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Unformatted text preview: Quantum or Wave Mechanics Quantum or Wave Mechanics de Broglie ((1924) proposed
de Broglie 1924) proposed
that all moving objects
that all moving objects
have wave properties.
have wave properties.
For light: E = mc 22
For light: E = mc
E = hν = hc // λ
E = hν = hc λ
L. de Broglie
(18921987) Therefore, mc = h // λ
Therefore, mc = h λ
and for particles
and for particles Experimental proof of wave
properties of electrons angles.
— the region of space within which an
electron is found.
location of the electron. EQUATION e with velocity =
1.9 x 108 cm/sec Solution gives set of math
expressions called WAVE
expressions
WAVE
E. Schrodinger
FUNCTIONS, Ψ
FUNCTIONS,
18871961 λ = 0.388 nm Each describes an allowed energy
state of an eQuantization introduced naturally. Uncertainty Principle • Each Ψ corresponds to an ORBITAL
Each
ORBITAL • Ψ2 is proportional to the probability of He developed the WAVE
He
WAVE λ = 1.3 x 10 32 cm • Ψ is a function of distance and two
is • Ψ does NOT describe the exact Schrodinger applied idea of ebehaving as a wave to the
problem of electrons in atoms. Baseball (115 g) at
100 mph ((mass)(velocity) = h // λ
mass)(velocity) = h λ WAVE FUNCTIONS, Ψ
WAVE Quantum or Wave Mechanics W. Heisenberg
19011976 Problem of defining nature
Problem of defining nature
of electrons in atoms
of electrons in atoms
solved by W. Heisenberg .
solved by W. Heisenberg.
Cannot simultaneously
Cannot simultaneously
define the position and
define the position and
momentum (= m•v) of an
momentum (= m•v) of an
electron.
electron.
We define e energy exactly
We define e energy exactly
but accept limitation that
but accept limitation that
we do not know exact
we do not know exact
position.
position. finding an e at a given point. Types of
Orbitals
s orbital
p orbital
d orbital Page 1 Orbitals
• No more than 2 e assigned to an
orbital
• Orbitals grouped in s, p, d (and f)
subshells s orbitals
d orbitals
s orbitals s orbitals p orbitals d orbitals Subshells & Shells
n=1
n=2
n=3
n=4 Subshells & Shells p orbitals p orbitals d orbitals No.
orbs. 1 3 5 No.
e 2 6 10 • Subshells grouped in shells.
• Each shell has a number called
the PRINCIPAL QUANTUM
PRINCIPAL
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. QUANTUM NUMBERS
Each orbital is a function of 3 quantum
numbers: n (major)
>
(major)
>
l (angular) >
ml (magnetic) >
(magnetic) shell
subshell
subshell
designates an orbital
within a subshell
within Page 2 QUANTUM NUMBERS Symbol Values n (major) 1, 2, 3, .. Description Orbital size
and energy
where E = R(1/n 2)
l (angular)
0, 1, 2, .. n1
Orbital shape
or type
or
(subshell)
ml (magnetic) l..0..+l
Orbital
Orbital
orientation
orientation
# of orbitals in subshell = 2 l + 1 Shells and Subshells
Shells and Subshells
When n = 1, then l = 0 and m l = 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) s Orbitals
s Orbitals 1s Orbital All s orbitals are spherical in shape . This subshell is labeled s (“ess”)
Each shell has 1 orbital labeled s,
and it is SPHERICAL in shape.
and
SPHERICAL in 2s Orbital See Figure 7.14 on page 319 and
See Figure 7.14 on page 319 and
Screens 7.10 and 7.11.
Screens 7.10 and 7.11. 3s Orbital p Orbitals Typical p orbital
Typical p orbital When n = 2, then ll = 0 and 1
When n = 2, then = 0 and 1
Therefore, in n = 2 shell
Therefore, in n = 2 shell
there are 2 types of
there are 2 types of
planar node
orbitals — 2 subshells
planar node
orbitals — 2 subshells
For ll = 0 mll = 0
For = 0 m = 0
When l = 1, there is
tthis is a s subshell
his is a s subshell
a
PLANAR NODE
For ll = 1 m ll = 1, 0, +1
For = 1 m = 1, 0, +1
thru
tthis is a p subshell
his is a p subshell
the nucleus.
with 3 orbitals
with 3 orbitals
See Screens 7.11 and 7.13 Page 3 2px Orbital p Orbitals
p Orbitals 2py Orbital 3px Orbital 3py Orbital pz 90o A p orbital px
py The three p
orbitals lie 90o
apart in space 2pz Orbital Page 4 d Orbitals
d Orbitals 3pz Orbital When n = 3, what are the values of l? 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, ml = 2, 1, 0, +1, +2
> 3dxy Orbital d subshell with 5 orbitals 3dxz Orbital Page 5 d Orbitals
d Orbitals typical d orbital 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 planar node planar node See Figure 7.16
See Figure 7.16 3dyz Orbital 3dz2 Orbital 3dx2 y2 Orbital f Orbitals
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, m l = 3, 2, 1, 0, +1, +2, +3
> f subshell with 7 orbitals
> Shell Principal Quantum Number, n
1
2
3
Relate to n
No.
Subshells
No.
Orbitals 1 2 3 =n 1 4 9 = n2 No. e 2 8 18 = 2 n2 Page 6 ...
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 Summer '08
 ROMANMANETSCH
 Organic chemistry

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