### Slide 1

```AP Chapter 6
Electronic Structure of Atoms
HW: 5 7 29 35 63 67 69 71 73 75
6.1 – Wave Nature of Light
-Electromagnetic Radiation = Emission and transmission of energy
in the form of waves
-examples: visible light, infrared, UV, X-Rays
-Electromagnetic wave = Travels at the speed of light = 3.0x108
m/s in a vacuum
Electromagnetic Spectrum =
(display of electromagnetic radiation by wavelength)
6.1 – Wave Nature of Light
-Wavelength = l = Distance between identical points on successive
waves. Unit = Angstrom (A), nm, mm
-Frequency = n = # of waves passing a point in a given unit of time
(typically 1 second). Unit = Hz = 1/s
-Speed of the wave = c = ln
-Amplitude = Height
-Node = Amplitude = 0
A high frequency wave must have a
short wavelength
A low frequency wave must have a long
wavelength
6.1 – Wave Nature of Light
Calculate:
The yellow light given off by a sodium vapor lamp
used for public lighting has a wavelength of 589
nm. What is the frequency of this radiation?
(answer = 5.09 x 1014 s-1)
6.2 – Quantized Energy and Photons
• Wave nature alone cannot explain all
behaviors of light
– Emission of light from hot objects
– Emission of electrons from metal
surfaces on which light shines
(photoelectric effect)
– Emission of light from electronically
excited gas atoms (emission spectra)
6.2 – Quantized Energy and Photons
• He concluded that energy of a single quantum is equal
to a constant times the frequency of the radiation:
E = hn
where h is Planck’s constant, 6.63  10−34 Js.
• Max Planck explained it by assuming that energy
comes in “chunks” called quanta.
• Quantum = The smallest quantity of energy that can
be emitted or absorbed
• Quantum Theory – Atoms and molecules emit and
absorb energy in discrete quantities only
• Photon = A quantum of light energy
• Therefore, if one knows the
wavelength of light, one can
calculate the energy in one
photon, or packet, of that
light:
c = ln
E = hn
6.2 – Quantized Energy and Photons
a) A laser emits light with a frequency of 4.69 x 1014
s-1. What is the energy of one photon of the
b) If the laser emits a pulse of energy containing 5.0
x 1017 photons, what is the total energy of that
pulse?
c) If the laser emits 1.3 x 10-2 J of energy during a
pulse, how many photons are emitted during the
pulse?
a) 3.11 x 10-19 J
b) 0.16 J
c) 4.2 x 1016 photons
6.3 – Line Spectra and the Bohr Model
Emission Spectrum = Spectrum of radiation emitted by a
substance/energy source – can be continuous or line spectrum
depending on the substance
(continuous spectrum)
When observing the emission spectra of
atoms/molecules, only a line spectrum of discrete
wavelengths is observed.
(line spectrum)
6.3 – Line Spectra and the Bohr Model
The energy absorbed or emitted from the process of
electron promotion or demotion can be calculated by
the equation:
E = -RH (
1
nf2
-
1
ni 2
)
where RH is the Rydberg constant, 2.18  10−18 J, and ni
and nf are the energy levels of the electron
-If nf is smaller than ni, then the e- moves closer to the
nucleus and E is negative
-If nf is larger than ni, then the e- moves farther from
the nucleus and E is positive
-Each line on the line spectrum of Hydrogen can be
calculated using this equation.
6.3 – Line Spectra and the Bohr Model
Ground State = Lowest energy state for the
electron
Excited State = A higher energy state
6.3 – Bohr’s Model of the Hydrogen Atom
•
assumption and explained these
phenomena in this way:
1. Electrons in an atom can only
occupy certain orbits
(corresponding to certain energies).
2. Electrons in permitted orbits have
specific, “allowed” energies; these
energies will not be radiated from
the atom.
3. Energy is only absorbed or emitted
in such a way as to move an
electron from one “allowed” energy
state to another; the energy is
defined by
E = hn
Quantum Mechanics Preview:
6.4 - The Wave Behavior of Matter
• Louis de Broglie posited that if light can
have material properties, matter (electrons
in atoms) should exhibit wave properties.
• He demonstrated that the relationship
between mass and wavelength was:
h
l = mn
This equation relates the wave (l) and particle (m) natures
6.4 – The Wave Behavior of Matter
• Heisenberg Uncertainty Principle:
Heisenberg showed that the more precisely the
momentum of a particle is known, the less
precisely its position known
It is impossible to know both the momentum and
the position of an electron
6.5 - Quantum Mechanics
• Erwin Schrödinger
developed a mathematical
treatment (Schrodinger
Wave Equation) into which
both the wave and particle
nature of matter could be
incorporated.
• It is known as quantum
mechanics.
6.5 -Quantum Mechanics
• The wave equation 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
certain statistical likelihood of
being at any given instant in
time = electron density
Orbitals and Quantum Numbers
• Solving the wave equation gives a set of
wave functions, or orbitals, and their
corresponding energies.
• Each orbital describes a spatial distribution
of electron density.
• An electron is described by a set of four
quantum numbers.
Principal Quantum Number, n
• The principal quantum number, n,
describes the energy level on which the
orbital resides.
• It is a measure of the distance from the
nucleus.
• The values of n are integers ≥ 0.
• Now 1-7
Angular Momentum Quantum
Number, l
• This quantum number 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.
Angular Momentum
Quantum Number, l
Value of l
0
1
2
3
Type of orbital
s
p
d
f
Magnetic Quantum Number, m l
• Describes the three-dimensional orientation of
the orbital.
• Values are integers ranging from - l to l :
−l ≤ ml ≤ l
• Therefore, on any given energy level, there can
be up to
–
–
–
–
s = 0 = one s orbital
p = -1, 0, 1 = three p orbitals
d= -2,-1,0,1,2 = five d orbitals,
f=-3,-2,-1,0,1,2,3 = seven f orbitals
Magnetic Quantum Number, m l
• Orbitals with the same value of n form a shell.
– Ex – The n=3 shell has an s orbital, three p orbitals and
five d orbitals
• The set of orbitals with the same shape within a
shell form a subshells.
– Ex = there are three orbitals in a p subshell)
Spin Quantum Number
• Each e- in one orbital must have opposite
spins
• Symbol – ms
• +½,-½
– Two “allowed” values and corresponds to
direction of spin
6.6 – Representation of Orbitals
The s Orbital
• Value of l = 0.
• Spherical in shape.
increases with increasing
value of n.
increases with increasing
energy of the electron(s).
p Orbitals
• Value of l = 1.
• Have two lobes with a node (no probability of
finding electron) between them.
d Orbitals
• Value of l is 2.
• Four of the five
orbitals have 4
lobes; the other
resembles a p
orbital with a
doughnut
around the
center.
f Orbitals
Higher than f not currently needed…
AP EXAM QUESTIONS:
List the four quantum numbers for the
valence electrons in magnesium.
List in order – n, l, m l , ms
Valence electrons: 3s2
1
Electron 1 = 3,0,0, 2
Electron 2 = 3,0,0,- 1
2
AP EXAM QUESTIONS:
List the four quantum numbers for the valence
electrons in Nitrogen.
Energies of Orbitals
• For a one-electron
hydrogen atom,
orbitals on the same
energy level have the
same energy.
• That is, they are
degenerate.
6.7 – Many Electron Atoms
• As the number of
electrons increases,
though, so does the
repulsion between them.
• Therefore, in manyelectron atoms, orbitals
on the same energy level
(principle quantum
number) are no longer
degenerate.
• This is the order we use
from the periodic table to
fill orbitals = Aufbau
Principle = electrons fill
from low to high energy
Pauli Exclusion Principle
• No two electrons in the
same atom can have
exactly the same energy.
• Also means that no two
electrons in the same atom
can have identical sets of
quantum numbers.
6.8 - Electron Configurations
• Shows the distribution of
all electrons in an atom
• Consist of
– Number denoting the
energy level
Electron Configurations
• Distribution of all
electrons in an atom
• Consist of
– Number denoting the
energy level
– Letter denoting the type of
orbital
Electron Configurations
• Distribution of all
electrons in an atom.
• Consist of
– Number denoting the
energy level.
– Letter denoting the type of
orbital.
– Superscript denoting the
number of electrons in
those orbitals.
Practice: N, Zr, Bi
Orbital Diagrams
• Each box represents one
orbital.
• Half-arrows represent the
electrons.
• The direction of the
arrow represents the spin
of the electron.
Practice: B, Si
Hund’s Rule
“For degenerate orbitals, the lowest energy is
attained when the number of electrons with the
same spin is maximized.”
(In a p, d or f subshell, fill each orbital with ONE
electron before pairing any)
• Diagmagnetism = Repelled by a magnet =
Has all paired electrons with opposite spins
• Paramagnetism = Attracted to a magnet =
has at least one unpaired electron
• Shielding = Inner electrons block outer
electrons from the electrostatic force of
the nucleus
• Valence electrons = Outer-shell electrons
involved in bonding
Condensed Electron Configurations
• Begin at the NOBLE GAS (Has full valence shell)
before the element. Write that symbol in
[brackets]
• Continue on with the rest of the configuration
Practice: Na, As, Ag, At
Periodic Table
• Different blocks on
the periodic table,
then correspond to
different types of
orbitals.
Some Anomalies
Some irregularities
occur when there
are enough
electrons to half-fill
s and d orbitals on
a given row.
Some Anomalies
Group 6:
Ex - Chromium is
[Ar] 4s1 3d5
rather than the
expected
[Ar] 4s2 3d4.
Group 11:
Ex - Copper is
[Ar] 4s1 3d10
rather than the
expected
[Ar] 4s2 3d9.
Some Anomalies
• This occurs because
the 4s and 3d
orbitals are very
close in energy and a
half-filled d is more
stable than
“missing” 1 e-.
• These anomalies
occur in f-block
atoms, as well (Sm
and Pu and Tm and
Md)
```