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CHEMISTRY 161
Chapter 7
Quantum Theory and Electronic Structure of the Atom
www.chem.hawaii.edu/Bil301/welcome.html
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REVISION
= c
E h
1. light can be described as a waves of a
wavelength and frequency
2. light can be emitted or absorbed only in discrete quantities (quantum – package - photon)
3. duality of wave and corpuscle
hp mc
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cathode (-)
anode (+)
focus anode (+) fluorescent screen
Deflection of Cathode Rays
particles are negatively charged; particles are defined as ‘electrons’
2. Properties of Electrons
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hp mc
h
mc
de Broglie wavelength
h
mu
each particle can be described as a
wave with a wavelength λ
(interferences)
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out of phase wave add
destructive interference
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in phase wave add
constructive interference
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electrometer
gold foil
electron gun
angle (
curr
ent
interference patterns
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Diffraction of an electron beam (metal crystal)
WAVE-PARTICLE DUALITY
ph
mh v
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matter and energy show particle and wave-like properties
WAVE-PARTICLE DUALITY
MASS INCREASES
h
m v ph
mh v
WAVELENGTH GETS SHORTER
MASS DECREASES WAVELENGTH GETS LONGER
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What are the wavelengths of a 0.10 kg ball moving at 35
m/s and an electron moving at 1.0 x 107 m/s?
vmh
)/35)(10.0(10626.6 34
smkgJs
1J = kg m2 s-2
= 1.9 x 10-34 m
Ball:
h = 6.626 x 10-34 J sSolution:
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What are the wavelengths of a 0.10 kg ball moving at 35
m/s and an electron moving at 1.0 x 107 m/s?
Solution: h = 6.626 x 10-34 J s
vmh
1J=kg m2 s-2
)/101)(1011.9(10626.6
731
34
smkgJs
= 7.3 x 10-11 m
Electron: kgm 311011.9
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What are the wavelengths of a 0.10 kg ball moving at 35
m/s and an electron moving at 1.0 x 107 m/s?
Solution: h = 6.626 x 10-34 J s
vmh
1J=kg m2 s-2
= 1.9 x 10-34 m
= 7.3 x 10-11 mElectron:
Ball:
massive particles have immeasureably small wavelengths
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Wave-likeParticle-like
Baseball Proton PhotonElectron
WAVE-PARTICLE DUALITY
large pieces of matter are mainly particle-like, with
very short wavelengths
small pieces of matter are mainly wave-like with longer
wavelengths
MASS
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1. light behaves like wave and particle
2. electron behaves like wave and particle
3. electrons are constituents of atoms
4. light is emitted/absorbed from atoms in discrete quantities (quanta)
E h
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Einitial
Efinal
EMISSION OF A PHOTON
E h
atoms and molecules
emit discrete photons
electrons in atoms and molecules have discrete
energies
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EMISSION SPECTRAwhite light passing through a prism gives a
continuous spectrum
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we can analyze the wavelengths of the light emitted
HYDROGEN DISCHARGE
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EMISSION SPECTRAanalyze the wavelengths of the light emitted
only certain wavelengths observed
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white light
(continuous spectrum)
experimental evidence
only certain energies are allowed in the hydrogen atom
hydrogen gas
(line spectrum)
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CHARACTERISTIC LINE SPECTRUM OF HYDROGEN
Balmer found that these lines have frequencies related
1152
1029.31
41
s
nv
n=3n=4n=5
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Niels Bohr
THE BOHR ATOM
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THE BOHR ATOM
electrons move around the nucleus in only certain allowed circular orbits
e-
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e-
THE BOHR ATOM
as long as an electron remains in a given orbit its energy remains constant and no light is emitted
Bohr’s postulate
electrons move around the nucleus in only certain allowed circular orbits
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WHY THE ELECTRON DOES NOT CRASH INTO THE NUCLEUS?
Bohr postulated that the wavelength of the electron just fits the radius of the orbit.
three wavelengths
STABLE
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WHY THE ELECTRON DOES NOT CRASH INTO THE NUCLEUS?
five wavelengths
STABLE
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electrons move around the nucleus in only certain allowed circular orbits
e-
THE BOHR ATOM
each orbit has a quantum number associated with it
QUANTUM NUMBERS
n is a QUANTUM NUMBER
n= 1,2,3,4……...
n = 4
n = 3
n = 2
n = 1
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n = 4
n = 3
n = 2
n = 1
THE BOHR ATOMQUANTUM NUMBERS and the ENERGY
2
2
n
AZEn
Z = atomic number of atom
A = 2.178 x 10-18 J = Ry
THIS ONLY APPLIES TO ONE ELECTRON ATOMS
OR IONS
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BOHR ATOM ENERGY LEVEL DIAGRAM
2
2
n
AZEn
Z=1
2nA
En
HYDROGEN ATOM!
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2nA
En En
EN
ER
GY
n=1-A
AA
E 21 1
BOHR ATOM ENERGY LEVEL DIAGRAM
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n=1-A
n=2-A/4
En
2nA
En
EN
ER
GY
4222
AAE
BOHR ATOM ENERGY LEVEL DIAGRAM
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n=1-A
n=2-A/4
En
n=3-A/9n=4
2nA
En
EN
ER
GY
BOHR ATOM ENERGY LEVEL DIAGRAM
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n=1-A
n=2-A/4
En
0n=3-A/9n=4
En
erg
y
-A/16
e-
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n=1-A
n=2-A/4
En
0n=3-A/9n=4
En
erg
y
-A/16
e-
ELECTRON EXCITATION
2nA
En
excite electron to a higher energy level
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n=1-A
n=2-A/4
En
0n=3-A/9n=4
En
erg
y
e-
to excite the electron we need energy
this can be in the form of a photon
Ephoton = h
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n=1-A
n=2-A/4
En
0n=3-A/9n=4
En
erg
y
e-
ELECTRON DE-EXCITATION
emission of energy as a photon
e-
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ni
nf
only a photon of the correct energy will do
photonEhE
ABSORPTION OF A PHOTON
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2
2
ii
n
AZE
ni
nf
hEEE if ABSORPTION OF A PHOTON
2
2
ff
n
AZE
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2
2
2
2
if n
AZ
n
AZE
222 11
fi nnAZE
ni
nf
hEEE if ABSORPTION OF A PHOTON
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222 11
fi nnAZE
ni
nf
bsorption)1,2,3...(a if nn
ABSORPTION OF A PHOTON
This means energy is absorbed!
E0
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nf
ni
(emission)...3,2,1 fi nn
EMISSION OF A PHOTON
222 11
fi nnAZE
E0This means energy is emitted!
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hydrogen emission spectrum
n = 1 Ground state
n = 2
n = 3n = 4n = Ion8
Excited states
...
En
erg
yFor the Lyman series, nf= 1 and ni = 2,3,4…
For the Balmer series, nf = 2 and ni = 3,4,5…
For the Paschen series, nf = 3 and ni = 4,5,6…
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222 11
fi nnAZE
ni
nf
fn
IONIZATION OF AN ATOM
This means energy is absorbed!
E0
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E
the ionization energy for one mole is
IONIZATION ENERGY
= 2.178x 10-18 J atom-1 x 6.022x1023 atoms mol-1
=13.12 x 105 J mol-1
= 1312 kJ mol-1
= 2.178 x 10-18 J for one atom
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WAVELENGTH OF PHOTON
IE = 2.178 x 10-18 J for one H atomH H+ + e–
E hc
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e-
QUANTUM NUMBERS
n = 4
n = 3
n = 2
n = 1
SUMMARY
THE BOHR ATOM
222 11
fi nnAZE
Z = atomic number of atom
A = 2.178 x 10-18 J = Ry
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Homework
Chapter 7, pages 252-263 problems