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Quantum Theory and theElectronic Structure of Atoms
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Properties of Waves
Wavelength() is the distance between identical points onsuccessive waves.
Amplitudeis the vertical distance from the midline of a
wave to the pea or trou!h.".#
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Properties of Waves
Frequency() is the number of waves that pass throu!h a
particular point in # second ($% & # cycle's).
The speed (u
) of the wave &
".#
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awell (#*"+), proposed that visible li!ht consists of
electroma!netic waves.
Electromagnetic
radiationis the emission
and transmission of ener!y
in the form of
electroma!netic waves.
Speed of li!ht (c) in vacuum & +.-- #-*m's
Allelectroma!netic radiation
= c".#
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".#
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x= c
= c/
= +.-- #-*m's/.- #-/$%= 0.- #-+m
1adio wave
A photon has a fre2uency of .- #-/$%. 3onvert
this fre2uency into wavelen!th (nm). 4oes this fre2uency
fall in the visible re!ion5
= 0.- #-#6nm
".#
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ystery 7#, 89lac 9ody Problem:
Solved by Planc in #;--
Ener!y (li!ht) is emitted or
absorbed in discrete units
(2uantum).
E & h
Planc?s
".#
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@i!ht has both
#. wave nature
6. particle nature
h& BE C 9E
ystery 76, 8Photoelectric Effect:
Solved by Einstein in #;-0
Photonis a 8particle: of li!ht
BE & h= 9E
h
BE e=
".6
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E & h
E & .+ #-=+/(>?s) +.-- #- *(m's) ' -.#0/ #-=;(m)
E & #.6; #- =#0>
E & h c '
".6
When copper is bombarded with hi!h=ener!y electrons,
D rays are emitted. 3alculate the ener!y (in oules)
associated with the photons if the wavelen!th of the D
rays is -.#0/ nm.
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".+
@ine Emission Spectrum of $ydro!en Atoms
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".+
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#. e=can only have specific(2uanti%ed) ener!y
values
6. li!ht is emitted as e=
moves from one ener!y
level to a lower ener!y
level
Bohrs Model of
the Atom (1913)
En& =1$ ( )
#
n6
n(principal 2uantum number) & #,6,+,F
1$(1ydber! constant) & 6.#* #-=#*>
".+
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E & h
E & h
".+
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Ephoton& E & Ef= Ei
Ef& =1$ ( )#
n6f
Ei& =1$ ( )#
n6i
i f
E & 1$( )#
n6#
n6
nf & #
ni & 6
nf & #
ni & +
nf & 6
ni & +
".+
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Ephoton& 6.#* #-=#*
> (#'60 = #';)Ephoton& E & =#.00 #-
=#;>
& .+ #-=+/(>?s) +.-- #-* (m's)'#.00 #-=#;>
*- nm
3alculate the wavelen!th (in nm) of a photon
emitted by a hydro!en atom when its electron
drops from the n& 0 state to the n& + state.
Ephoton& h c '
& h c ' Ephoton
i f
E & 1$( )#
n6#
n6Ephoton&
".+
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4e 9ro!lie (#;6/) reasoned
that e=is both particle and
wave.
Why is e=ener!y 2uanti%ed5
"./
u & velocity of e=
m & mass of e=
2r & n =h
mu
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= h'mu
= .+ #-=+/' (6.0 #-=+ #0.)
= #." #-=+6m & #." #-=6+nm
What is the de 9ro!lie wavelen!th (in nm)
associated with a 6.0 ! Pin!=Pon! ball
travelin! at #0. m's5
m in !h in >?s u in (m's)
"./
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Chemistry in Action: Laser The !lendid Li"ht
@aser li!ht is (#) intense, (6) monoener!etic, and (+) coherent
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Chemistry in Action: #lectron Microsco!y
TM ima"e of iron atoms
on co!!er s$rface
e& -.--/ nm
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Schrodin!er Wave E2uation
Gn #;6 Schrodin!er wrote an e2uation that
described both the particle and wave nature of the e=
Wave function () describes
#. ener!y of e=with a !iven
6. probability of findin! e=in a volume of space
Schrodin!er
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Schrodin!er Wave E2uation
= fn(n, l, ml, ms)
principal 2uantum number n
n& #, 6, +, /, F.
n n&6 n&+
".
distance of e=from the nucleus
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Where ;-H of the
e=
density is foundfor the #s orbital
".
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& fn(n, l, ml, ms)
an!ular momentum 2uantum number l
for a !iven value of n, l& -, #, 6, +, F n=#
n & #, l = 0
n & 6, l& - or#
n & +, l& -, #, or6
Shape of the 8volume: of space that the e=occupies
l& - s orbital
l& # p orbital
l& 6 d orbital
l& + f orbital
Schrodin!er Wave E2uation
".
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l& - (s orbitals)
l& # (p orbitals)
".
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l& 6 (d orbitals)
".
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& fn(n, l, ml, ms)
ma!netic 2uantum number ml
for a !iven value of lml& =l, F., -, F. Cl
orientation of the orbital in space
if l& # (p orbital), ml& =#, -, or#
if l& 6 (d orbital), ml& =6, =#, -, #, or6
Schrodin!er Wave E2uation
".
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ml& =# ml& - ml& #
ml& =6 ml& =# ml& - ml& # ml& 6".
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& fn(n, l, ml, ms)
spin 2uantum number ms
ms& CI or=I
Schrodin!er Wave E2uation
ms& =Ims& CI
".
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Eistence (and ener!y) of electron in atom is described
by its uniquewave function .
Pauli exclusion principle= no two electrons in an atom
can have the same four 2uantum numbers.
Schrodin!er Wave E2uation
& fn(n, l, ml, ms)
Each seat is uni2uely identified (E, 1#6, S*)
Each seat can hold only one individual at a
time
".
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".
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Schrodin!er Wave E2uation
& fn(n, l, ml, ms)
Shell J electrons with the same value of n
Subshell J electrons with the same values of nandl
Krbital J electrons with the same values of n, l, andml
$ow many electrons can an orbital hold5
Gf n, l, and mlare fied, then ms& I or = I
& (n, l, ml, I) or & (n, l, ml, =I)
An orbital can hold 6 electrons ".
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$ow many 6p orbitals are there in an atom5
6p
n&6
l& #
Gf l& #, then ml& =#, -, or C#
+ orbitals
$ow many electrons can be placed in the +d
subshell5
+d
n&+
l& 6
Gf l& 6, then ml& =6, =#, -, C#, or C6
0 orbitals which can hold a total of #- e=
".
Ener!y of orbitals in a single electron atom
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Ener!y of orbitals in a singleelectron atom
Ener!y only depends on principal 2uantum number n
En& =1$ ( )#
n6
n
n&6
n&+
"."
Ener!y of orbitals in a multi electron atom
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Ener!y of orbitals in a multi=electron atom
Ener!y depends on nand l
n l& -
n&6 l& -n&6 l& #
n&+ l& -n&+ l& #
n&+ l& 6
"."
8Lill up: electrons in lowest ener!y orbitals (Aufbau principle)
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Lill up electrons in lowest ener!y orbitals (Aufbau principle)
$ # electron
$ #s#
$e 6 electrons
$e #s6
@i + electrons
@i #s66s#
9e / electrons
9e #s66s6
9 0 electrons
9 #s66s66p#
3 electrons
5 5
".;
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3 electrons
The most stable arran!ement of electrons
in subshells is the one with the !reatest
number of parallel spins (Hunds rule).
3 #s66s66p6
M " electrons
M #s66s66p+
K * electrons
K #s66s66p/
L ; electrons
L #s66s66p0
Me #- electrons
Me #s66s66p
"."
Krder of orbitals (fillin!) in multi electron atom
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Krder of orbitals (fillin!) in multi=electron atom
#s N 6s N 6p N +s N +p N /s N +d N /p N 0s N /d N 0p N s"."
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Electron configurationis how the electrons are
distributed amon! the various atomic orbitals in an
atom.
#s#
principal 2uantumnumber n an!ular momentum2uantum number l
number of electrons
in the orbital or subshell
rbital diagram
$
#s#
".*
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What is the electron confi!uration of !5
! #6 electrons
#s N 6s N 6p N +s N +p N /s#s66s66p+s6 6 C 6 C C 6 & #6 electrons
".*
Abbreviated as OMe+s6 OMe #s66s66p
What are the possible 2uantum numbers for the
last (outermost) electron in 3l5
3l #" electrons #s N 6s N 6p N +s N +p N /s#s66s66p+s6+p0 6 C 6 C C 6 C 0 & #" electrons
@ast electron added to +p orbital
n & + l& # ml& =#, -, or C# ms& I or =I
Kutermost subshell bein! filled with electrons
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Kutermost subshell bein! filled with electrons
".*
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".*
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Paramagneticunpaired electrons
6p
!iamagneticall electrons paired
6p".*
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Chemistry Mystery: %isco&ery of 'eli$m
Gn #**, Pierre >anssen detected a new dar line in the solar
emission spectrum that did not match nown emission lines
Gn #*;0, William 1amsey discovered helium in a mineral of
uranium (from alpha decay).
ystery element was named $elium