circumference into which a whole number of wavelength of the standing electron will fit.

ψ = wave function : describes x, y, z of the electron
H = Hamiltonian operator
E = Total Energy of the atom (Ep e-p + Ek e)

– probability of finding an electron at some point is proportional to Ψ Ψ *. Ψ * is the complex conjugate

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The Schrödinger equation
The probability distributions and allowed energy levels for electrons

in atoms and molecules can be calculated using the Schrödinger equation

– second order differential equation

– equation has a large number of different solutions
» each corresponds to a different possible probability distribution for the electron

– probability of finding an electron at some point is proportional to Ψ Ψ *. Ψ * is the complex conjugate

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Schrodinger Wave Equation

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Kinetic Energy of the
Electron Motion
Potential Energy of the
Electron. The

result of
electrostatic attraction
between the electron
and the nucleus. It is
commonly designated as V

Hamiltonian for one Electron

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Kinetic Energy
Potential Energy

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Cartesian and Spherical Coordinate

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The wavefunction
Atomic wavefunctions are usually expressed in spherical polar coordinates
–

give value of Ψ at any point in space specified by r, θ and φ
Can write Ψ(r, θ, φ)=R(r) Y(θ, φ)
– R(r) is radial part of wavefunction
– Y(θ, φ) is angular part of wavefunction

Quantum Numbers and Atomic Wavefunctions

https://www.youtube.com/watch?v=sT8JIn7Q_Fo
https://www.youtube.com/watch?v=NpgKGIaE9Zc

x = rsinθcosφ
y = rsinθsinφ
z = rcosθ

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Homework-2
Please solve problems ;
Chapter 3
6, 9, 10, 12, 14, 16 and

17
Due on Wednesday. Recitation time

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Wave Equation for the Hydrogen Atom
– R(r) is radial part of

wavefunction
Describes electrons density at different
distances from the nucleus
– Y(θ, φ) is angular part of wavefunction
Describes the shape of the orbitals and
its orientation in space.
In other words:
How the probability changes from point to
point at a given distance from the
center of the atom.

x = rsinθcosφ
y = rsinθsinφ
z = rcosθ

Ψ(x, y, z)= Ψ(r, θ, φ) = R(r) Y(θ, φ)

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Quantum numbers :
Quantum numbers :
n = principal quantum number : size

and energy of the orbital
l = angular momentum quantum number : 0 to n-1 : shape of the orbital
ml = magnetic quantum number : -l to +l : orientation in space of the angular momentum

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Radial and Angular Wave Function for 1s derived from Schrodinger Equation

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Plot of Radial Wave Function = f(r)

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s orbitals
Size : 1s<2s<3s.
Energy : 1s<2s<3s.
Surface of 0 probability = nodal

surface / node.
Number of node = n-1 for s orbitals.

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Physical Meaning of Orbitals
The wave function has no easy physical meaning.
The

square of the WV at a certain point in space = probability to find an electron near that point = probability distribution.

For 1s orbital : arbitrary accepted size = radius of the sphere that encloses 90% of total electron probability.

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a1 = 52.9pm radius at n =1 for hydrogen

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a1 = 52.9pm radius at n =1 for hydrogen

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p orbitals
Two lobes separated by a node.
Sine function : +

and - ? same for the orbital.
Px, Py, Pz following their orientation

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d orbitals
2 different shapes : dxz,dyz,dxy, dx2-y2 and dz2

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f orbitals
Very complex shapes

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Schrödinger Equation
Each solution ψ of the Schrödinger equation has a specific

value for E.
A specific wave function for a given electron = orbital
An orbital ≠ orbit.
How does an electron move in an orbit? We don’t know!

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Heisenberg uncertainty principle
There is a fundamental limitation to just how precisely

we can know both the position and the momentum of a particle at a given time.
Negligible for macro particles (ball, etc.) but not for small particles!

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The Hydrogen Atom : summary
The quantum mechanical model : electron =

wave
Series of wave function (orbitals) that describe the possible energies and spatial distributions available to the electrons.
Heisenberg : the electron motion can’t be defined.
The square of the WF = probability distribution of the electron in an orbital.
The size of the orbital is arbitrarily defined .
Surface that contains 90% of the total electron probability.
The H atom has many orbitals.
In the ground state : e- in 1s.

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Polyelectronic Model
Schrödinger equation can be solved exactly only for hydrogen.
Schrödinger equation

cannot be solved exactly for polyelectronic atoms.
It has to be approximated : SCF : Self-Consistent Field by Hartree.
1- A WF (orbital) is guessed for each electron except for electron 1.
2- Schrödinger equation is solved for electron 1
3- The repulsion between 1 and the others electrons are computed
4- ψ1 is found
5- ψ2, etc. are computed
6- The entire process start again until a self-consistent field is obtained

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Self-Consistent Field Method
http://www.youtube.com/watch?v=UVkTuOwfOh0

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https://www.youtube.com/watch?v=A6DiVspoZ1E
Review this link at home

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Many Electron Atoms
Electron spin,
Aufbau principle,
Anomalies in electronic configuration, Structure

of Periodic table

Part V

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Electron Spin and Pauli Principle
A 4th quantum number describe the electron

: ms : electron spin quantum number.
The electron doesn’t really “spin” = name for the intrinsic angular moment.
ms = +1/2 or -1/2
Pauli exclusion principle : in a given atom no two electrons can have the same set of four quantum numbers.
– An orbital can hold only two electrons and they must have opposite spin.

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History of the Periodic Table
Dmitri Mendeleev : ми́трий Менделе́ев
One of first

to arrange known elements into a chart
Allowed prediction of element properties
Arranged known elements according to increasing atomic masses
Mendeleev first stated the periodic law
“The properties of the elements are a periodic function of their atomic
masses”

1834 – 1907
Saint Petersburg - Russia

Later, after more observations, the table was correctly arranged in ORDER OF INCREASING ATOMIC NUMBER

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The Aufbau Principle
Principle to populate orbitals.

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Valence electrons
Valence electrons = electrons from the outermost principal quantum level

of an atom.
Group : Elements in a column : Same valence configuration

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Rules

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Rules
After 4s2, we fill 3d.
Mn : [Ar]4s23d5 – Fe [Ar]4s23d6
Additional Rules:
The

(n+1) orbitals always fill before the nd orbitals.
After lanthanum, the lanthanide series occur. ? filling of 4f instead of 5d
After actinium, the actinide series occur. ? filling 5f instead of 6d
Groups 1A?8A indicate the total number of valance electrons.
Groups 1A?8A are main group elements.
2 exceptions to learn by heart : Cr [Ar]4s1d5 and Cu [Ar]4s13d10

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Rules
Element above 118
are generally unstable
G contain 9 orbitals l = n-1

= 4 so -4,-3,-2, -1, 0, 2, 3, 4 each

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Rules

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Hund’s Rule
The lowest energy configuration for an atom is the one

having the maximum number of unpaired electrons allowed by the Pauli Principle.
Configuration of Ne? 1s22s22p6
Configuration of Na? [Ne]3s1

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Pauli Exclusion Principle
Pauli Exclusion principle ; no two electrons in an

atom can have the same quantum numbers n, l, ml, and ms
– this means that an orbital can never have more than two electrons in it
Hund’s Rule
Hund’s rule of maximum multiplicity requires that electrons be placed in orbitals to give the maximum total spin possible (the maximum number of parallel spin)

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Penetration Effect
Why do we fill s, p and then d?.
Core

electrons : 1s, 2s and 2p are shielding 3s, 3p, 3d from the nuclear charge.
Even if 3s has a max around 200pm, it has a small/significant prob. of being quite close to the nucleus ? Penetration effect.
3p has less chance to be near the nucleus
3d shows much less penetration than 3p. E3s < E3p < E3d

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Penetration Effect
The penetration effect also explains why 4s is filled before

3d.

Potassium : 1S22S22P63S23P64S1 rather than 1S22S22P63S23P63d1

An electron in a 4S penetrate much more than an electron in a 3d orbital, as shown
Graphically. (qualitative explanation)

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4s
5g
5s
3p
3s
2p
2s
Slater rules provide an approximate
Guide explain why certain orbitals
fill

before others.

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https://en.wikipedia.org/wiki/Effective_nuclear_charge

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Slater’s Rules The rules were devised semi-empirically by John C. Slater and published in 1930
Identify Zeff

(as a measure of attraction) for any electron
Z* = Z – S
Where Z = nuclear charge
S = shielding constant

https://www.youtube.com/watch?v=5flvrGhT40U & https://www.youtube.com/watch?v=9mXQJUrOhxk
https://www.youtube.com/watch?v=RSf98oxyVm8

Rule-1. The atoms electronic structure is written in order of increasing quantum numbers n and l grouped as follows:
(1s) (2s,2p) (3s,3p) (3d) (4s,4p) (4d) (4f) (5s, 5p) (5d) etc.
Rule-2. Each group to the right do not shield electrons to their left.

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Slater’s Rules The rules were devised semi-empirically by John C. Slater and published in 1930
Rules for

determining S
S = shielding constant

https://www.youtube.com/watch?v=5flvrGhT40U & https://www.youtube.com/watch?v=9mXQJUrOhxk
https://www.youtube.com/watch?v=RSf98oxyVm8

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Slater’s Rules for determining S for a specific electron
The shielding constant

(S) ns and np valence electrons:
3a) Each electron in the same (ns, np) group contributes 0.35 to the value of S for each other electron in the group.
Except. A 1s electron contributes 0.30 to S of another 1s electron.
EXAMPLE: 2s2p5, in a particular 2p electron has 6 other electron in (2s, 2p) group. Each of these contribute 0.35 to the value of S, for a total contribution to S of 6×0.35=2.10

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Slater’s Rules for determining S for a specific electron
Rule -3b: Each

electron in n-1 group contribute 0.85 to S
Rule -3c: Each electron in n-2 group or lower shells contribute 1.00 to S
EXAMPLE: 3s electrons of sodium (1s22s2p63S1) , there are 8 electrons in n-1 (2s, 2p) group, each of these contribute 0.85 to the value of S, for a total contribution to S of 8×0.85=6.80. There are two electrons in n-2(1S) 2 ×1 = 2, S = 8.80

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Z* for Na = Z – S = 11 – 8.8

= 2.2

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Slater’s Rules for determining S for a specific electron
Rule -4a: Each

electron in nd and nf valence
Each electron in the same group (nd) or (nf) group contribute 0.35 to the value of S to each other electron in the group (same rule as 3a)
Rule -4b:
Each electron in groups to the left contribute 1 to the value of S.

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Nickel
Use slater rules to calculate the shielding constant S and effective

nuclear charge of 3d and 4s electrons. Compare

Explain why the most common oxidation state
of Ni have [Ar]3d8

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Solution
Rule-1 : the electron configuration is written using slater’s groupings:
(1s2)(2s2, 2p6)(3s2,

3p6)(3d8)(4s2)
To calculate S for 3d valence electron:
Rule 4a : each electron in the group(3d8) contributes 0.35 to S. Total contribution = 7×0.35=2.45
Rule 4b : each electron in the group to the left of (3d8) Contribute 1 to S. Total contribution = 18×1=18.00
Total S = 2.45 +18.00= 20.45
The effective nuclear charge Z*=28-20.45=7.55

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Solution
Rule-1 : the electron configuration is written using slater’s groupings:
(1s2)(2s2, 2p6)(3s2,

3p6)(3d8) (4s2)
To calculate S for 4s valence electron:
Rule 3a : each electron in the 4s group contribute 0.35 1× 0.35
Rule 3b : each electron in the n-1 group contribute 0.85 (0.85.16) = 13.60
Rule 3c : each electron on the left of n-1 Contribute 1 to S. Total contribution = 10×1=10.00
Total S = 0.35 + 13.60 + 10.00= 23.95
The effective nuclear charge Z*=28-23.95=4.05

Слайд 89

Comparison of The effective nuclear charge
3d electrons
The effective nuclear charge

Z*=28-20.45=7.55
4s electrons
Z*=28-23.95=4.05
Ni : [Ar]3d8
All transition Metals loose ns electrons more readily than (n-1) d electrons

Слайд 90

Periodic Properties of Atoms : Ionization Energy
Ionization Energy : Energy required

to remove an electron from a gaseous atom or ion. IE in kJ or eV (1 eV = 1.602x10-19J)
X(g) ? X+(g) + e-
Koopmans’ theorem : IE of an electron = energy of the orbital from which it came. (Approx because it doesn’t take into account a reorganization)
Al(g) ? Al+(g) + e- I1 = 580 kJ/mol
Al+(g) ? Al2+(g) + e- I2 = 1815 kJ/mol
Al2+(g) ? Al3+(g) + e- I3 = 2740kJ/mol
Al3+(g) ? Al4+(g) + e- I4 = 11 600kJ/mol
[Ne]3s23p1 : First e- come from 3p, second from 3s
I1I4 is very high : Al3+ : 1s22s22p6 : core electrons are bound very tight!

Слайд 91

Trend in Atomic Properties : Ionization Energy
IE core electrons >>
IE >>

from left to right in a period

X(g)→ X+(g) +1e-

The first ionization energy increases across a period and decreases down a group

Слайд 92

Слайд 93

Слайд 94

Trend in Atomic Properties : Ionization Energy
Li: 1s22s1 (3 electrons)
Be:

1s22s2 (3 electrons)
Expected since Be electrons
do shield each other completely

Be: 1s22s2 (3 electrons)
B: 1s22s22p1 (3 electrons)
Expected since 2s electrons
do shield each 2p electrons effectively

Слайд 95

Trend in Atomic Properties : Ionization Energy
IE goes down along a

group.
The removed electron is away from the core

Слайд 96

Trend in Atomic Properties : Atomic Radius
Atomic Radius: half the distance

between the nuclei in a molecule consisting of identical atoms.

Слайд 97

END
END

Слайд 98

Alkali Metals – 1A
Low melting point
Lose easily an electron
Strong reducer
Li

> K > Na

Na and K react more violently with water than Li
due to its high melting point.

Abnormal: Order is due to the hydration energies.

Слайд 99

ρsinφ
Δρ
Angle =
Arc Length
radius of the circle

Слайд 100

Atomic structure and properties. (Chapter 3)

Содержание

Picture of the AtomElectromagnetic radiation and Atomic Spectra The Nature of

3.1.1 Atomic concept, 3.1.2 Subatomic particles, 3.1.3 Atomic structure: first ideasPart

Dalton Atomic Theory Elements are made of tiny particles called atoms2.

J.J. Thomson’s Cathode TubeCharge-to-mass ratio

The Atom : J. J. Thomson (1856-1940)e/m = -1.76 x 108

The Atom based on Thomson’s experimentA ray of particles is producedbetween

Mass of electronMass of a single electrone= -1.6x10-19 C m =

Rutherford ExperimentErnest Rutherford – 1911With Thomson Model : a particles should

Rutherford Experiment

The NucleusErnest Rutherford – 1911Conclusion : Dense positive center with electrons

Modern View

3.2. Electromagnetic Radiation and Quantization3.2.1: Electromagnetic Radiation3.2.2: Quantization3.2.3: The Atomic Spectrum

Spectrum

Electromagnetic radiationLightX-rayMRIMicrowaveTravel like a waveTravel with the speed of light

Electromagnetic RadiationElectromagnetic Radiation = a way for energy to travel.2 oscillating

ELECTROMAGNETIC RADIATION

Electromagnetic Radiation - Characteristicsλ = wavelength = distance between two peaks

Radio in the 909kHz. What wavelength does it correspond to?λ =

Nature of MatterAt the end of the 19th century : Matter

Photoelectric effectWhen UV radiation hits a metal surface, electrons are ejected

E = h x νE = 6.63 x 10-34 (J•s) x

Dual Nature of LightEnergy – Mass relationship :A particle but also

De Broglie 1924λ = h/mνλ Proportional to h/mνH :Planck ConstantM :

DiffractionWhat is the wavelength for an electron?Me = 9.11x10-31 kg Ve

How to test the wave properties of an electron?

How to test the wave properties of an electron?

DiffractionWhen X-rays are scattered by ordered atoms ? Diffraction pattern.

ConclusionAll matter exhibits both particulate and wave properties. Large particles : mainly

Atomic Spectrum of HydrogenWhen a high energy discharge is passed through

Table 3.4. The atomic spectrum of hydrogen

Atomic Spectrum of HydrogenWhy do we have a line spectrum for

3.3.2: The Bohr Model

The Bohr ModelGeneral Idea :The electron in a hydrogen atom moves

The Bohr ModelExample : Energy emitted from n=6 to ground state

Wave Function and Atomic Orbitals3.5.1 Wave properties of matter, Heisenberg uncertainty

De BroglieAll moving particles have wave propertiesλ= hmu= Wavelengthh = Planck

2.2 SCHRONDINGER EQUATIONEnter

Quantum Mechanical Description of the AtomHeisenberg – de Broglie – SchrödingerOnly

The Schrödinger equationThe probability distributions and allowed energy levels for electrons

Schrodinger Wave Equation

Kinetic Energy of the Electron MotionPotential Energy of the Electron. The

Kinetic Energy Potential Energy

Cartesian and Spherical Coordinate

The wavefunction Atomic wavefunctions are usually expressed in spherical polar coordinates–

Homework-2Please solve problems ;Chapter 36, 9, 10, 12, 14, 16 and

Wave Equation for the Hydrogen Atom– R(r) is radial part of

Quantum numbers :Quantum numbers :n = principal quantum number : size

Radial and Angular Wave Function for 1s derived from Schrodinger Equation

Plot of Radial Wave Function = f(r)

s orbitalsSize : 1s<2s<3s.Energy : 1s<2s<3s.Surface of 0 probability = nodal

Physical Meaning of OrbitalsThe wave function has no easy physical meaning.The

a1 = 52.9pm radius at n =1 for hydrogen

a1 = 52.9pm radius at n =1 for hydrogen

p orbitalsTwo lobes separated by a node. Sine function : +

d orbitals2 different shapes : dxz,dyz,dxy, dx2-y2 and dz2

f orbitalsVery complex shapes

Schrödinger EquationEach solution ψ of the Schrödinger equation has a specific

Heisenberg uncertainty principleThere is a fundamental limitation to just how precisely

The Hydrogen Atom : summaryThe quantum mechanical model : electron =

Polyelectronic ModelSchrödinger equation can be solved exactly only for hydrogen.Schrödinger equation

Self-Consistent Field Methodhttp://www.youtube.com/watch?v=UVkTuOwfOh0

https://www.youtube.com/watch?v=A6DiVspoZ1EReview this link at home

Many Electron AtomsElectron spin, Aufbau principle, Anomalies in electronic configuration, Structure

Electron Spin and Pauli PrincipleA 4th quantum number describe the electron

History of the Periodic TableDmitri Mendeleev : ми́трий Менделе́евOne of first

The Aufbau PrinciplePrinciple to populate orbitals.

Valence electrons Valence electrons = electrons from the outermost principal quantum level

Rules

RulesAfter 4s2, we fill 3d.Mn : [Ar]4s23d5 – Fe [Ar]4s23d6Additional Rules:The

RulesElement above 118are generally unstableG contain 9 orbitals l = n-1

Rules

Hund’s RuleThe lowest energy configuration for an atom is the one

Pauli Exclusion PrinciplePauli Exclusion principle ; no two electrons in an

Picture of the Atom
Electromagnetic radiation and Atomic Spectra
The Nature of

3.1.1 Atomic concept,
3.1.2 Subatomic particles,
3.1.3 Atomic structure: first ideas
Part

Dalton Atomic Theory
Elements are made of tiny particles called atoms
2.

J.J. Thomson’s Cathode Tube
Charge-to-mass ratio

The Atom : J. J. Thomson (1856-1940)
e/m = -1.76 x 108

The Atom based on Thomson’s experiment
A ray of particles is produced
between

Mass of electron
Mass of a single electron
e= -1.6x10-19 C m =

Rutherford Experiment
Ernest Rutherford – 1911
With Thomson Model : a particles should

The Nucleus
Ernest Rutherford – 1911
Conclusion : Dense positive center with electrons

3.2. Electromagnetic Radiation and Quantization
3.2.1: Electromagnetic Radiation
3.2.2: Quantization
3.2.3: The Atomic Spectrum

Electromagnetic radiation
Light
X-ray
MRI
Microwave
Travel like a wave
Travel with the speed of light

Electromagnetic Radiation
Electromagnetic Radiation = a way for energy to travel.
2 oscillating

Electromagnetic Radiation - Characteristics
λ = wavelength = distance between two peaks

Radio in the 909kHz. What wavelength does it correspond to?
λ =

Nature of Matter
At the end of the 19th century :
Matter

Photoelectric effect
When UV radiation hits a metal surface, electrons are ejected

E = h x ν
E = 6.63 x 10-34 (J•s) x

Dual Nature of Light
Energy – Mass relationship :
A particle but also

De Broglie 1924
λ = h/mν
λ Proportional to h/mν
H :Planck Constant
M :

Diffraction
What is the wavelength for an electron?
Me = 9.11x10-31 kg
Ve

Diffraction
When X-rays are scattered by ordered atoms ? Diffraction pattern.

Conclusion
All matter exhibits both particulate and wave properties.
Large particles : mainly

Atomic Spectrum of Hydrogen
When a high energy discharge is passed through

Atomic Spectrum of Hydrogen
Why do we have a line spectrum for

The Bohr Model
General Idea :
The electron in a hydrogen atom moves

The Bohr Model
Example : Energy emitted from n=6 to ground state

Wave Function and Atomic Orbitals
3.5.1 Wave properties of matter, Heisenberg uncertainty

De Broglie
All moving particles have wave properties
λ=
h
mu
= Wavelength
h = Planck

2.2 SCHRONDINGER EQUATION
Enter

Quantum Mechanical Description of the Atom
Heisenberg – de Broglie – Schrödinger
Only

The Schrödinger equation
The probability distributions and allowed energy levels for electrons

Kinetic Energy of the
Electron Motion
Potential Energy of the
Electron. The

Kinetic Energy
Potential Energy

The wavefunction
Atomic wavefunctions are usually expressed in spherical polar coordinates
–

Homework-2
Please solve problems ;
Chapter 3
6, 9, 10, 12, 14, 16 and

Wave Equation for the Hydrogen Atom
– R(r) is radial part of

Quantum numbers :
Quantum numbers :
n = principal quantum number : size

s orbitals
Size : 1s<2s<3s.
Energy : 1s<2s<3s.
Surface of 0 probability = nodal

Physical Meaning of Orbitals
The wave function has no easy physical meaning.
The

p orbitals
Two lobes separated by a node.
Sine function : +

d orbitals
2 different shapes : dxz,dyz,dxy, dx2-y2 and dz2

f orbitals
Very complex shapes

Schrödinger Equation
Each solution ψ of the Schrödinger equation has a specific

Heisenberg uncertainty principle
There is a fundamental limitation to just how precisely

The Hydrogen Atom : summary
The quantum mechanical model : electron =

Polyelectronic Model
Schrödinger equation can be solved exactly only for hydrogen.
Schrödinger equation

Self-Consistent Field Method
http://www.youtube.com/watch?v=UVkTuOwfOh0

https://www.youtube.com/watch?v=A6DiVspoZ1E
Review this link at home

Many Electron Atoms
Electron spin,
Aufbau principle,
Anomalies in electronic configuration, Structure

Electron Spin and Pauli Principle
A 4th quantum number describe the electron

History of the Periodic Table
Dmitri Mendeleev : ми́трий Менделе́ев
One of first

The Aufbau Principle
Principle to populate orbitals.

Valence electrons
Valence electrons = electrons from the outermost principal quantum level

Rules
After 4s2, we fill 3d.
Mn : [Ar]4s23d5 – Fe [Ar]4s23d6
Additional Rules:
The

Rules
Element above 118
are generally unstable
G contain 9 orbitals l = n-1

Hund’s Rule
The lowest energy configuration for an atom is the one

Pauli Exclusion Principle
Pauli Exclusion principle ; no two electrons in an