Download s Orbitals

Test II
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9
37.3
25 pt.
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Midterm Grades
Based only on Test 1 (75.7%) and
OWL (24.2%)
The last day to drop without academic penalty:
March 3d, by 11:59 pm;
limited to five withdrawals per college life
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Chem 1211
Class 13
Atomic Structure
Chapter 6
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Atomic Line Spectra and
Niels Bohr
Niels Bohr
(1885-1962)
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Bohr’s theory was a great
accomplishment.
Rec’d Nobel Prize, 1922
Problems with theory —
• theory only successful for H.
• introduced quantum idea
artificially.
• So, we go on to QUANTUM or
WAVE MECHANICS
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Quantum or Wave Mechanics
L. de Broglie
(1892-1987)
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de Broglie (1924) proposed
that all moving objects
have wave properties.
For light: E = mc2
E = h = hc / 
Therefore, mc = h / 
and for particles
(mass)(velocity) = h / 
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Quantum or Wave Mechanics
Baseball (115 g) at
100 mph
 = 1.3 x 10-32 cm
PLAY MOVIE
Experimental proof of wave
properties of electrons
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e- with velocity =
1.9 x 108 cm/sec
 = 3.88 x 10-10 m =
0.388 nm
Uncertainty Principle
W. Heisenberg
1901-1976
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Problem of defining nature
of electrons in atoms
solved by W. Heisenberg.
Cannot simultaneously
define the position and
momentum (= m•v) of an
electron.
We define e- energy exactly
but accept limitation that
we do not know exact
position.
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Quantum or Wave Mechanics
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Schrodinger applied idea of ebehaving as a wave to the
problem of electrons in atoms.
He developed the WAVE
EQUATION
Solution gives set of math
expressions called WAVE
FUNCTIONS,  (psi)
E. Schrodinger
Each describes an allowed energy
1887-1961
state of an eQuantization introduced naturally.
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WAVE FUNCTIONS, 
•  is a function of distance and two angles.
• Each  corresponds to an ORBITAL — the
region of space within which an electron is
found.
•  does NOT describe the exact location of
the electron.
• 2 is proportional to the probability of
finding an e- at a given point.
There is a set of numbers that are parameters of
: they are called quantum numbers
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QUANTUM NUMBERS
The shape, size, and energy of each orbital is a
function of 3 quantum numbers:
n (principal) → shell
l (angular) → subshell
ml (magnetic) → designates an orbital
within a subshell
According to that numbers, electrons in atom
grouped in shells and subshells
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Subshells & Shells
• Subshells grouped in shells.
• Each shell has a number called
the PRINCIPAL QUANTUM
NUMBER, n
• The principal quantum number
of the shell is the number of the
period or row of the periodic
table where that shell begins.
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Subshells & Shells
n=1
n=2
n=3
n=4
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Types of Orbitals
s orbital
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p orbital
d orbital
Orbitals
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• No more than 2 e- assigned to an orbital
• Orbitals grouped in s, p, d (and f)
subshells
s orbitals
d orbitals
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p orbitals
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s orbitals
p orbitals
d orbitals
s orbitals
p orbitals
No.
orbs.
1
3
5
No.
e-
2
6
10
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d orbitals
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QUANTUM NUMBERS
Symbol
Values
Description
n (major)
1, 2, 3, ..
l (angular)
0, 1, 2, .. n-1
ml (magnetic)
-l..0..+l
Orbital size
and energy
where E = -R(1/n2)
Orbital shape
or type
(subshell)
Orbital
orientation
# of orbitals in subshell = 2l
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+1
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Types of
Atomic
Orbitals
See Active Figure 6.14
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Shells and Subshells
When n = 1, then
l = 0 and ml = 0
Therefore, in n = 1, there is 1 type of
subshell
and that subshell has a single orbital
(ml has a single value → 1 orbital)
This subshell is labeled s (“ess”)
Each shell has 1 orbital labeled s,
and it is SPHERICAL in shape.
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s Orbitals— Always Spherical
Dot picture of
electron
cloud in 1s
orbital.
Surface
density
4πr2y versus
distance
See Active Figure 6.13
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Surface of
90%
probability
sphere
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1s Orbital
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2s Orbital
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3s Orbital
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p Orbitals
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When n = 2, then l = 0 and 1
Therefore, in n = 2 shell there
are 2 types of orbitals — 2
subshells
For l = 0
ml = 0
this is a s subshell
For l = 1
ml = -1, 0, +1
this is a p subshell
with 3 orbitals
See Screen 6.15
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When l = 1, there is
a PLANAR
NODE thru the
nucleus.
p Orbitals
The three p orbitals lie 90o apart in space
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2px Orbital
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3px Orbital
d Orbitals
When n = 3, what are the values of s?
l = 0, 1, 2
and so there are 3 subshells in the shell.
For l = 0, ml = 0
→ s subshell with single orbital
For l = 1, ml = -1, 0, +1
→ p subshell with 3 orbitals
For l = 2, m l = -2, -1, 0, +1, +2
→d
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subshell with 5 orbitals
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d Orbitals
s orbitals have no planar
node (l = 0) and so are
spherical.
p orbitals have l = 1, and
have 1 planar node,
and so are “dumbbell”
shaped.
This means d orbitals (with
l = 2) have 2 planar
nodes
See Figure 6.15
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3dxy Orbital
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3dxz Orbital
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3dyz Orbital
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2
2
3dx - y
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Orbital
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2
3dz Orbital
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f Orbitals
When n = 4, l = 0, 1, 2, 3 so there are 4 subshells
in the shell.
For l = 0, ml = 0
→ s subshell with single orbital
For l = 1, ml = -1, 0, +1
→ p subshell with 3 orbitals
For l = 2, ml = -2, -1, 0, +1, +2
→ d subshell with 5 orbitals
For l = 3, ml = -3, -2, -1, 0, +1, +2, +3
→ f subshell with 7 orbitals
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f Orbitals
One of 7 possible f
orbitals.
All have 3 planar nodal
surfaces.
Can you find the 3
surfaces here?
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Spherical Nodes
2 s orbital
•Orbitals also have spherical
nodes
•Number of spherical nodes
=n-l-1
•For a 2s orbital:
No. of nodes = 2 - 0 - 1 = 1
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Arrangement of
Electrons in Atoms
Electrons in atoms are arranged as
SHELLS (n)
SUBSHELLS (l)
ORBITALS (ml)
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