Download ENERGY LEVELS

Ch 5: Electronic
structure
(aka Quantum Theory)
5.3: Electromagnetic Radiation
(aka “Light”)
5.1 & 5.2: Bohr model &
Quantum-mechanical model
Review of Basic Atomic Structure
1. PROTONS – in nucleus, determine
the identity of an atom (what
element it is)
2. NEUTRONS – in nucleus,
contribute to mass
3. ELECTRONS – move around in the
empty space around the nucleus
Determine the way an atom
BEHAVES chemically (how it reacts
or doesn’t react….)
Remember!!!!
Models are made to fit the data…..
If new data is discovered, models
must be changed to fit the new
data.
Quick Review of older models
DATA:
Mass
conservation
experiments
MODEL:
Dalton’model: Thompson’s
1800-1803
plum-pudding
model, 1897
Rutherford’s
nuclear atomic
model, 1911
So, what new data made it necessary
to come up with the QUANTUM
ATOMIC MODEL?
EVIDENCE: Atomic emission spectra of
HYDROGEN
SPECTRAL TUBE—
tube filled with an element in gas form.
When you apply a voltage, it emits light.
Here’s a little something to compare
with… white, natural sunlight has an
emission spectrum like this….
LAB-related question:
How do you split up light
into its component parts?
DISPERSION BY PRISM or USE OF DIFFRACTION
GRATING—separates light into its components
(what we see as one color may actually be
composed of light of various colors)
NEW DATA that led to the
QUANTUM atomic model
___________’s atomic
HYDROGEN
emission spectrum is
DISCRETE, not CONTINUOUS
_______________________
Violet
410nm
Blue
434nm
Blue-Green
486 nm
Red
656nm
Balmer
Series
I don’t
get it –
why are
those
LINES
such a big
deal?!
In order to understand WHY/ HOW the
emission spectra relates to the
the quantum atomic model, you need
to understand….
LIGHT
aka
“Electromagnetic
Radiation”
INTRODUCTION TO “LIGHT”
LIGHT is also known as
ELECTROMAGNETIC
radiation (EM radiation)
___________________________________.
WAVE
EM radiation acts like both a _________
and a ____________________________
DISCRETE PARTICLE (i.e. photon)
Waves
Wave: a rhythmic disturbance
in both time and space which
transfers energy, but not
matter.
Wave Categories
• Mechanical Waves: require a medium.
Examples:
• Water waves (Tsunami) & Earthquake waves
• Sound waves (speed= 340 m/s in air but varies
for different media, faster in solids)
• Electromagnetic Waves: do not require a
medium. Can travel through space (vacuum).
Example: Light from the sun reaches us
Note: All EM waves have a speed of
3.00 x 108 m/s when in a vacuum.
TYPES OF WAVES
1. TRANSVERSE WAVES - The particles vibrate
perpendicular to the direction of the wave's propagation
(ex: waves along a string, electromagnetic waves).
2. LONGITUDINAL WAVES - The particle displacement is
parallel to the direction of wave propagation (ex: sound)
TYPES OF WAVES (cont’d)
3. ELLIPTICAL WAVES Result when longitudinal and
transverse waves are
superpositioned. (ex: surface
water waves)
4. TORSIONAL WAVES
http://youtu.be/m686UO68AXI
Parts of a wave
Wavelength, l ”lambda”:
The distance from the crest to
crest or trough to trough.
Crest:
High Point
Equilibrium (Baseline)
Amplitude, A: The
distance from the
equilibrium (baseline) to
the crest or trough
Trough:
Low point
Low vs. High amplitude
In light, amplitude is related to intensity or brightness
Frequency
the number of
waves IN ONE
SECOND
– Symbol is ν = “nu”
– SI unit is Hertz
(Hz) or 1/s or s-1
Relationship between
Frequency & Wavelength
INVERSELY RELATED
DECREASES
As Wavelength INCREASES, frequency _________
As Wavelength DECREASES, frequency INCREASES
_________
EM radiation (low  high E)
Type of radiation
Wavelengths(m)
i.
Radio
570 - 2.8
TV
5.6 - 0.34
ii.
Microwave
0.1 - 0.001
iii. Infrared radiation (IR) 10-3 - 10-7
iv. Visible light
red
700x10-9 (700nm)
ROYGBIV
violet
400x10-9 (400nm)
v.
Ultraviolet (UV)
10-7 - 10-10
vi. x-rays
10-10 -10-12
vii. Gamma rays
less than 10-12
Speed of a Wave
speed= distance/time
c = l/t
c =l ν
REFRACTION:
When a wave travels from
one medium to a
different medium, the
speed changes, but the
frequency stays the
same.
A wave’s speed is constant
in a given medium. In a
vacuum, any EM radiation
travels at the speed of light:
c = 3.00 x 108 m/s
Speed of Light – 3.00 x 108 m/s
Frequency
c = lv
(in 1/s or Hz)
Wavelength (in m)
1) Find the wavelength of 93.3 MHz in meters
3 x 108 m/s =
93.3 x 106 1/s
l (93.3 x 106 1/s)
93.3 x 106 1/s
3.22 m
WAVELENGTH
CONVERSIONS
When you use the formula, λ must be in
METERS.
Sample conversion:
• nanometers to meters (1 nanometer = 10-9 meter)
• 600 nm = ? m
600 nm x
10-9 meter = 600 x 10-9 m = 6 x 10-7 m
1 nm
You Try:
• What is the frequency of a light wave with a
wavelength of 550 nm?
• What color light is it? (Hint: 400 nm is violet;
700 nm is red)
Energy of a wave (measured in joules, J)
Frequency
E = hn
(in 1/s or Hz)
Planck’s Constant 6.626 x 10-34 J*s
1) Find the energy of 93.3 MHz in meters
E = (6.626 x 10-34 J*s) ( 93.3 x 106 1/s)
6.18 x 10-26 joules
Electromagnetic Spectrum
Low  High Energy:
OY G BIV
Summary of Light
c = ln
c
l= n
c
n=
l
Therefore:
wavelength and
frequency are
inversely
proportional.
Therefore: energy
High frequency = more energy is directly
proportional to the
Low frequency = less enery
frequency.
E = hn
Questions of the Day
1) List the seven types of EM radiation in order
from low to high energy.
2) What’s the relationship btwn. λ & ν? E & ν?
3) What is the lower energy light? One with λ
= 450 (violet/ blue) nm or λ = 700 nm (red)
4) Calculate the frequency for yellow light with
a wavelength of 589 nm.
8 m/s = (589 x 10-9 m) ν
3
x
10
c = ln
5.09 x 1014 1/s
4) What is the energy of this light?
-34 j*s) ( 5.09 x 1014 1/s)
E
=
(6.626
x
10
E = hn
3.37 x 10-19 J
QUANTUM ATOMIC
THEORY
Data: Hydrogen’s Emission Spectrum
1st model: Bohr’s Model
Planck’s Equation
E=hv
E=energy in joules
H=planck’s constant=6.63E-34J*s
V=frequency (per second or Hz)
The energy(E) & the
frequency(V) of an
electromagnetic
wave are directly
related.
Electromagnetic Wave Equation
C=λv
C=speed of light=3.00E8m/s
λ=wavelength in meters
V=frequency (per second or Hz)
Frequency &
wavelength are
inversely related
AND
wavelength & energy
are inversely related.
NEW DATA that led to the
QUANTUM atomic model
___________’s atomic
HYDROGEN
emission spectrum is
DISCRETE, not CONTINUOUS
_______________________
Violet
410nm
Blue
434nm
Blue-Green
486 nm
Red
656nm
Balmer
Series
Quantized vs. Continuous
Quantized
Continuous
• Comes in discrete
packages
• Example: second hand
on clock that “ticks”
• STAIRS or
LADDER
• Flowing
• Example: second hand
on clock that moves
continuously
• RAMP or
ESCALATOR
Quantum theory
1. Electrons can only have certain
“allowed”
____________energies.
2. To change (jump) from one “allowed” energy
to another “allowed” energy, the electron
absorb or emit
must _____________the
exact difference
between these energies—this is called a
___________.
QUANTUM
Niel Bohr’s atomic model, 1913
(aka planetary model)
EACH RING REPRESENTS AN ALLOWED ENERGY LEVEL.
• Electrons orbit the nucleus in
circular paths (___________)
rings or orbits
of fixed energy (_________).
energy levels
• Electrons in rings closer to
the nucleus are
LOWER
___________in
energy.
• Electrons in rings farther
away from the nucleus are
HIGHER in energy.
__________
Bohr’s model (electron transitions)
• An electron transition from
n= 1 to n=3 is a ___________
excitation
because the electron goes
from having a low energy
high energy.
• An electron transition from n
relaxation
= 3 to n=2 is a _________
because the electron goes
from having a high energy 
low energy.
• What is shown in this
a relaxation
picture?_______________
Bohr’s model (energy changes)
EXCITATION
_____________occurs
when
an electron
__________________
ABSORBS or TAKES IN energy,
so that the electron is in an
EXCITED STATE
_____________.
___________________
RELAXATION
occurs when an electron
EMITS or GIVES OFF energy.
__________________
If the electron relaxes
completely, the electron is in
GROUND STATE
a _________
Excited State & Ground State
• Ground state: the lowest possible energy level
an electron be in.
• Excited state: any energy level higher than the
ground state.
Bohr Atom Animation
• http://higheredbcs.wiley.com/legacy/college/
halliday/0471320005/simulations6e/index.ht
m?newwindow=true
EXCITATION
• Let’s look at the Hydrogen atom
• If heat, electricity, or light are absorbed, the
electron can move up energy levels (EXCITATION)
RELAXATION
• As the electron falls back (RELAXATION) to
ground state it gives the energy back as light
(emission).
SERIAL RELAXATION
• May fall down in steps
• Each with a different energy
Calculation of Energy
• The energy absorbed or emitted
during an excitation or relaxation is
equal to the
DIFFERENCE
___________________________
between the initial energy level
and the final energy level.
or difference in energy
• ΔE = change
_________________________
between
two energy levels
_____________________
QUANTUM
(aka… a “_________________”)
E3 – E1 or ΔE = _________
E1 – E3
In this example, ΔE = _______
(the amount absorbed or emitted is the same!)
Energy of Emitted Photon
Energy of the
emitted photon,
Ephoton=
Difference in
energy between
two states,
E
A quantum of energy is the amount of
energy required to move an electron from
one energy level to another.
An Analogy for Bohr’s Model
Increasing energy
Fifth
Fourth
Third
Second
First
Nucleus
• The energy levels
are like the rungs
of a ladder, but are
NOT equally
spaced.
• There is no “in
between” energy
How the Bohr model explains the
emission spectrum of H:
Absorption vs. Emission
spectrum of H
ABSORPTION SPECTRUM—black lines represent
ENERGY absorbed as electron EXCITES
_________________________________
EMISSION SPECTRUM—colored lines represent
ENERGY emitted as electron RELAXES
__________________________________
Questions of the Day
1) The lowest energy level that an electron
occupies is its _______________.
2) When an electron jumps to a higher energy
level, we called this level the _________
state.
3) When it jumps back down to a lower energy
level, this electron movement is called a
__________ and is accompanied by a
__________ of energy.
4) Why are there sometimes different energy
photons/ wavelengths of light emitted when
an electron jumps back down?
QUANTUM ATOMIC
THEORY
Data: Emission Spectrum of OTHER ELEMENTS
2nd model: Wave-Mechanical Model
I was the first to
come up with
QUANTUM
ATOMIC MODEL,
and the idea of
quantized energy
levels…
Bohr
Quick review of Bohr:
THE MODEL
THE ENERGY DIAGRAM FOR H
(quantized energy levels)
Why we had to move on….
• Why a new model?
-The Bohr model didn’t fit the emission spectra of
_____________________.
elements other than H
-According to classical physics, if Bohr’s planetary
atomic model were true, the electron would lose
energy as it orbits and spiral into the nucleus,
resulting in ____________…
UV death…
-Also… Bohr had no explanation for WHY
_____electrons had
quantized energy….
-
quantized energy levels
But… his idea of ______________________
was VERY IMPORTANT
UV DEATH!!!!!
Quick review of Bohr:
THE MODEL
THE ENERGY DIAGRAM FOR H
(quantized energy levels)
EVIDENCE #1:
Emission spectra of OTHER ELEMENTS!
E.g. Argon/Neon Spectral Tubes
MORE EMISSIONS IN THE VISIBLE
RANGE THAN ACCOUNTED FOR BY
BOHR’S ENERGY DIAGRAM!
•Excited in an electrical
discharge
•Spectrum: DISCRETE bands
of color
•Spectrum: DISCRETE bands of
orange, yellow and green
SPECTRAL TUBE
USE OF DIFFRACTION GRATING/ PRISM
Line
Spectra
of Other
MORE
EMISSIONS
THE Elements
VISIBLE
 Every
element
has
itIN
own

RANGE THAN(DIFFERENT)
ACCOUNTEDpattern
FOR BYof
characteristic
BOHR’S
ENERGY
electron
energy
levels.DIAGRAM!
Therefore, each element emits is own
characteristic (DIFFERENT) pattern of
light frequencies.
Excited Gases
& Atomic
Structure
EVIDENCE #2:
Photoelectric effect
Every metal has
a e
e
e
DIFFERENT Threshold Energy!
radiation
Surface of metal
Observed with METALS; the basis for Solar Energy.
If the Ephoton is equal to or greater than the Ethreshold for
metal , then an e- is ejected (electrical current!)
Before we continue… a quick review!!!
• What is the piece of evidence that made it necessary
to come up with a new quantum model of the atom?
The atomic emission spectra of elements OTHER
THAN HYDROGEN.
• What does a diffraction grating or prism do?
It splits light up into its component parts.
• How is the atomic emission spectra for elements
different from the atomic emission spectrum for
white light/ sunlight?
The elements have spectra that have discreet bands
of colored light; sunlight has a spectra that is
continuous.
Before we continue… a quick review!!!
• With what type of elements is the photoelectric effect
observed?
It is observed with metals
• What is the photelectric effect?
It is the observation when LIGHT that has an energy
equal or greater to a certain threshold energy shines
on a metal, electrical current is produced. If it doesn’t
have enough energy, no current is produced.
Ideas that led to the
Quantum Mechanical Model
1920’s
1. Louis de Broglie (electron has wave
properties, “Wave-Particle Duality of Matter”)
2. Werner Heisenberg (“Uncertainty Principle”)
3. Erwin Schrodinger (mathematical equations
using probability, quantum numbers
quantitatively describe electron as a wave
“Schrodinger’s wavefunctions”)
Hullo!
Louis
de
Broglie
Ideas
 Wave-mechanical model :
1. DeBroglie’s wave-particle
duality for matter (1923)
• states that all matter has
____________properties….
wave-like
especially when particles
are very small and very
electrons
fast….. like ____________
• thought of the electrons as
__________________
standing waves
Why standing waves?
• Because standing waves are quantized too…
You see this:
but not this:
De Broglie wavelength
•Since light waves have a particle behavior (as
shown by Einstein in the Photoelectric Effect), then
particles could have a wave behavior.
De Broglie wavelength (in m)
l= h
mv
Mass (in kg)
Planck’s Constant
6.626 x 10-34 J*s
Velocity (in m/s)
Example:
• Determine the de Broglie wavelength for an
electron moving at a speed of 9. x 106m/s.
(me= 9.1 x 10 -31 kg) Remember h=6.7 x 10-34 JS
Answer: 8.18 x 10 -11 m
Werner
Heisenberg
Ideas
 Wave-mechanical model :
2. Heisenberg’s Uncertainty Principle
• states that you cannot
precisely know the
Position, x and the
_________
Velocity, v of any particle
__________
simultaneously…. as you
determine one, it’s harder to
determine the other
• THEREFORE, any accurate
atomic model must deal with
______________
probability
Erwin
Schrodinger
Ideas  Wave-mechanical model:
3. Schrodinger’s Wavefunctions, 1925
• came up with mathematical functions called
wavefunctions, Ψ(r) to describe the electrons as
____________________
waves rather than particles….
• FINALLY!!!! something mathematical that could be used
probability (although if
to calculate an electron’s _____________
we’re talking about waves, it might be better to think of
intensity
it as an electron’s _____________.
radial
wavefunctions, Ψ(r)
-describe an electron
as a wave
radial
probability plots, [Ψ(r)]2
Probability Curve for Hydrogen
When the probability plots
are graphed….
• Instead of rings, you get orbitals….
of space where most of
• ORBITALS: regions
____________________________
the
electron’s wave is found (A region in space
_______________________________________
in
which
there
is
high
probability
of
finding
an
_______________________________________
electron.)… There are 4 major types.
_______________________________________
NOTICE! Energy is still quantized—but there are
no more rings!
aka “Electron Cloud”
The electron cloud
represents positions
where there is probability
of finding an electron.
The higher the electron
density, the higher the
probability that an
electron may be found in
The Electron Cloud for a Sodium ion that region.
The Orbital (aka “Electron Cloud”) for Hydrogen
90% probability
of finding the
electron within this
space
examples of “s” orbitals
“spherical”
three “p” orbitals
“dumbbell shaped”
http://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif
five “d”
orbitals
“clovershaped”
seven “f” orbitals
“multi-lobed”
W-M model structure
ORBITALS – a region of space where there is a high
probability of finding an electron (of a certain
energy). Each orbital can hold 2 electrons MAX.
(4 shapes you need to know – s, p, d, f)
SUBSHELLS – all orbitals with the SAME SHAPE in a
particular shell (distance of the orbital’s outer
edge from the nucleus)
SHELLS/ ENERGY LEVELS “n” – all subshells of a
given size (distance from the nucleus) – the
MAXIMUM number of electrons in a shell is 2n2
Schrodinger’s Quantum
Wave-mechanical model
• Mathematically generated by thinking of the
electron as a wave and location as wave intensity or
probability
• Electrons have signs, nodes where they change signs
because electron position or amplitude has sign…
Wave-mechanical vs. Bohr
1.
Electrons are located in specific energy
levels. To go from one level to another, the
exact different (aka “quantum”) must be
absorbed or emitted (similar to Bohr).
2.
There is no exact path around the nucleus.
(different from Bohr)
3.
The model estimates the probability of
finding an electron in a certain region of
space. (different from Bohr)
Energy level
diagram
aka
ATOMIC
ORBITAL
_________________
DIAGRAM
_________________
_________________
-each _______
dash
represents an
orbital
-each level is a
________ of orbitals
subshell
with a particular energy
RULES:
PRINCIPLE
1. AUFBAU
_________________—electrons
fill in lower energy
levels FIRST.
EXCLUSION PRINCIPLE
2. PAULI
_________________________—an
orbital can
hold only 2 electrons, and they must have opposite
spins. No 2 electron in an atom can share the same
set of four quantum numbers. __
HUND’S RULE
3. _______________—in
a set of SAME ENERGY
degenerate
(___________)orbitals,
the electrons will fill the
orbitals in a way that would give the maximum
number of parallel spins. One electron has to go in
each degenerate orbital before e-’s pair up __ __ __
not __ __ __
Blocks in the Periodic Table
Orbital
Diagram/
Notation for
Carbon
Orbital Notation (ON)
• Another word for “Atomic Orbital
Diagram,” shows the electrons in their
orbitals, from low to high energy
Carbon: 1s __ 2s__ 2p __ __ __
Electron Configuration (ECN)
• An quicker way of describing the atomic
orbital diagram
Carbon: 1s22s22p2
(the superscripts add up to the number of electrons in an atom)
Info given by ON or ECN
• The energy of the electrons
in an atom or ion
• The probable location
(orbital) of the electrons in
an atom or ion
Important Terms
• “VALENCE” electrons
– electrons farthest away from
the nucleus (highest shell)
• “CORE” or “KERNEL” electrons
– electrons closer to the
nucleus (lower shells)
Important Terms
• “PARAMAGNETIC” ECN or ON
-having unpaired electrons, responds to
a magnetic field (paramagnetic
substances tend to be colorful)
• “DIAMAGNETIC” ECN or ON
-having only paired electrons, does NOT
respond to a magnetic field
(diamagnetic substances tend to be
white/ clear)
What you need to know about the
wave-mechanical model (NOW):
• what a wave function is (in general) and how
its square gives the probability density plot
• what an orbital is (as opposed to Bohr’s
orbits/ rings)
• names, shapes, and number of 4 orbital types
• how to fill in atomic orbital diagrams…
• Next…. Electron configurations
Abbreviated/ Noble Gas Shorthand
ECN or ON
1. Find the noble gas BEFORE the
element and put it in [ ]. This
represents most (or sometimes all) of
the “CORE” electrons
2. Continue the ECN or ON from the
noble gas.
Ex.
Mg 1s2 2s2 2p6 3s2
Shorthand:
[Ne] 3s2
SPECIAL ECNs & ONs
• If an element has 1 less e- than a
HALF or FULL “d” or “f” SUBSHELL, 1
e- is taken from the valence “s” and
placed in the “d” or “f” to make it half
or fully filled
• There is special stability from half or
fully filled “d” or “f” subshells….
THE ECN or ON of CATIONS
• Only METALS form CATIONS
• CATIONS – remove electron(s) from the highest
shell first (preferably the highest energy
subshells first) – electrons are NOT removed
from the core!
Ex. Mg+2 (remove 2 electrons)
Mg : 1s2 2s2 2p6 3s2 Mg+2 : 1s2 2s2 2p6
Ex. Pb+4 (remove 4 electrons)
Pb: [Xe] 6s2 4f14 5d10 6p2
Pb+4 : [Xe] 4f14 5d10
THE ECN or ON of ANIONS
• ONLY NONMETALS FORM ANIONS
• ANIONS – add electron(s)
Ex. N-3 (add 3 electrons)
N: 1s2 2s2 2p3 N-3 : 1s2 2s2 2p6
Important Terms
• “ISOELECTRONIC”
-having the same electron
configuration as another atom
or ion
-3
E.G. N is “isoelectronic” with
-2
O and with Ne.
Four Quantum Numbers
Influence the orbital defined by a particular
wavefunction
Describe ONE particular electron
1. Principal Quantum Number
2. Orbital Quantum Number
3. Magnetic Quantum Number
4. Spin Quantum Number
Principal Quantum Number, n
• Indicates main energy levels
n = 1, 2, 3, 4…
• Each main energy level has “n” possible sublevels/ subshells
Ex.
The 1st energy level has 1 possible subshell (s)
The 2nd energy level has 2 possible subhells (s,p)
The 3rd energy level has 3 possible subshells (s, p, d)
Orbital Quantum Number, ℓ
(Angular Momentum Quantum Number)
• Indicates shape of orbital sublevels
• ℓ can equal integers {0  n-1}
ℓ
sublevel
#orbitals #electrons
0
s
1
2
1
p
3
6
2
d
5
10
3
f
7
14
Magnetic Quantum Number, ml
• Indicates the orientation of the orbital in space.
• ml can equal integers { - ℓ  + ℓ}
• The number of values represents the number of
orbitals.
Ex. If ℓ = 2, then we are looking at a “d” subshell
ml = {-2,-1,0,1,2} = 5 values so 5 different
orientations or orbitals for the “d” subshell
Electron Spin Quantum Number, (ms or s)
• Indicates the spin of the electron (clockwise or
counterclockwise).
• Values of ms: +1/2, -1/2 (spin up or spin down,
respectively)
Example:
• List the values of the four quantum numbers
for electrons in the 3d sublevel.
• Answer:
n=3
l=2
ml = -2,-1, 0, +1, +2
ms = +1/2, -1/2 for each pair of electrons