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Quantum Theory and the
Electronic Structure of Atoms
Chapter 7
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
What is light?
• A form of _____________________________
– energy that exhibits wavelike behavior as it travels
through space
Wave Properties
_____________________:
• distance between
corresponding points on
adjacent waves
• Unit:
____________________:
• number of waves that
pass a given point per unit
time (usually 1 sec)
• Unit:
Properties of Light
• How are frequency and wavelength related?
A photon has a frequency of 6.0 x 104 Hz. Convert
this frequency into wavelength (nm). Does this frequency
fall in the visible region?
Max Planck proposed …
Energy needed for electrons to move was
quantized, or a quantum of energy is needed to
move an electron.
E = hn
E = hn
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.
ELECTRON MOVEMENT
Electrons are always moving!
• The farther the electron is from the nucleus,
the more energy it has.
• Electrons can change energy levels and
emit a __________________________
–
–
Definitions
• Ground State:
– ALL electrons are in the lowest possible energy levels
• Excited State:
– Electrons absorb energy and are boosted to a higher
energy level
• Emission:
– when an electron falls to a lower energy level, a
photon is emitted
• Absorption:
– energy must be added to an atom in order to move an
electron from a lower energy level to a higher energy
level
Bohr’s Model of
the Atom (1913)
1. e- can only have specific
(quantized) energy
values
2. light is emitted as emoves from a higher
energy level to a lower
energy level
Line Spectrum
• Every element has a different number of
electrons.
• Every element will have different transitions of
electrons between energy levels.
• Each element has their own unique bright line
emission spectrum created from the release
of photons of light.
When are photons released?
Line Emission Spectrum of Hydrogen Atoms
Ephoton = DE = Ef - Ei
Calculate the wavelength (in nm) of a photon
emitted by a hydrogen atom when its electron
drops from the n = 4 state to the n = 3 state.
“Dual Nature” of Light
And Matter
Light has both:
1. particle nature
(energy released as a photon)
2. wave nature
(energy has a specific wavelength and frequency that can be calculated)
Even large objects have a wavelegnth!
Heisenberg Uncertainty Principle
• Electrons have a dual nature:
– If it is a wave: then we know how fast it is
moving
– If it is a particle: then we know its position
Schrodinger Wave Equation
equation that describes both the particle and wave
nature of the eWe do not know the exact position or speed, but:
Schrodinger’s equation can only be solved exactly for
the hydrogen atom. Must approximate its solution for
other atoms.
What did your graph of electron density look like?
We do not know the exact location
of an electron, but we do our best
to DESCRIBE it’s location.
The first four principle energy levels in
the atom.
ENERGY
LEVEL
SUBLEVEL
The first four principle energy levels
and their sub-levels.
SUBLEVEL
ORBITAL
The first four principle energy levels,
their sub-levels, and orbitals.
4f
4d
5s
4p
Energy
3d
4s
3p
3s
2p
2s
1s
Aufbau
Principle
Electrons are added one at a time
Starting at the lowest available
Energy orbital.
4f
4d
5s
4p
Energy
3d
4s
3p
3s
2s
1s
2p
Electron
Configuration for:
Boron
How many electrons can an orbital hold?
Pauli Exclusion
Can not have same set of Quantum Numbers
Principle An orbital holds a max of 2 electrons.
Must have opposite spins.
4f
4d
5s
4p
Energy
3d
4s
3p
3s
2s
1s
2p
Electron
Configuration for:
Boron
Hund’s
Rule
Electrons occupy equal energy orbitals
So that a maximum number of unpaired
Electrons results.
4f
4d
5s
4p
Energy
3d
4s
3p
3s
2s
1s
2p
Electron
Configuration for:
Oxygen
What is the electron configuration of Mg?
4d
5s
Energy
4p
3d
4s
3p
3s
2p
2s
1s
What is the electron configuration of Cl?
4d
5s
Energy
4p
3d
4s
3p
3s
2p
2s
1s
Exceptions
• Chromium
• Copper
Paramagnetic
unpaired electrons
2p
Diamagnetic
all electrons paired
2p
Quantum Numbers
Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
principal quantum number: n
n = 1, 2, 3, 4, ….
n=1
n=2
n=3
Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
angular momentum quantum number: l
for a given value of n, l = 0, 1, 2, 3, … n-1
n = 1, l = 0
n = 2, l = 0 or 1
n = 3, l = 0, 1, or 2
n = 4, l = 0, 1, 2, or 3
l=0
l=1
l=2
l=3
s orbital
p orbital
d orbital
f orbital
Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
magnetic quantum number: ml
for a given value of l
ml = -l, …., 0, …. +l
if l = 0 (s orbital), ml = 0
if l = 1 (p orbital), ml = -1, 0, 1
if l = 2 (d orbital), ml = -2, -1, 0, 1, 2
if l = 3 (f orbital), ml = -3, -2, -1, 0, 1, 2, 3
ml = 0
ml = -1 ml = 0 ml = 1
ml = -2 ml = -1 ml = 0 ml = 1 ml = 2
ml = -3 ml = -2 ml = -1 ml = 0 ml = 1 ml = 2 ml = 3
Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
spin quantum number: ms
ms = +½ or -½
ms = +½
ms = -½
Summary
What are the possible magnetic quantum
numbers for 2p?
How many electrons can have the quantum
numbers: n = 3 and ms = +1/2 ?
What are all the possible quantum numbers for
an electron in 4f?
What are the possible quantum numbers for the
last (outermost) electron in Cl?