CHEMISTRY 161
Chapter 7
Quantum Theory and Electronic Structure of the Atom
www.chem.hawaii.edu/Bil301/welcome.html
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
cathode (-)
anode (+)
focus anode (+) fluorescent screen
Deflection of Cathode Rays
particles are negatively charged; particles are defined as ‘electrons’
2. Properties of Electrons
hp mc
h
mc
de Broglie wavelength
h
mu
each particle can be described as a
wave with a wavelength λ
(interferences)
out of phase wave add
destructive interference
in phase wave add
constructive interference
electrometer
gold foil
electron gun
angle (
curr
ent
interference patterns
Diffraction of an electron beam (metal crystal)
WAVE-PARTICLE DUALITY
ph
mh v
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
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:
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
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
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
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
Einitial
Efinal
EMISSION OF A PHOTON
E h
atoms and molecules
emit discrete photons
electrons in atoms and molecules have discrete
energies
EMISSION SPECTRAwhite light passing through a prism gives a
continuous spectrum
we can analyze the wavelengths of the light emitted
HYDROGEN DISCHARGE
EMISSION SPECTRAanalyze the wavelengths of the light emitted
only certain wavelengths observed
white light
(continuous spectrum)
experimental evidence
only certain energies are allowed in the hydrogen atom
hydrogen gas
(line spectrum)
CHARACTERISTIC LINE SPECTRUM OF HYDROGEN
Balmer found that these lines have frequencies related
1152
1029.31
41
s
nv
n=3n=4n=5
Niels Bohr
THE BOHR ATOM
THE BOHR ATOM
electrons move around the nucleus in only certain allowed circular orbits
e-
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
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
WHY THE ELECTRON DOES NOT CRASH INTO THE NUCLEUS?
five wavelengths
STABLE
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
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
BOHR ATOM ENERGY LEVEL DIAGRAM
2
2
n
AZEn
Z=1
2nA
En
HYDROGEN ATOM!
2nA
En En
EN
ER
GY
n=1-A
AA
E 21 1
BOHR ATOM ENERGY LEVEL DIAGRAM
n=1-A
n=2-A/4
En
2nA
En
EN
ER
GY
4222
AAE
BOHR ATOM ENERGY LEVEL DIAGRAM
n=1-A
n=2-A/4
En
n=3-A/9n=4
2nA
En
EN
ER
GY
BOHR ATOM ENERGY LEVEL DIAGRAM
n=1-A
n=2-A/4
En
0n=3-A/9n=4
En
erg
y
-A/16
e-
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
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
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-
ni
nf
only a photon of the correct energy will do
photonEhE
ABSORPTION OF A PHOTON
2
2
ii
n
AZE
ni
nf
hEEE if ABSORPTION OF A PHOTON
2
2
ff
n
AZE
2
2
2
2
if n
AZ
n
AZE
222 11
fi nnAZE
ni
nf
hEEE if ABSORPTION OF A PHOTON
222 11
fi nnAZE
ni
nf
bsorption)1,2,3...(a if nn
ABSORPTION OF A PHOTON
This means energy is absorbed!
E0
nf
ni
(emission)...3,2,1 fi nn
EMISSION OF A PHOTON
222 11
fi nnAZE
E0This means energy is emitted!
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…
222 11
fi nnAZE
ni
nf
fn
IONIZATION OF AN ATOM
This means energy is absorbed!
E0
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
WAVELENGTH OF PHOTON
IE = 2.178 x 10-18 J for one H atomH H+ + e–
E hc
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
Homework
Chapter 7, pages 252-263 problems