Download Lecture 10

Announcements
• Print worksheet #10 prior to your Thursday discussion
section
• LON-CAPA assignment #6 due Tuesday, Oct. 5 at 9am
• Next week’s quiz will be on Tuesday – atomic history
and electron configurations
• Online gradebook now includes…
–
–
–
–
Exam 1 raw and scaled scores
LON-CAPA grades for assignments 1-5
Clicker points for lectures 3-9
Quizzes 1-4 (5?)
Please check for errors now
Quantum Mechanics and Atomic Orbitals
During the last lecture we discussed…
Bohr and Einstein
particle nature of light
de Broglie
wave nature of particles
Now let’s meet some more scientists. These are the founders
of quantum mechanics!
Schrödinger
Heisenberg
Dirac
Quantum Mechanics 101
quantum mechanics focuses on theoretical and probabilistic
descriptions of atoms
Solutions to Schrödinger’s Equation tell us everything we
need to know about an atom
ĤΨ=EΨ
Ĥ is known as the Hamiltonian operator
Ψ is called a wavefunction
When the Hamiltonian operator is applied to a wavefunction,
the result is a constant (energy) times the wavefunction
Quantum Mechanics 101
The tricky part of quantum mechanics is determining the
equation for Ψ – this often involves very complex differential
equations
Don’t worry, we won’t actually solve Schrödinger’s Equation
in this class (but you can look forward to that in Chem 442)
You need to know three things at this point:
1. Every allowed electron state has a unique Ψ
2. Specific Ψ’s are called orbitals
3. An orbital is NOT the same as a Bohr orbit
Quantum Mechanics 101
So how does this help us understand atomic structure?
Quantum mechanics tells us that we do not know exactly how
an electron travels around an atom (but it definitely is not
confined to a circular orbit!).
Ψ2 = the probability of finding an electron at a particular
distance from the nucleus of an atom
1s orbital
orbitals require 3 quantum numbers
n l ml
magnetic
-l, …, l
orientation
angular momentum
0, 1, 2, …, (n - 1)
shape
principal
1, 2, 3, …
size and energy
“address”
orbitals require 3 quantum numbers
n l ml
The principal quantum number determines the size of an
orbital, as well as its energy
as n increases, orbitals become larger, and the probability of
finding an electron further from the nucleus increases
n=1
n=2
n=3
n=4
n=5
n=6
n=7
orbitals require 3 quantum numbers
n l ml
The angular momentum quantum number determines the
shape of an orbital (designated by letters)
n=1
n=2
n=3
n=4
l=0
l = 0, 1
l = 0, 1, 2
l = 0, 1, 2, 3
l=0
l=1
l=2
l=3
s orbital
p orbital
d orbital
f orbital
The periodic table can be divided into s, p, d and f regions
l=0
l=1
s orbital
p orbital
l=2
l=3
d orbital
f orbital
s
p
n=1
n=2
n=3
n=4
n=5
n=6
n=7
d
f
orbitals require 3 quantum numbers
n l ml
The magnetic quantum number ranges from –l, -l+1…l-1, l
and determines the orientation of an orbital
Row 1 of the periodic table is associated with the principal
quantum number n=1:
n=1
l=0
ml = 0
(1s)
Row 2 of the periodic table is associated with the principal
quantum number n=2:
n=2
l=0
ml = 0
(2s)
l=1
ml = -1, 0, 1
(2p)
Note: there are a total of three 2p orbitals
Row 3 of the periodic table is associated with the principal
quantum number n=3:
n=3
l=0
ml = 0
(3s)
l=1
ml = -1, 0, 1
(3p)
l=2
ml = -2, -1, 0, 1, 2 (3d)
Note: there are a total of five 3d orbitals
Each orbital can hold a total of 2 electrons. We need one
more quantum number to distinguish between the two
electrons within an orbital
ms is the spin quantum number, and it can only have the
values +1/2 (up) or -1/2 (down) ↑ ↓
s orbitals are spherical
2
ψ
1s orbital
2s and 3s ψ2
p orbitals have a dumbbell shape
These are the three 2p orbitals
3p, 4p, 5p etc. have similar shapes but are larger
Most d orbitals are shaped like a cloverleaf
These are the five 3d orbitals
4d, 5d etc. have similar shapes but are larger
Atoms with more than 1 electron (polyelectronic)
The Pauli Exclusion Principle states that no 2 electrons can
have the same set of 4 quantum numbers
Electron configurations are constructed by filling the
orbitals with the lowest energy (starting with 1s) until all
electrons have been assigned
Hydrogen has 1 electron
1s1
↑
Helium has 2 electrons
1s2
↑↓
Which orbital fills next?
H
He
Li
Be
B
C
N
O
F
1s 2s 2px 2py 2pz 3s 3px 3py 3pz 4s 3d 3d 3d 3d 3d
Ne
Na [Ne]
Place 2 electrons into each s orbital
before moving on to the next orbital
When you get to the p orbitals, place
one electron into each orbital before
going back and adding the second
electron
Noble gas shorthand notation can
reduce repetition. Write the symbol
for a noble gas in brackets and then
write the configuation for the
remaining electrons
Cr and Cu do NOT follow the
standard rules (see Wkst #10)