Transcript Watchung Hills Regional High School

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 electromagnetic radiation:
– energy that exhibits wavelike behavior as it travels
through space
HIGH
ENERGY
Light is organized on the
Electromagnetic Spectrum
V I
B
G
Y
O
R
LOW
ENERGY
Wave Properties
Wavelength (λ) :
• distance between
corresponding points on
adjacent waves
• Unit: meters or nanometers
Frequency (ν):
• number of waves that pass a
given point per unit time
(usually 1 sec)
• Unit: 1/s = s-1 = Hertz (Hz)
Properties of Light
• How are frequency and wavelength related?
c = λν
c : speed of light (m/s)
c = 3.00 x 108 m/s
λ : wavelength (m)
ν : frequency of wave (s−1 = 1/s = Hz)
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?
l
lxn=c
n
l = c/n
l = 3.00 x 108 m/s / 6.0 x 104 Hz
l = 5.0 x 103 m
l = 5.0 x 1012 nm
Radio wave
Max Planck proposed …
Energy needed for electrons to move was
quantized, or a quantum of energy is needed to
move an electron.
E = hν
E : energy of light emitted (J)
h : Planck’s constant (J·s)
h = 6.626 × 10−34 J·s
ν : frequency of wave (s−1 = 1/s = Hz)
E = hn
E = hn
Electrons can only
move with a
quantum of energy.
Every color
represents a
different amount of
energy released.
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.
E=hxn
E=hxc/l
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
Louis de Broglie proposed …
• that electrons be considered waves
confined to the space around an atomic
nucleus.
– electron waves could exist only at specific
frequencies (energy is still quantized!)
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 photon of light.
– Photon: packet of energy
–Ephoton = hν
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
ni = 3
ni = 2
nf = 2
nf = 1
Ephoton = DE = Ef - Ei
Calculate the wavelength (in nm) of a photon
emitted from an electronic transition from the
n = 4 state to the n = 2 state.
Ephoton = DE = Ef - Ei
Ephoton = DE = 10. x 10-19 – 1.0 x 10-19
Ephoton = DE = 9.0 x 10-19 J
Ephoton = h x c / l
l = h x c / Ephoton
l= 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)
9.0 x 10-19 J
l = 2.2 x 10-7m = 2.2 x 102 nm = 220 nm
“Dual Nature” of Light
And Matter
Light and matter behave as both particles and waves
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
WE CANNOT KNOW AN
ELECTRONS EXACT POSITION OR
SPEED AT THE SAME TIME
Schrodinger Wave Equation
equation that describes both the particle and wave nature of the electron
We do not know the exact position or speed, but:
90% probability of finding e- in a volume of space
Schrodinger’s equation can only be solved exactly for
the hydrogen atom. Must approximate its solution for
other atoms.
Where 90% of the
e- density is found
for the 1s orbital
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.
DO NOW
Get 4 colors from the bin in front.
Answer the question below.
• How would you describe your current
location? Start off really broad, as in Earth,
and describe your location to be more
specific.
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?
An orbital can hold 2 electrons
ms = +½ or -½
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
- Unpaired electron
2p
- Paired electrons
1s
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?
Mg 12 electrons
2 + 2 + 6 + 2 = 12 electrons
4d
5s
Energy
4p
3d
4s
3p
3s
2p
2s
1s
What is the electron configuration of Cl?
Cl 17 electrons
2 + 2 + 6 + 2 + 5 = 17 electrons
4d
5s
Energy
4p
3d
4s
3p
3s
2p
2s
1s
Sublevels on the Periodic Table
Exceptions
• Chromium
• Copper
Paramagnetic
unpaired electrons
2p
Diamagnetic
all electrons paired
2p
Outermost subshell being filled with electrons
Quantum Numbers
Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
principal quantum number: n
distance of e- from the nucleus
n = 1, 2, 3, 4, ….
Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
angular momentum quantum number: l
Shape of the “volume” of space that the e- occupies
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
orientation of the orbital in space
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
direction of electron spin
ms = +½ or -½
ms = +½
ms = -½
Summary
What are the possible magnetic quantum
numbers for 2p?
n=2
If l = 1, then ml = -1, 0, or +1
2p
l=1
How many electrons can have the quantum
numbers: n = 3 and ms = +1/2 ?
If n = 3
then available orbitals are in 3s, 3p, and 3d
How many electrons are only spin up in these orbitals?
What are all the possible quantum numbers for
an electron in 4f?
n=3
l=2
ml = -2, -1, 0, +1 , +2 ms = +½ or -½
What are the possible quantum numbers for the
last (outermost) electron in Cl?
1s22s22p63s23p5
Last electron added to 3p orbital
n=3
l=1
ml = 0
ms = -½