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THE NATURE OF LIGHT
- Light is also known as electromagnetic radiation.
- Light is emitted by oscillating charges.
- Oscillating charges create oscillating electric and magnetic fields.
+
- Light is very peculiar in that it is a particle and a wave at the same time.
- Our physical intuition tells us that this is impossible.
- Waves are spread out as in ocean waves
- Particles are in one place (localized) as in a bowling ball.
Q: How can something be spread out and localized at the same time?
A: Who knows? It is a mystery of nature.
THE WAVE NATURE OF LIGHT
- Light moves at a constant speed through a particular medium.
- c – speed of light in a vacuum ( air)
- c = 2.997 x 108 m/s (670,000,000 mi/hr)
- Waves have two components.
- wavelength -  (Greek lambda)
- distance between wave crests
1
1
0.5
sin ( x )
0
0.5
1
1
0
0
5

10
x
15
20
18.85
- frequency -  (Greek nu)
- how often wave crest moves up and down at a single point
- number of beats per second: Hertz – Hz
- 1 Hz = 1 /s = 1 s-1
- think of a boat bouncing up and down on waves
- Frequency and wavelength are related
=c
2
- if we know , we can calculate 
Example: If light has a frequency of a mercury vapor lamp is 6.879  1014 Hz, what
is the wavelength of the light?
- if we know , we can calculate 
Example: If a medical x-ray coming from tungsten metal has a wavelength of 2.09 
10-11 m, what is the frequency of the light?
THE PARTICLE NATURE OF LIGHT
- light comes as particles called photons
- energy of a photon is proportional to frequency
E=h
- h = Planck’s constant h = 6.626 x 10-34 J  s
Example: How much energy does a photon coming from the KVNO radio tower
with a frequency of 90.7 x 106 Hz have?
Photoelectric Effect
- Light shining on a metal surface may cause electrons to be ejected from the surface.
-
e
- Frequency of light needs to be above threshold frequency to induce to escape from
the surface of the metal.
- Albert Einstein proposed that the electrons are knocked off the surface with a
particle of light!
- Nobel – 1921
- The photoelectric effect can be explained as a collision between an electron and a photon.
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ELECTROMAGNETIC SPECTRUM
Name
Radio
Microwave
Infrared
Visible
Ultraviolet
X-ray
Gamma
Wavelength
300 km to 0.3 m
30 cm to 1 mm
1.0 mm to 780 nm
780 nm to 390 nm
390 nm to 1 nm
10 Å to 0.06 Å
1.5 Å to 0.3 ym
Frequency (Hz)
103 – 109
109 – 3  1011
3  1011 – 4  1014
4  1014 – 8  1014
8  1014 – 3  1017
3  1017 – 5  1019
2  1018 – 1033
LINE SPECTRA OF THE ELEMENTS
The light emitted by pure elements has specific energies.
- Therefore light of only specific wavelengths can be seen. (i. e., different colors can
be seen)
- This emitted light is called a line spectrum. (pl. spectra)
Line spectra tell us that atoms can only have certain energy levels.
- The atoms cannot have any arbitrary value of energy.
ATOMIC STRUCTURE HISTORY (Review)
Thomson
- discovered “cathode rays”, i.e., electrons
Milliken
- found charges come in discrete units, charge of electron is fundamental.
Rutherford
- found that atom has a very small, yet very heavy nucleus.
BOHR’S MODEL OF THE HYDROGEN ATOM
History
- Scientists before Bohr knew atom was made of nucleus and electrons.
- They didn’t know where the electrons were or how they behaved.
- They also knew each element had a distinct line spectrum.
1913 – Model
- Bohr assumed electrons traveled in orbits around nucleus.
- Bohr also assumed that electrons could only have specific orbits.
- Specific orbits were labeled with a quantum number
- Energies of orbits are
1
E n   R H  2 n  1,2,3,4,
n
RH = Rydberg constant (for hydrogen)
= 2.18 x 10-18 J
- Won Nobel Prize – 1922
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SCHEMATIC OF BOHR MODEL
Orbits are quantized.
Electrons can not exist
between defined orbits.
+
Using the Bohr Model to Calculate Spectra
Spectra result from light being emitted or absorbed when atom changes energy, i. e.
when electron goes to different orbit.
- emission – energy of atom decreases, i. e. electron orbits closer to nucleus
- absorption – energy of atom increases, i. e., electron orbits further from
nucleus
- Change in energy is all or nothing. Electron can not be in between energy levels.
- ground state – lowest possible energy state
- excited state – any other state
- when energy in an atom changes, we can calculate the change as
E = Ef – Ei
E   R H 
 1
1 
1
1
2    RH  2   RH  2  2 
nf 
ni 
 ni nf 
- also consider that since E is the energy of the photon emitted or absorbed.
Eatom = Ephoton

Ef – Ei = h 
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- an equation for the frequency of the photon can be written as
 1
1
h    RH  2  2 
 ni n f 


RH  1
1
 2  2 
h  ni nf 
Example: What frequency of light is emitted when the H atom changes its electron
energy level from n = 6 to n = 3?
Note: Negative sign relates that radiation was emitted.
(Frequencies usually reported as positive.)
THE DUAL NATURE OF MATTER
- Bad News: The Bohr model is wrong!
- Electrons don’t behave like planets.
- Electrons have a wave nature that makes them spread out.
We have seen that light can behave as a wave and a particle.
This dual nature of light is also true for matter.
*All matter behaves as a particle and a wave.*
- I. e., an electron, an atom or a baseball all behave like a wave.
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DE BROGLIE WAVES (MATTER WAVES)
All moving particles have a wavelength.
Wavelength of particle is inversely proportional to particle’s momentum.
Recall: Momentum is defined as mass  velocity
p=mv
or
1
p
Thus proportionality is  
note: smaller p implies higher 
higher p implies smaller 
The proportionality constant is Planck’s constant
Therefore the wavelength of a particle is
h
p

(De Broglie’s Relation)
Picture of a de Broglie wave
0.981
1
0.5
f( x )
0
0.5
0.981
1
3
2.99
2
1
0
x
1
2
3
2.99
- note that the wave is localized somewhat
- as wavelength decreases wave becomes more localized (Note: momentum has
increased.)
0.976
1
0.5
g( x )
0
0.5
0.976
1
3
2.999
2
1
0
x
1
2
3
2.999
In the macroscopic world, objects do not have large enough wavelengths to exhibit
wave-like behavior.
Only in the microscopic world (as in the atom) do objects exhibit wave-like behavior.
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Let us illustrate with a couple of examples.
Example: Calculate the wavelength of an electron when the electron is moving
2.18 x 106 m/s.
me = 9.109 x 10-31 kg
h = 6.626 x 10-34 Js

34
h
h
6.626 x10 J  s
J s


 3.34 x1010
 3.34 x1010
6
31
p m  v 9.109 x10 kg  2.18 x10 m / s
kg  m
2
m2 2
s
s2
kg  m
kg 
 3.34 x1010 m  3.34 Å
- Note: The wavelength is about the same as the size of the atom.
Example: Calculate the wavelength of a baseball moving 60 mi/hr (26.8 m/s). The
mass of baseball is 0.14 kg.

h
h
6.626 x1034 J  s
J  s2


 1.8 x1034
 1.8 x1034 m
p m  v 0.14 kg  26.8 m / s
kg  m
- Note: This is an extremely small wavelength, especially when compared to the
size of the baseball.
To summarize:
Microscopic objects when moving become wave-like.
Experimental confirmation for wave-like properties has been found for electrons,
protons, neutrons, hydrogen atoms, sodium atoms, bucky balls, et al.
- matter waves interfere with each other just like light waves (or any waves)
Macroscopic objects have a wave-like nature when moving, but the wave nature is
insignificant compared to its particle nature.
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HEISENBERG UNCERTAINTY PRINCIPLE
The Heisenberg uncertainty principle limits the precision of measuring quantities in
the microscopic world.
- This limitation is a fundamental principle of physics and not just a technology
problem.
To understand measuring in the microscopic world, let us concentrate first on
measuring in the macroscopic world.
Macroscopic Measurement
Measuring the velocity a ball rolling on the floor, we need to measure at least the
position of the ball at two different times. r  r
r
v 2 1 
t 2  t1  t
How do we measure the position at both times?
We see the light reflected off the ball at t1 and note the position r1.
Then we see the light reflected off the ball at t2 and note the position r2.
Key Point: We need the light to measure the position accurately. We can’t measure
the position in the dark.
Microscopic Measurement
To measure the velocity of an electron, we need to measure its position at two
different times by seeing light reflected off the electron.
The problem (and the crux of the argument) is that when a photon hits the electron, it
moves the electron.
Thus the act of measuring disturbs the system. Note that measuring the macroscopic
object did not disturb the system.
Heisenberg’s Uncertainty Principle tells us we are not able to measure the position of
an object and its velocity with infinite precision.
I.e., there is inherent fuzziness in measuring certain quantities at the same time.
As an equation, Heisenberg’s Uncertainty Principle can be stated as
r p  h/4
r – uncertainty of position measurement
p – uncertainty of momentum (velocity) measurement
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Consequences of Heisenberg’s Uncertainty Principle
- There is always a trade-off of precision when measuring the position of an electron and
its velocity.
- If we want to know the position with total precision, we will have no idea how fast
it is going.
- If we want to know the velocity of the electron, we will have no idea where it is.
ATOMIC ORBITALS
The wave nature of the electron expresses itself within an atom as an orbital (electron
cloud).
ATOMIC ORBITALS AND QUANTUM NUMBERS
- Bohr model has one quantum number.
- Orbital model has three quantum numbers.
1. Principal quantum number – n
a) has values of n = 1, 2, 3, 4, …
b) related to distance away from nucleus
c) nearly same as n quantum number in Bohr model
d) all the energy levels in an atom with the same n value are called a shell
2. Azimuthal quantum number – l
a) has values of l = 0, 1, 2 ,…, n-1
- note dependence on n
Example: If n = 1 what are the possible l values?
A: l = 0
Example: If n = 2 what are the possible l values?
A: l = 0 or l = 1
Example: If n = 3 what are the possible l values?
A: l = 0, l = 1, or l = 2
b) For a given shell, all the energy levels in an atom with the same l are called a
subshell.
- subshell is labeled with n quantum number and letter for l quantum number.
c) Letters are used to represent the value of l.
l
subshell
0
s
1
p
2
d
3
f
4
g
5, …
h, …
d) related to the shape of the orbital (more in a little bit.)
orbital – an electron cloud in an atom with specific quantum numbers, i.e, same n, l,
ml
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e) Note for a given shell, n possible number of subshells exist.
n=1

1s
n=2

2s
2p
n=3

3s
3p
3d
n=4

4s
4p
4d
4f
3. Magnetic quantum number – ml
a) has values of ml = l, l-1, l-2, …, -( l-1), -l
- note dependence on l
Example: What are the possible ml values for the d subshell?
d subshell  l = 2
l = 2  ml = +2, +1, 0, -1, -2
Example: What are the possible ml values for the s subshell?
s subshell  l = 0
l = 0  ml = 0
Example: What are the possible ml values for the p subshell?
p subshell  l = 1
l = 1  ml = +1, 0, -1
Example: What are the possible ml values for the f subshell?
f subshell  l = 3
l = 3  ml = +3, +2, +1, 0, -1, -2, -3
b) related to orientation of orbital
c) Note # of orbitals in a subshell is 2l + 1
Review examples with quantum numbers
For n = 1, what are the possible values for l and ml?
n = 1  l = n-1 = 0
ml = l = 0
For n = 2, what are the possible values for l and ml?
n=2l=0
ml = 0
l =1
ml = +1, 0, -1
For n = 3, what are the possible values for l and ml?
n=3l=0
ml = 0
l=1
ml = +1, 0, -1
l=2
ml = +2, +1, 0, -1, -2
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For n = 4, what are the possible values for l and ml?
n=4l=0
ml = 0
l=1
ml = +1, 0, -1
l=2
ml = +2, +1, 0, -1, -2
l=3
ml = +3, +2, +1, 0, -1, -2, -3
Shapes of the orbitals
s orbital
- spherical shape
- one orbital per subshell
- electron cloud is densest at nucleus
+
p orbital
- “dumbbell” shape
- three orbitals per subshell
- electron cloud is not densest at nucleus
- orbital has a node at the nucleus where e- density is zero
+
d orbital
- “cloverleaf shape
- five orbitals per subshell
- electron cloud is not densest at nucleus
- orbital has 2 nodes.
+
f orbitals
- more complicated shapes
- seven orbitals per subshell
- electron cloud is not densest at nucleus
Orientation of orbitals
- The ml quantum number indicates the orientation of the orbital within the atom.
- Number of possible ml values indicates number of possible orientations.
- Consider the orbitals of the 2p subshell as an example.
z
z
y
x
2py  ml = -1
z
y
x
y
x
2pz  ml = 1
Note: values of ml have been assigned arbitrarily.
2px  ml = 0
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PROBABILITY DENSITY OF AN ORBITAL
Representing the electron wave as an electron cloud is a way representing as a
probability density
The value of probability density at a particular point in an orbital gives the chances of
finding the electron at the point (when measured as a particle!).
Where the electron cloud is “thicker”, the probability of finding an electron increases.
Where the electron cloud is zero, the orbital has a node and the probability of finding
an electron is zero.
So – so probability of finding electron here
No probability of finding electron here (a node!)
Highest probability of finding electron here
ENERGY LEVELS OF THE ORBITALS
The three quantum numbers, n, l, ml, not only describe the size, shape and orientation
of an orbital.
More important, the quantum numbers describe the energy of electrons in the orbital
3d
4s
3p
3s
2p
2s
1s
Notes about energy levels of orbitals
- bigger change in energy is between shells
- lesser change in energy between subshells
- no change in energy between orbitals in same subshell (orbitals are degenerate)
- note: energy of 4s orbital is less than energy of 3d orbitals
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MULTI-ELECTRON ATOMS
Electron Spin
- electron behaves as if it is spinning
- electron spin has only two orientations
- spin quantum number – ms
- two values -½, +½
- by convention
+½ is spin up
-½ is spin down
- Therefore, four quantum numbers fully describe where electrons are within an atom.
- two electrons with opposite spins per orbital
- The energies of the two electrons within an orbital are degenerate.
Pauli Exclusion Principle
- In an atom, electrons can’t share same set of quantum numbers.
- I. e., two electrons can’t be in the same place at the same time.
- This may seem obvious, however two photons can be in the same place at
the same time.
Aufbau Principle
- Electrons in ground state atom are in lowest possible energy.
- Electrons “fill” into orbitals from low energy to high energy.
Hund’s Principle
- Electrons fill into degenerate orbitals as to maximize the total spin of the
electrons in the atom.
- I. e., electrons would rather go to another orbital rather than pair with another
electron.
ORBITAL DIAGRAMS AND ELECTRONIC CONFIGURATIONS
Electronic Configuration is a list of subshells and the number of electrons within them.
Orbital Diagrams are energy level diagrams that indicate the occupation of the
orbitals and the spins of the electrons.
Examples:
Hydrogen
Elec. Config. 1s1
Orbital Diagram
1s
Hydrogen is the fuel in “fuel cell” cars.
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Helium
Elec. Config. 1s2
Orbital Diagram
1s
Helium is used to replace to nitrogen is deep-sea air tanks because nitrogen at high pressure acts as a
narcotic.
Lithium
Elec. Config. 1s22s1
Orbital Diagram
2s
1s
Lithium (as Li2CO3) is used to treat bipolar disorder and to add the color red to fireworks.
Beryllium
Elec. Config. 1s22s2
Orbital Diagram
2s
1s
Beryllium is alloyed with copper to make “spark-proof” tools to be in industrial plants where
flammables are stored.
Boron
Elec. Config. 1s22s22p1
Orbital Diagram
2p
2s
1s
Boron (as Na2B4O7) is added to glass to make it heat-resistant. (Pyrex)
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Carbon
Elec. Config. 1s22s22p2
Orbital Diagram
2p
2s
1s
- note application of Hund’s rule.
Carbon is added to tires to make them tougher. It is also an excellent material to use in water filters.
Nitrogen
Elec. Config. 1s22s22p3
Orbital Diagram
2p
2s
1s
The nitrogen we breathe cannot be used by our bodies. We must get nitrogen from plant or animal matter.
Oxygen
Elec. Config. 1s22s22p4
Orbital Diagram
2p
2s
1s
- note pairing of electrons in the 2p subshell
Ozone, O3, is toxic to humans, but essential in the atmosphere to protect us from the sun’s UV rays.
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Fluorine
Elec. Config. 1s22s22p5
Orbital Diagram
2p
2s
1s
Fluorine is very corrosive, yet it is an important part of Teflon where it doesn’t react with anything.
Neon
Elec. Config. 1s22s22p6
Orbital Diagram
2p
2s
1s
Neon glows orange-red when exposed to high voltage (20,000 V).
Sodium
Elec. Config.
Orbital Diagram
Liquid sodium is used in some nuclear reactors as a coolant, but bursts into flame when exposed to
water.
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Sulfur
Elec. Config.
Orbital Diagram
Sulfur is added to rubber and heated to create rubber tough enough for tires. This process, called
vulcanization, was discovered by Charles Goodyear.
Noble gas abbreviations
When only the valence (outermost) electrons need to be considered, the core
(innermost) electrons can be represented by the elemental symbol of the closest noble
gas preceding the atom that is being examined.
Examples:
Oxygen: [1s2]2s22p4  [He]2s22p4
Chlorine: [1s22s22p6]3s23p5  [Ne]3s23p5
ELECTRONIC CONFIGURATIONS AND THE PERIODIC TABLE
Periodic table tells us subshell of valence electrons.
p valence e-
d valence e-
f valence eExample: Tellurium is an element that is added to rubber to make it more resistant to
oil. Give the full and abbreviated electronic configuration of the ground
state tellurium atom.
Full: 1s22s22p63s23p64s23d104p65s24d105p4
Abbr:
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Example: Thallium is an extremely toxic element used in specialty lenses. Give the
full and abbreviated electronic configuration of the ground state thallium
atom.
Full:
Abbr:
Example: Vanadium is the crucial element in Damascus steel used to make the
highest quality edged weapons in the Middle Ages. What is the orbital
diagram and electron configuration of the ground state vanadium atom?