Where are we?
We have measured mass of proton: 1.66 x 10-24 g
We have measured mass of electron: 1836 times lighter than proton
We have measured charge of proton: +1.602 x 10-19 Coulombs
We have measured charge of electron: -1.602 x 10-19 Coulombs
We know protons are at the center of atom.
Neutrons were found—fixed the problem of “missing” atomic masses.
We expect neutrons to be at the center of atom, too (why?).
We imagine electrons are distributed around the atom somehow,
like satellites in orbit.
Because the electrons are so fast, we imagine them doing most of
work of chemistry: the currency of chemistry is electrons!
Pinpointing Electron Positions
….required 2 breakthroughs, one conjecture,
and a lot of theoretical work.
The Einstein/Planck breakthrough (early 1900s).
1) Light can have particle properties!
2) The particles are called photons
3) Each photon carries energy of:
E
hc

h = Planck’s constant
c= speed of light
Graceful swans
vs. hummingbirds
Hey, what what are the
units of energy?
Energy is the capacity to do work.
It has work units.
Work is force times distance.
Force is mass times acceleration.
So…. E  W = f  d = m  a  d
Units: kg  (m/s2)  m = kgm2/s2
This thing is called a Joule
Joule, Calorie, Speed of Light
1 Joule = 1 ntm = kg m2/s2
4.184 Joule = 1 Calories = 0.001 Food Calories
(more later about this).
Planck’s constant: 6.63 x 10-34 Js
c = 3  108 m/s (= 186,000 miles per second)
Sample problem
Remember Emission Spectra
Bohr atom (the conjecture):
electrons have to stay on specific
paths.
Dotted orbit: the “ground” state of hydrogen.
Solid orbit: one of the excited states of
hydrogen in a discharge tube.
When electron in excited state
drops to lower state, light given
off.
When an electron comes out of a high orbit, into
a lower one, light is given off. (Think space
shuttle landing). From the wavelength, you can
calculate the difference in energies between the
orbits.
D E = hc /
Also interested in periodicity, Bohr
proposes that the number of
electrons each orbit can support
grows with the energy of that orbit,
described by an “energy quantum
number”, n:
# of electrons =
n = 1, 2, 3….
2
2n = 2, 8, 18…
2
2n
Hey, it works….for small atoms.
1st row of periodic table: 2 atoms
2nd row: 8 atoms
3rd row: ooops!
That is a big “ooops” and, besides, Bohr
was not able to explain WHY the electrons
had to traverse these discrete, quantized orbits.
The de Broglie Breakthrough
(1924)
Wave-particle duality
 = h/mv or... mv= h
m = mass, v = velocity
Problems
Stop here?
But now we need to understand
waves.
pronounced “lambda”
pronounced “nu”
Oldest physics joke: what’s n?
Waves diffract. They stand.
Wave addition is weird.
Bohr’s circular orbits turn out to
be wrong, but we can at least
see why orbits have to be
quantized.
When you work the math…
•the actual position of electrons can't really be specified
•best we can do is say where they PROBABLY are
•they are likely to be in cloud-like zones (called orbitals, not orbits)
of varied shape
•electrons with more energy can assume orbitals of increasingly
bizzarre shape. These shapes sort of "fall out of" the mathematics,
and it is not really easy to get a physical feel for them.
•these shapes are described by "secondary quantum numbers" (the
orbital number, n, proposed by Bohr is the primary quantum
number).
Shapes of atomic orbitals
http://www.albany.net/~cprimus/orb/
n=1, l=0, m=0
n=2, l=1, m=0
n=3, l=2, m=0
n=2, l=0, m=0
n=3, l=1, m=0
n=4, l=3, m=1
s-type
p-type
d-type (top)
f-type (bottom)
Quantum Numbers
Our purpose
•Introduce the four quantum numbers
•Explain how they relate to chemical periodicity
•Explain how they relate to orbital shape & size
•Give some more examples of physical periodicities
•These are really the keys--keys as in open the door
to molecular understanding.
•So pay attention!
The Energy quantum number
determines how much diversity you
can have. Energy-rich electrons can
"buy" more “fancy” quantum states
than energy-poor ones.
Shapes of atomic orbitals
http://www.albany.net/~cprimus/orb/
n=1, l=0, m=0
n=2, l=1, m=0
n=3, l=2, m=0
n=2, l=0, m=0
n=3, l=1, m=0
n=4, l=3, m=1
s-type
p-type
d-type (top)
f-type (bottom)
Example 1 (row 1)
if n = 1, then you can have l = 0 only.
You can only have ml = 0. ms can be +1/2 or - 1/2.
Notice: there are only two elements, H and He, on
top line of periodic table.
Example 2 (row 2)
if n = 2, you can have l = 0 or 1
For l = 0, you can have ml = 0 only.
ms can be +1/2 or - 1/2.
Check out Li and Be
For l = 1, you can have ml = 0 or +1 or -1
For each of these three ml values, you can have
ms = +1/2 or - 1/2 for a total of SIX states
Check out the six elements: B,C,N,O,F,Ne
Crayola Periodic Table
1s
2s
2p
3s
3p
4s
4p
3d
Electron Configurations
There are all kinds of mnemonic
devices for this (see your textbook)
but the easy solution is:
Just follow the periodic table!
Example:
Calcium = 1s22s22p63s23p64s2
Why does Calcium behave
rather like Barium?
Because both end in s2
What's it mean? The ending electron
is the one with highest-energy. This is the
one that does the most work. Its “work
habits” are the same in either element.
Daily Evaluation/Amusement
Q.
Q.
What is quantize?
Ions vs. isotopes.
Q.
What are Joules?
A. To make or be discrete!
A. different neutrons vs.
different electrons.
A. A measure of energy;
4.184 of them can heat 1
mL of water by one degree
centigrade.
Scientific notation & using it: see me!
Why everything can be a wave.
Some in my pocket to read out loud.
Less amusing, but important
• Will we get some kind of study guide for the
exam?
• What info on the exam?
• Why don’t we do more homework problems
in class?
• What to put on cheat sheet.
• Why homework problems are assigned that
do not have answers in the back of the book.
Announcements
Reminder: homework posted, due March 1
•Midterm #1, Thursday, Feb. 24 (next week!)
•Help session: Tuesday, Feb. 22, 5 p.m.,
• some classroom on this floor—TBA.
•Graded team homeworks will be outside of my
office Friday ~ 10 a.m. Sorted by team.
•I retain the “official” answers, but you can take
your individual answers for study.
•The graders worked pretty hard to make
CORRECTIONS and SUGGESTIONS!
•Answer key will be posted in display case near
my office. (Maybe also on web).
What was the single most important thing
you learned today?
What one thing do you wish you understood better?
What is your action item?