Transcript CHEMISTRY 161 Chapter 7 Quantum Theory and Electronic Structure of the Atom www.chem.hawaii.edu/Bil301/welcome.html

CHEMISTRY 161
Chapter 7
Quantum Theory and Electronic Structure of the Atom
www.chem.hawaii.edu/Bil301/welcome.html
REVISION
1. light can be described as a waves of a
wavelength and frequency
 = c
2. light can be emitted or absorbed only in discrete quantities
(quantum – package - photon)
E  h
3. duality of wave and corpuscle
p
h

 mc
2. Properties of Electrons
Deflection of Cathode Rays
anode (+)
cathode (-) focus anode (+)
fluorescent screen
particles are negatively charged; particles are defined as ‘electrons’
de Broglie wavelength
p
h

h

mc
 mc
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
q
electrometer
gold foil
current
electron gun
angle (q)
interference patterns
Diffraction of an electron beam (metal crystal)
h
h


mv p
WAVE-PARTICLE DUALITY
WAVE-PARTICLE DUALITY
matter and energy show particle and wave-like properties
mv 
h

h
h


mv p
MASS INCREASES
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?
Solution:
h

mv
h = 6.626 x 10-34 J s
1J = kg m2 s-2
Ball:
 34
6.626  10
Js

(0.10kg )(35m / s )
 = 1.9 x 10-34 m
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:
1J=kg m2 s-2
Electron:
h

mv
h = 6.626 x 10-34 J s
m  9.11  10
 34
 31
kg
6.626  10 Js

 31
7
(9.11  10 kg )(1  10 m / s )
 = 7.3 x 10-11 m
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:
1J=kg m2 s-2
h

mv
h = 6.626 x 10-34 J s
Ball:
 = 1.9 x 10-34 m
Electron:
 = 7.3 x 10-11 m
massive particles have
immeasureably small wavelengths
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
Baseball Proton
Particle-like
Electron
Photon
Wave-like
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 
EMISSION OF A PHOTON
atoms and molecules
Einitial
emit discrete photons
E  h 
Efinal
electrons in atoms and
molecules have discrete
energies
EMISSION SPECTRA
white light passing through a prism gives a
continuous spectrum
HYDROGEN DISCHARGE
we can analyze the wavelengths of the light emitted
EMISSION SPECTRA
analyze the wavelengths of the light emitted
only certain wavelengths observed
white light
(continuous spectrum)
hydrogen gas
(line spectrum)
experimental evidence
only certain energies are allowed in the hydrogen atom
CHARACTERISTIC LINE
SPECTRUM OF HYDROGEN
n=5 n=4
n=3
Balmer found that these lines have frequencies related
1 1

15 1
v    2   3.29  10 s
4 n 
THE BOHR ATOM
Niels Bohr
THE BOHR ATOM
e-
electrons move around the nucleus in only
certain allowed circular orbits
THE BOHR ATOM
electrons move around the nucleus in only
certain allowed circular orbits
as long as an electron remains in a given orbit its
energy remains constant and no light is emitted
e-
Bohr’s postulate
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
THE BOHR ATOM
electrons move around the nucleus in only
certain allowed circular orbits
QUANTUM NUMBERS
n=4
n=3
n=2
n=1
e-
each orbit has a quantum
number associated with it
n is a QUANTUM NUMBER
n= 1,2,3,4……...
THE BOHR ATOM
QUANTUM NUMBERS and the ENERGY
n=4
n=3
n=2
n=1
En  
AZ
n
2
2
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
En  
Z=1
AZ
n
2
2
HYDROGEN ATOM!
A
En   2
n
BOHR ATOM ENERGY LEVEL DIAGRAM
ENERGY
En
-A
A
En   2
n
A
E1   2   A
1
n=1
BOHR ATOM ENERGY LEVEL DIAGRAM
En
ENERGY
-A/4
-A
A
En   2
n
A
A
E2   2  
2
4
n=2
n=1
BOHR ATOM ENERGY LEVEL DIAGRAM
En
-A/4
n=2
ENERGY
-A/9
n=4
n=3
-A
n=1
A
En   2
n
En
-A/4
n=2
Energy
0
-A/9
-A/16
n=4
n=3
-A
e-
n=1
En
0
-A/9
n=2
-A
A
En   2
n
excite electron to a
higher energy level
Energy
-A/4
e-
-A/16
n=4
n=3
ELECTRON EXCITATION
n=1
En
to excite the electron we
need energy
n=4
n=3
-A/4
n=2 this can be in the form of
a photon
Energy
0
-A/9
-A
Ephoton = h
e-
n=1
ELECTRON DE-EXCITATION
En
n=4
n=3
0
-A/9
e-
Energy
-A/4
-A
n=2
emission of energy as a photon
e-
n=1
ABSORPTION OF A PHOTON
nf
only a photon of the correct
energy will do
ni
E  h  E
photon
ABSORPTION OF A PHOTON
E  E f  Ei  h
nf
AZ
Ei   2
ni
2
AZ
Ef   2
nf
ni
2
ABSORPTION OF A PHOTON
E  E f  Ei  h
nf
ni
 AZ 2   AZ 2 
E    2     2 
 n   n 
f 
i



1
1
2

E  AZ

 n2 n2 
f 
 i
ABSORPTION OF A PHOTON
nf


1
1
2

E  AZ

 n2 n2 
f 
 i
n f  ni  1,2,3...(absorption)
E0
ni
This means energy is absorbed!
EMISSION OF A PHOTON
ni


1 
2 1
E  AZ

 n2 n2 
f 
 i
ni  n f  1,2,3...(emission)
E0
nf
This means energy is emitted!
hydrogen emission spectrum
For 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…
8
Energy
...
n=
Ion
n=4
Excited
n=3
states
n=2
n = 1 Ground state
IONIZATION OF AN ATOM
nf
ni


1
1
2

E  AZ

 n2 n2 
f 
 i
nf  
E0
This means energy is absorbed!
IONIZATION ENERGY
E = 2.178 x 10-18 J for one atom
the ionization energy for one mole is
= 2.178x 10-18 J atom-1 x 6.022x1023 atoms mol-1
=13.12 x 105 J mol-1
= 1312 kJ mol-1
WAVELENGTH OF PHOTON
H+ + e–
H
IE = 2.178 x 10-18 J for one H atom
E  h
c  
SUMMARY
THE BOHR ATOM
QUANTUM NUMBERS
n=4
n=3
n=2
n=1
 1
1 
E  AZ

 n2 n2 
f 
 i
2
eZ = atomic number of atom
A = 2.178 x 10-18 J = Ry
Homework
Chapter 7, pages 252-263
problems