1. Chapter 7 Electronic Structure
Chemistry 111/112 Chapter 9
Chapter 7 Electronic Structure
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2. Chemistry 111/112 Chapter 9
Waves
Waves are periodic disturbances – they repeat at regular intervals of time and distance.
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3. Chemistry 111/112 Chapter 9
Properties of Waves
Wavelength (l) is the distance between one peak and the next.
Frequency (n) is the number of waves that pass a fixed point each second.
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4. Electromagnetic Radiation
Chemistry 111/112 Chapter 9
Electromagnetic Radiation
Light or electromagnetic radiation consists of oscillating electric and magnetic fields.
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5. Chemistry 111/112 Chapter 9
Speed of Light
All electromagnetic waves travel at the same speed in a vacuum, 3.00×108 m/s.
The speed of a wave is the product of its frequency and wavelength, so for light:
So, if either the wavelength or frequency is known, the other can be calculated.
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6. Example: Electromagnetic Radiation
Chemistry 111/112 Chapter 9
Example: Electromagnetic Radiation
An FM radio station broadcasts at a frequency of MHz (1 Hz = 1 s-1). Calculate the wavelength of this electromagnetic radiation.
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7. Kinds of Electromagnetic Radiation
Chemistry 111/112 Chapter 9
Kinds of Electromagnetic Radiation
Visible light is only a very small portion of the electromagnetic spectrum.
Other names for regions are gamma rays, x rays, ultraviolet, infrared, microwaves, radar, and radio waves.
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8. Quantization of Energy
Chemistry 111/112 Chapter 9
Quantization of Energy
In 1900, Max Planck proposed that there is a smallest unit of energy, called a quantum. The energy of a quantum is
where h is Planck’s constant, 6.626×10-34 J·s.
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9. The Photoelectric Effect
Chemistry 111/112 Chapter 9
The Photoelectric Effect
The photoelectric effect: the process in which electrons are ejected from a metal when it is exposed to light.
No electrons are ejected by light with a frequency lower than a threshold frequency, n0.
At frequencies higher than n0, kinetic energy of ejected electron is hn – hn0.
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10. Photoelectric Effect (cont.)
Chemistry 111/112 Chapter 9
Photoelectric Effect (cont.)
Einstein suggested an explanation by assuming light is a stream of particles called photons.
The energy of each photon is given by Planck’s equation, E = hn.
The minimum energy needed to free an electron is hn0.
Law of conservation of energy means that the kinetic energy of ejected electron is hn – hn0.
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11. Dual Nature of Light? Is light a particle, or is it a wave?
Chemistry 111/112 Chapter 9
Dual Nature of Light?
Is light a particle, or is it a wave?
Light has both particle and wave properties, depending on the property.
Particle behavior, wave behavior no longer considered to be exclusive from each other.
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12. Chemistry 111/112 Chapter 9
Spectra
A spectrum is a graph of light intensity as a function of wavelength or frequency.
The light emitted by heated objects is a continuous spectrum; light of all wavelengths is present.
Gaseous atoms produce a line spectrum – one that contains light only at specific wavelengths and not at others.
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13. Line Spectra of Some Elements
Chemistry 111/112 Chapter 9
Line Spectra of Some Elements
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14. Chemistry 111/112 Chapter 9
The Rydberg Equation
Study of the spectrum of hydrogen, the simplest element, show that the wavelengths of lines of light can be calculated using the Rydberg equation:
n1 and n2 are whole numbers and RH = 1.097×107 m-1.
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15. Example: Rydberg Equation
Chemistry 111/112 Chapter 9
Example: Rydberg Equation
Calculate the wavelength (in nm) of the line in the hydrogen atom spectrum for which n1 = 2 and n2 = 3.
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16. The Bohr Model of Hydrogen
Chemistry 111/112 Chapter 9
The Bohr Model of Hydrogen
Bohr assumed:
that the electron followed a circular orbit about the nucleus; and
that the angular momentum of the electron was quantized.
Using these assumptions, he found that the energy of the electron was quantized:
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17. Bohr Model and the Rydberg Equation
Chemistry 111/112 Chapter 9
Bohr Model and the Rydberg Equation
Assume that when one electron transfers from one orbit to another, energy must be added or removed by a single photon with energy hn.
This assumption leads directly to the Rydberg equation.
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18. Hydrogen Atom Energy Diagram
Chemistry 111/112 Chapter 9
Hydrogen Atom Energy Diagram
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19. Chemistry 111/112 Chapter 9
Matter as Waves
Louis de Broglie proposed that matter might be viewed as waves as well as particles.
de Broglie suggested that the wavelength of matter is given by
where h is Planck’s constant, p is momentum, m is mass, and v is velocity.
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20. Example: de Broglie Wavelength
Chemistry 111/112 Chapter 9
Example: de Broglie Wavelength
At room temperature, the average speed of an electron is 1.3×105 m/s. The mass of the electron is about 9.11×10-31 kg. Calculate the wavelength of the electron under these conditions.
What is the wavelength of a marathon runner moving at a speed of 5 m/s?
(mass of the runner is 52 kg)
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21. Uncertainty h (x) (mv)  4
Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:
Cannot know precisely where and with what momentum an electron is.
New ideas for determining this information based on probability
Quantum Mechanics was born
(x) (mv)  h 4

22. Chemistry 111/112 Chapter 9
Standing Waves
The vibration of a string is restricted to certain wavelengths because the ends of the string cannot move.
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23. de Broglie Waves in the H Atom
Chemistry 111/112 Chapter 9
de Broglie Waves in the H Atom
The de Broglie wave of an electron in a hydrogen atom must be a standing wave, restricting its wavelength to values of l = 2pr/n, with n being an integer.
This leads directly to quantized angular momentum, one of Bohr’s assumptions.
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24. Schrödinger Wave Equation
Chemistry 111/112 Chapter 9
Schrödinger Wave Equation
The wave function (Y) gives the amplitude of the electron wave at any point in space.
Y2 gives the probability of finding the electron at any point in space.
There are many acceptable wave functions for the electron in a hydrogen (or any other) atom.
The energy of each wave function can be calculated, and these are identical to the energies from the Bohr model of hydrogen.
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25. Quantum Numbers in the H Atom
Chemistry 111/112 Chapter 9
Quantum Numbers in the H Atom
The solution of the Schrödinger equation produces quantum numbers that describe the characteristics of the electron wave.
Three quantum numbers, represented by n, l, and ml, describe the distribution of the electron in three dimensional space.
An atomic orbital is a wave function of the electron for specific values of n, l, and ml.
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26. The Principal Quantum Number, n
Chemistry 111/112 Chapter 9
The Principal Quantum Number, n
The principal quantum number, n, provides information about the energy and the distance of the electron from the nucleus.
Allowed value of n are 1, 2, 3, 4, …
The larger the value of n, the greater the average distance of the electron from the nucleus.
The term principal shell (or just shell) refers to all atomic orbitals that have the same value of n.
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27. Angular Momentum Quantum Number, l
Chemistry 111/112 Chapter 9
Angular Momentum Quantum Number, l
The angular momentum quantum number, l, is associated with the shape of the orbital.
Allowed values: 0 and all positive integers up to n-1.
The l quantum number can never equal or exceed the value of n.
A subshell is all possible orbitals that have the same values of both n and l.
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28. Notations for Subshells
Chemistry 111/112 Chapter 9
Notations for Subshells
To identify a subshell, values for both n and l must be assigned, in that order.
The value of l is represented by a letter:
l etc.
letter s p d f g h etc.
Thus, a 3p subshell has n = 3, l = 1.
A 2s subshell has n = 2, l = 0.
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29. Magnetic Quantum Number, ml
Chemistry 111/112 Chapter 9
Magnetic Quantum Number, ml
The magnetic quantum number, ml, indicates the orientation of the atomic orbital in space.
Allowed values: all whole numbers from –l to l, including 0.
A wave function described by all three quantum numbers (n, l, ml) is called an orbital.
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30. Allowed Combinations of n, l, ml
Chemistry 111/112 Chapter 9
Allowed Combinations of n, l, ml n l ml
# orbitals 1 2
-1, 0, +1 3
-2, -1, 0, +1, +2 5 4
-3, -2, -1, 0, +1, +2, +3 7
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31. Example: Quantum Numbers
Chemistry 111/112 Chapter 9
Example: Quantum Numbers
Give the notation for each of the following orbitals if it is allowed. If it is not allowed, explain why.
(a) n = 4, l = 1, ml = 0
(b) n = 2, l = 2, ml = -1
(c) n = 5, l = 3, ml = +3
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32. Chemistry 111/112 Chapter 9
Test Your Skill
For each of the following subshells, give the value of the n and the l quantum numbers.
(a) 2s
(b) 3d
(c) 4p
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33. Chemistry 111/112 Chapter 9
Electron Spin
An electron behaves as a small magnet that is visualized as coming from the electron spinning.
The electron spin quantum number, ms, has two allowed values: +1/2 and -1/2.
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34. Electron Density Diagrams
Chemistry 111/112 Chapter 9
Electron Density Diagrams
Different densities of dots or colors are used to represent the probability of finding the electron in space.
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35. Chemistry 111/112 Chapter 9
Contour Diagrams
In a contour diagram, a surface is drawn that encloses some fraction of the electron probability (usually 90%).
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36. Chemistry 111/112 Chapter 9
Shapes of p Orbitals
p orbitals (l = 1) have two lobes of electron density on opposite sides of the nucleus.
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37. Orientation of the p Orbitals
Chemistry 111/112 Chapter 9
Orientation of the p Orbitals
There are three p orbitals in each principal shell with an n of 2 or greater, one for each value of ml.
They are mutually perpendicular, with one each directed along the x, y, and z axes.
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38. Shapes of the d Orbitals
Chemistry 111/112 Chapter 9
Shapes of the d Orbitals
The d orbitals have four lobes where the electron density is high.
The dz2 orbital is mathematically equivalent to the other d orbitals, in spite of its different appearance.
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39. Energies of Hydrogen Atom Orbitals
Chemistry 111/112 Chapter 9
Energies of Hydrogen Atom Orbitals
The energies of the hydrogen atom orbitals depend only on the value of the n quantum number.
The s, p, d, and f orbitals in any principal shell have the same energies.
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40. Other One-Electron Systems
Chemistry 111/112 Chapter 9
Other One-Electron Systems
The energy of a one-electron species also depends on the value of n, and are given by the equation
where Z is the charge on the nucleus.
This equation applies to all one-electron species (H, He+, Li2+, etc.).
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41. Effective Nuclear Charge
Chemistry 111/112 Chapter 9
Effective Nuclear Charge
In multielectron atoms, the energy dependence on nuclear charge must be modified to account for interelectronic repulsions.
The effective nuclear charge is a weighted average of the nuclear charge that affects an electron in the atom, after correction for the shielding by inner electrons and interelectronic repulsions.
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42. Effective Nuclear Charge
Chemistry 111/112 Chapter 9
Effective Nuclear Charge
Electron shielding is the result of the influence of inner electrons on the effective nuclear charge.
The effective nuclear charge that affects the outer electron in a lithium atom is considerably less than the full nuclear charge of 3+.
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43. Chemistry 111/112 Chapter 9
Energy Dependence on l
The 2s electron penetrates the electron density of the 1s electrons more than the 2p electrons, giving it a higher effective nuclear charge and a lower energy.
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44. Multielectron Energy Level Diagram
Chemistry 111/112 Chapter 9
Multielectron Energy Level Diagram
Within any principal shell, the energy increases in the order of the l quantum number: 4s < 4p < 4d < 4f.
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45. Increasing Energy Order
Chemistry 111/112 Chapter 9
Increasing Energy Order
Based on experimental observations, subshells are usually occupied in the order
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p
< 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d
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46. Electrons in Multielectron Atoms
Chemistry 111/112 Chapter 9
Electrons in Multielectron Atoms
Each electron in a multielectron atom can be described by hydrogen-like wave functions by assigning values to the four quantum numbers n, l, ml, and ms.
These wavefunctions differ from those in the hydrogen atom because of interelectronic repulsions.
The energy of these wave functions depends on both n and l.
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47. Pauli Exclusion Principle
Chemistry 111/112 Chapter 9
Pauli Exclusion Principle
The Pauli Exclusion Principle: no two electrons in the same atom can have the same set of four quantum numbers.
A difference in only one of the four quantum numbers means that the sets are different.
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48. Chemistry 111/112 Chapter 9
The Aufbau Principle
The aufbau principle: as electrons are added to an atom one at a time, they are assigned the quantum numbers of the lowest energy orbital that is available.
The resulting atom is in its lowest energy state, called the ground state.
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49. Chemistry 111/112 Chapter 9
Orbital Diagrams
An orbital diagram represents each orbital with a box, with orbitals in the same subshell in connected boxes; electrons are shown as arrows in the boxes, pointing up or down to indicate their spins.
Two electrons in the same orbital must have opposite spins. ↑↓
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50. Electron Configuration
Chemistry 111/112 Chapter 9
Electron Configuration
An electron configuration lists the occupied subshells using the usual notation (1s, 2p, etc.). Each subshell is followed by a superscripted number giving the number of electrons present in that subshell.
Two electrons in the 2s subshell would be 2s2 (spoken as “two-ess-two”).
Four electrons in the 3p subshell would be 3p4 (“three-pea-four”).
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51. Electron Configurations of Elements
Chemistry 111/112 Chapter 9
Electron Configurations of Elements
Hydrogen contains one electron in the 1s subshell.
1s1
Helium has two electrons in the 1s subshell.
1s2 ↑ ↑↓
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52. Electron Configurations of Elements
Chemistry 111/112 Chapter 9
Electron Configurations of Elements
Lithium has three electrons.
1s2 2s1
Beryllium has four electrons.
1s2 2s2
Boron has five electrons.
1s2 2s2 2p1 ↑↓ ↑ ↑↓ ↑↓ ↑↓ ↑↓ ↑
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53. Orbital Diagram of Carbon
Chemistry 111/112 Chapter 9
Orbital Diagram of Carbon
Carbon, with six electrons, has the electron configuration of 1s2 2s2 2p2.
The lowest energy arrangement of electrons in degenerate (same-energy) orbitals is given by Hund’s rule: one electron occupies each degenerate orbital with the same spin before a second electron is placed in an orbital. ↑↓ ↑↓ ↑
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54. Other Elements in the Second Period
Chemistry 111/112 Chapter 9
Other Elements in the Second Period
N 1s2 2s2 2p3
O 1s2 2s2 2p4
F 1s2 2s2 2p5
Ne 1s2 2s2 2p6 ↑↓ ↑↓ ↑ ↑↓ ↑↓ ↑↓ ↑ ↑↓ ↑↓ ↑↓ ↑ ↑↓ ↑↓ ↑↓
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55. Electron Configurations of Heavier Atoms
Chemistry 111/112 Chapter 9
Electron Configurations of Heavier Atoms
Heavier atoms follow aufbau principle in organization of electrons.
Because their electron configurations can get long, larger atoms can use an abbreviated electron configuration, using a noble gas to represent core electrons.
Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d6 → [Ar] 4s2 3d6 Ar
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56. Anomalous Electron Configurations
Chemistry 111/112 Chapter 9
Anomalous Electron Configurations
The electron configurations for some atoms do not strictly follow the aufbau principle; they are anomalous.
Cannot predict which ones will be anomalous.
Example: Ag predicted to be
[Kr] 5s2 4d9; instead, it is
[Kr] 5s1 4d10.
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