1. 1411 Chapter 6 Electronic Structure of Atoms

2. Electronic Structure of Atoms
Electronic structure of atoms – the number of electrons in an atom and the energies and distribution of the electrons around the nucleus
To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.
Electromagnetic radiation (radiant energy) – a form of energy that has wave characteristics

3. Waves
The distance between corresponding points on adjacent waves is the wavelength ()
units: length
The number of waves passing a given point per unit of time is the frequency ()
units: inverse time, ie s-1 or 1/s
1 1/s = 1 hertz (Hz)

4. Electromagnetic Radiation: Nature of Energy: Wave-like
Heat from glowing fireplace
Breaks chemical bonds like in DNA of skin cells
Electromagnetic spectrum
range of all frequencies (or wavelengths) of electromagnetic radiation
All electromagnetic radiation travels at the same velocity: the speed of light (c),
3.00  108 m/s.
c = 
(so wavelength and frequency are inversely related)
Dentistry
Radiation cancer therapy
Microwaves,
Wi-Fi
Radio, TV, cell phones
The portion of the electromagnetic spectrum that the human eye can detect!

5. Example
An FM radio station broadcasts at a frequency of MHz. What is the wavelength of these radio waves expressed in kilometers?
c = 
c = 3.00 x 108 m/s
 = MHz
 = ? (km)
101.1 MHz
c =    = c/
 = (3.00 x 108 m/s) / (1.011 x 108 1/s)
 = m
2.967 m
106 Hz
1 MHz x
= x 108 Hz
= x 108 1/s = 
1 km
1000 m x
= x 10-3 km  2.97 x 10-3 km

6. Nature of Energy: Not just wave-like!
The wave nature of light does not explain how an object can glow when its temperature increases.
Max Planck
explained it by assuming that energy can be either released or absorbed by atoms only in discrete “chunks” of some minimum size
energy comes in packets called quanta (singular: quantum = “fixed amount”).
quantum – the smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation

7. Planck’s Quantum Theory
The energy E of a single quantum is proportional to its frequency:
E = h
where h is Planck’s constant,  10−34 J-s.
Matter is allowed to emit and absorb energy only in whole-number multiples of h, (ie h, 2h, 3h, etc)
So the allowed energies are quantized – values are restricted to certain amounts
Can be compared to climbing stairs – you only gain potential energy in set (quantized) levels of energy, as opposed to climbing a ramp, in which you gain PE in a continuous, uniform manner

8. Nature of Energy: Particle-like
photoelectric effect – the emission of electrons from a metal surface.
The radiant energy striking the metal surface behaves not like a wave, but like a stream of tiny particles or energy packets, called photons.
photon – the smallest increment (a quantum) of radiant energy; can be thought of as a “particle” of light
Einstein extended Planck’s quantum theory to conclude that each photon has an energy equal to…
Energy of a photon = E = h

9. Nature of Energy: Wave-like AND Particle-like
Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or particle, of that light:
c = 
E = h
So…. does light behave as a wave or does it consist of particles?
Light possesses the characteristics of BOTH!
So light can be more particle-like OR more wave-like, depending on situation

10. Nature of Energy: Spectra
When light is passed through a prism, the radiation is separated into its different wavelength components, to produce a spectrum.
From a white light source, one gets a continuous spectrum.
For atoms and molecules one instead only observes a line spectrum of discrete wavelengths.

11. Nature of Energy: Bohr’s Model
Niels Bohr assumed electrons “orbit” the nucleus of an atom, and he adopted Planck’s assumption and explained these phenomena in this way:
Only orbits of certain radii, corresponding to certain energies, are permitted for the electrons.
These energies of the electrons will not be radiated from the atom, so the electron doesn’t spiral into the nucleus.
Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy level to another; the energy is defined by
E = h

12. Nature of Energy: Bohr’s Model
Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy level to another; the energy is defined by
E = h
We call energy levels n, which represents the principal quantum number
Ground state (n = 1) – lowest energy level
Excited state (n = 2 or more) – higher energy level
Electrons can “jump” from lower energy levels to higher energy levels by absorbing photons (energy), which correspond exactly in energy to the difference in energy levels
Electronic transition: n = 1 to n = 2
When they “fall” back down, they emit energy
Electronic transition: n = 3 to n = 2
nucleus

13. Analysis of Bohr’s Model
Limitations
Problem with describing an electron merely as a small particle circling nucleus
Negatively charged particle circling positively charged nucleus would eventually fall into it
Only explains line spectra for hydrogen, but only applies crudely to other elements
Concepts still in use
Electrons exist only in certain discrete energy levels, which are described by quantum numbers
Energy is involved in moving an electron from one level to another

14. Wave Nature of Matter h mv  =
Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties.
He demonstrated that the relationship between mass and wavelength of any matter (electron or large object) was
 = h mv
 = wavelength
h = Planck’s constant (6.626 x J-s)
m = mass of object
v = velocity of object
momentum

15. The Uncertainty Principle
Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known (the uncertainty principle)
So we can’t locate exactly where an electron is within an atom, but we can describe its location in terms of probability of where we might find it.

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

17. Quantum Mechanics
The wave equation (describes the electron in an atom) is designated with a lower case Greek psi ().
The square of the wave equation, 2
gives a probability density map of where an electron has a likelihood of being at any given instant
2 is called the probability density or electron density

18. Quantum Numbers
Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies
Each orbital describes a specific distribution of electron density in space
So each orbital has a characteristic energy and shape
An orbital is described by a set of three quantum numbers:
n, l, ml

19. Quantum Numbers: Principal Quantum Number (n)
The principal quantum number, n, describes the energy level on which the orbital resides.
The allowed values of n are integers ≥ 1.
As n gets larger,
electrons have higher energy
orbital size gets larger
electrons are further from nucleus
electrons are less tightly bound to nucleus

20. Quantum Numbers: Angular Momentum Quantum Number (l)
The angular momentum quantum number, l, defines the shape of the orbital.
Allowed values of l are integers ranging from:
0 to (n − 1)
We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.
Value of l 1 2 3
Type of orbital s p d f

21. Quantum Numbers: Magnetic Quantum Number (ml)
The magnetic quantum number, ml, describes the three-dimensional orientation of the orbital
meaning, does it point in the x, y, or z direction on a 3D graph
Allowed values of ml are integers ranging from -l to l:
−l ≤ ml ≤ l
Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.
Replace last bullet point with “number of possible ml values gives the number of orbitals – the actual ml value doesn’t mean anything”

22. Quantum Numbers Orbitals with the same value of n form a shell.
Ex: All the orbitals that have n = 2 are in the second shell
Different orbital shapes within a shell are subshells.
That means they have the same n and l values
Designated by a number (n) and a letter (l value – s, p, d, or f)

23. Quantum Numbers
How to make predictions about quantum numbers and orbitals WITHOUT using the chart:
# possible values of l = # of subshells in a shell = n
In other words, the shell with principal quantum number n will consist of exactly n subshells
Ex: For n = 4, there are 4 possible values of l so there are 4 subshells (4s, 4p, 4d, and 4f)
# of orbitals in a subshell = # of possible values of ml = 2l + 1
In other words, each subshell consists of a specific number of orbitals, which equals the number of allowed values of ml (# allowed values of ml = 2l + 1)
Ex: Each d (l = 2) subshell has (2*2 + 1) = 5 orbitals because ml can be 2, 1, 0, -1, -2
# of orbitals in a shell = # of possible values of ml = n2
In other words, the total number of orbitals in a shell is n2
Ex: For n = 4, there are 42 = 16 possible values of ml so there are 16 orbitals

24. Quantum Numbers
How to make predictions about quantum numbers and orbitals WITHOUT using the chart:
# possible values of l = # of subshells in a shell = n
In other words, the shell with principal quantum number n will consist of exactly n subshells
Ex: For n = 4, there are 4 possible values of l so there are 4 subshells (4s, 4p, 4d, and 4f)
# of orbitals in a subshell = # of possible values of ml = 2l + 1
In other words, each subshell consists of a specific number of orbitals, which equals the number of allowed values of ml ( = 2l + 1)
Ex: Each d (l = 2) subshell has (2*2 + 1) = 5 orbitals because ml can be 2, 1, 0, -1, -2
# of orbitals in a shell = # of possible values of ml = n2
In other words, the total number of orbitals in a shell is n2
Ex: For n = 4, there are 42 = 16 possible values of ml so there are 16 orbitals

25. Quantum Numbers
How to make predictions about quantum numbers and orbitals WITHOUT using the chart:
# possible values of l = # of subshells in a shell = n
In other words, the shell with principal quantum number n will consist of exactly n subshells
Ex: For n = 4, there are 4 possible values of l so there are 4 subshells (4s, 4p, 4d, and 4f)
# of orbitals in a subshell = # of possible values of ml = 2l + 1
In other words, each subshell consists of a specific number of orbitals, which equals the number of allowed values of ml ( = 2l + 1)
Ex: Each d (l = 2) subshell has (2*2 + 1) = 5 orbitals because ml can be 2, 1, 0, -1, -2
# of orbitals in a shell = # of possible values of ml = n2
In other words, the total number of orbitals in a shell is n2
Ex: For n = 4, there are 42 = 16 possible values of ml so there are 16 orbitals

26. Quantum Numbers
How to make predictions about quantum numbers and orbitals WITHOUT using the chart:
# possible values of l = # of subshells in a shell = n
In other words, the shell with principal quantum number n will consist of exactly n subshells
Ex: For n = 4, there are 4 possible values of l so there are 4 subshells (4s, 4p, 4d, and 4f)
# of orbitals in a subshell = # of possible values of ml = 2l + 1
In other words, each subshell consists of a specific number of orbitals, which equals the number of allowed values of ml ( = 2l + 1)
Ex: Each d (l = 2) subshell has (2*2 + 1) = 5 orbitals because ml can be 2, 1, 0, -1, -2
# of orbitals in a shell = # of possible values of ml = n2
In other words, the total number of orbitals in a shell is n2
Ex: For n = 4, there are 42 = 16 possible values of ml so there are 16 orbitals
Examples:
How many orbitals are there in the fifth shell?
How many orbitals are there in the 2p subshell?
How many values of l are there in the 10th shell?
n2 = 52 = 25
2l + 1 = 2(1) + 1 = 3
# possible l values = n = 10

27. Picturing Orbitals: s Orbitals
They are spherical in shape.
l = 0 for s orbitals.
So ml is also 0
Only 1 ml possibility = only 1 s orbital for each value of n
This makes sense because there is no 3D direction because it is a sphere
Can have s orbitals when n = 1 or more
The radius of the sphere increases as n gets larger.
Reminders:
Allowed values:
n: integers ≥ 1
l: to (n − 1)
ml : −l to l
Value of l 1 2 3
Type of orbital s p d f

28. Picturing Orbitals: p Orbitals
They have two lobes with a node between them.
node - region where there is 0 probability of finding an electron
l = 1 for p orbitals
So ml can be -1, 0, 1
3 ml possibilities = 3 orbitals with different directions in space
Can have p orbitals when n = 2 or more
They get larger as n gets larger
Reminders:
Allowed values:
n: integers ≥ 1
l: to (n − 1)
ml : −l to l
Value of l 1 2 3
Type of orbital s p d f

29. Picturing Orbitals: d Orbitals
Four of the five have “4-leaf clover” shapes
The other resembles a p orbital with a doughnut around the center.
l = 2 for d orbitals
So ml can be -2, -1, 0, 1, or 2
5 ml possibilities = 5 different orbitals
Can have d orbitals when n = 3 or more
Reminders:
Allowed values:
n: integers ≥ 1
l: to (n − 1)
ml : −l to l
Value of l 1 2 3
Type of orbital s p d f

30. Picturing Orbitals: f Orbitals
Too complicated to picture
l = 3 for f orbitals
So ml can be -3, -2, -1, 0, 1, 2, or 3
7 ml possibilities = 7 different orbitals
Can have f orbitals when n = 4 or more
Reminders:
Allowed values:
n: integers ≥ 1
l: to (n − 1)
ml : −l to l
Value of l 1 2 3
Type of orbital s p d f

31. Energies of Orbitals
For a one-electron hydrogen atom, orbitals on the same energy level (same value of n) have the same energy.
That is, they are degenerate.

32. Energies of Orbitals
As the number of electrons increases, though, so does the repulsion between them.
So in many-electron atoms, orbitals on the same energy level are no longer degenerate.
In a many-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l
So 3s < 3p < 3d

33. Spin Quantum Number, ms
In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.
The “spin” of an electron describes its magnetic field, which affects its energy.
This led to a fourth quantum number, the spin quantum number, ms.
The spin quantum number has only 2 allowed values: +1/2 and −1/2.

34. Pauli Exclusion Principle
No two electrons in the same atom can have exactly the same energy.
Therefore, no two electrons in the same atom can have identical sets of quantum numbers (Pauli exclusion principle).
So one orbital can only hold a maximum of TWO electrons
one with ms = +1/2 and one with ms = -1/2

35. Examples
What is the maximum number of electrons that can exist in an atom with the following sets of quantum numbers?
n = 3
n = 6, l = 4
n = 4, l = 3, ml = -2
n = 2, ms = +1/2
n = 5, l = 3, ml = -1, ms = -1/2
# ml values = n2 = 32 = 9 orbitals *2 electrons = 18
# ml values = 2l + 1 = 2(4) + 1 = 9 orbitals *2 electrons = 18
# ml values = 1 orbital *2 electrons = 2
# ml values = n2 = 22 = 4 orbitals *1 electron = 4
No two electrons in an atom can have all 4 quantum #s the same, so only 1

36. Electron Configurations
Electron configuration - shows the distribution of all electrons in an atom.
Each component consists of:
A number denoting the energy level,
A letter denoting the type (shape) of orbital,
A superscript denoting the number of electrons in that subshell.
Number of electrons in that subshell
Energy level
4p5
The subshell
Orbital type

37. Using the Periodic Table to Determine Electron Configurations
We fill orbitals in increasing order of energy.
Different blocks on the periodic table (shaded in different colors in this chart) correspond to different types of orbitals.

38. Using the Periodic Table to Determine Electron Configurations
We fill the orbitals by starting with the first period and working our way across, with up to 2 electrons per orbital
Fill 1s with 2 electrons
Fill 2s with 2 electrons
Fill 2p with 6 electrons
Fill 3s with 2 electrons
Fill 3p with 6 electrons
Fill 4s with 2 electrons
Fill 3d with 10 electrons
Fill 4p with 6 electrons
Etc…

39. Using the Periodic Table to Determine Electron Configurations
Handy tip to remember how to fill subshells: 1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f

40. Electron Configurations
Determining electron configuration for an element or ion
Determine the number of electrons in the element or ion
Write the symbol for each occupied subshell
Add a superscript to indicate the number of electrons in each subshell
The orbitals are filled in order of increasing energy, with no more than two electrons per orbital
Examples: Write the electron configurations for the following atoms:
1s1
1s2
1s22s22p63s23p3
1s22s22p63s23p64s23d3 H He P V Tl
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p1

41. Electron Configurations
We can write a condensed electron configuration for an element by writing the noble gas preceding that element in brackets and then writing the rest of the electron configuration as normal
Example:
Ge: [Ar]4s23d104p2
Li: [He]2s1
inner-shell electrons = core electrons
outer-shell electrons = valence electrons

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

43. Some Anomalies
For instance, the electron configuration for chromium is
[Ar] 4s1 3d5
rather than the expected
[Ar] 4s2 3d4.

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

45. Orbital Diagrams Each box in the diagram represents one orbital.
Half-arrows represent the electrons.
The direction of the arrow represents the relative spin of the electron.

46. Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”
In other words, don’t start pairing up electrons until all orbitals in a subshell have been filled with unpaired electrons