chemistry 161 chapter 8 quantum mechanics 1. structure of an atom subatomic particles electrons...
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17p18n
17e
3517Cl
mass number
atomic number
18 neutrons
e-
classical physics predicts that electron
falls into nucleus
Why are atoms stable?
Frequency and Wavelength
= c
wavelength frequency speed of radiationmeter (m) Hz or s-1 m s-1
LONG WAVELENGTH, LOW FREQUENCY
James Maxwell
POSTULATE
visible light consist of
electromagnetic waves
speed of propagation
(speed of light)
c = 3 108 ms-1
Which color has the higher frequency?
1 = orange 2 = blue
= c
Wavelength (nanometers)
VISIBLE SPECTRUM
The wavelength of the yellow light from a lamp is 589 nm.
What is the frequency of the radiation?
c
7589 5.89 10nm m
1147
18
1009.51089.510998.2
s
mmsc
E h
CLASSICAL
any amount of energy can be emitted or absorbed
NON-CLASSICAL
energy can be emitted or absorbed only in discrete quantities (little packages)
E n h energy is not continuous
QUANTUM
smallest amount of energy which can be absorbed/ emitted
Albert Einstein
Electromagnetic radiation
can be viewed as a stream
of particle-like units called
photons
POSTULATE
hE
3. Properties of Photons
Einitial
Efinal
ABSORPTION OF A PHOTON
E h atoms and molecules
absorb discrete photons
(light quanta)
SUMMARY
= c E h
hp mc
1. light can be described as a wave of a
wavelength and frequency
2. light can be emitted or absorbed only in discrete quantities (quantum - photon)
3. duality of wave and corpuscle
E n h
hp mc
h
mc
de Broglie wavelength
h
mu
each particle can be described as a
wave with a wavelength λ
4. Properties of Electrons
matter and light (photons) show particle and wave-like properties
WAVE-PARTICLE DUALITY
MASS INCREASES
h h
mu p
WAVELENGTH GETS SHORTER
MASS DECREASES WAVELENGTH GETS LONGER
Wave-likeParticle-like
Baseball Proton PhotonElectron
WAVE-PARTICLE DUALITY
large pieces of matter are mainly particle-like
small pieces of matter are mainly wave-like
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
5. Electrons, Photons, Atoms
EMISSION SPECTRAanalyze the wavelengths of the light emitted
only certain wavelengths observed
only certain energies are allowed in the hydrogen atom
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
n=1-A
n=2-A/4
En
n=3-A/9n=4
2nA
En
EN
ER
GY
BOHR ATOM ENERGY LEVEL DIAGRAM
e-Ephoton = h
ELECTRON EXCITATION
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
e-
THE BOHR ATOM
QUANTUM NUMBERS
n = 4
n = 3
n = 2
n = 1
222 11
fi nnAZE
E0E0
1;i fn n
absorption
emission
ionization energy
6. HEISENBERG’S UNCERTAINTY PRINCIPLE
x is the uncertainty in the particle’s position
p is the uncertainty in the particle’s momentum
x ph
4
v mp
in the microscopic world you cannot determine the momentum (velocity) and location of a particle
simultaneously
EXP5
THE HEISENBERG UNCERTAINTY PRINCIPLE
Jsh 3410527.0
4
if particle is big then uncertainty small
123410527.0 skgm
x mh
v4
xh
m v
4
1
EXP5
This means we have no idea of the velocity of an electron if we try to tie
it down!
Alternatively if we pin down velocity we have no idea where
the electron is!
So for electrons we cannot know precisely where they are!
we cannot describe the electron as following a known path such as a circular orbit
Bohr’s model is therefore fundamentally incorrect in its description of how the electron behaves.
we cannot know precisely where electrons are!
The probability of finding an electron at a given location
is proportional to the square of
2
electron has wave properties
EXP VI
orbit of an electron at radius r (Bohr)
probability of finding an electron at a radius r
(Schroedinger, Born)
1. Schroedinger defines energy states an electron can occupy
2. square of wave function defines distribution of electrons around the nucleus
high electron density - high probability of finding an electron at this location
low electron density - low probability of finding an electron at this location
atomic orbital
wave function of an electron in an atom
each wave function corresponds to defined energy of electron
an orbital can be filled up with two electrons (box) EXPVII
most atoms have more than two electrons
each electron in an atom is different
electrons have different ‘labels’ called quantum numbers
QUANTUM NUMBERS
1.principle quantum number
2. angular momentum quantum number
3. magnetic quantum number
4. spin quantum number
1. principle quantum number
nn = 1, 2, 3, 4, 5…
hydrogen atom: n determines the energy of an atomic orbital
measure of the average distance of an electron from nucleus
n increases → energy increases
n increases → average distance increases
e-
n = 4
n = 3
n = 2
n = 1
n = 1 2 3 4 5 6
K L M N O P‘shell’
maximum numbers of electrons in each shell
2 n2
EXP6
2. angular momentum quantum number
l = 0, 1, … (n-1)
l = 0 1 2 3 4 5
s p d f g h
define the ‘shape’ of the orbital
3. magnetic quantum number
ml = -l, (-l + 1), … 0…… (+l-1) +l
defines orientation of an orbital in space
ORBITALS AND QUANTUM NUMBERS
1.principle quantum number
2. angular momentum quantum number
3. magnetic quantum number
4. spin quantum number
n = 1, 2, 3, 4, 5…
l = 0, 1, … (n-1)
ml = -l, (-l + 1), … 0…… (+l-1) +l
ms = -1/2; + 1/2
(n, l, ml, ms) ATOMIC ORBITALS
n l ml orbitals designation
1 0 0 1 1s
2 0 0 1 2s
1 -1,0,+1 3 2px,2py,2pz
3 0 0 1 3s
1 -1,0,+1 3 3px,3py,3pz
2 -2,-1,0,+1,+2 5 3dxy,3dyz,3dxz,
3dx2-y2,3dz2
4 … … … …
H Atom Orbital Energies
energy level diagram H atom
3s 3p 3d
2s 2p
1s
E
energy depends only on principal quantum number
orbitals with same n but different l are degenerate
1s
E
2s2p
3s3p
3d4s
4p5s
4d
MULTI-ELECTRON ATOM
orbitals with same n and different l are not degenerate
energy depends on n and ml
EXAMPLES [Xe]
Periodic Table of the Elements
period
group
chemical reactivity - valence electrons
ns1 ns2
ns2np6
ns2(n-1)dx
cations are smaller than their atoms
anions are larger than their atoms
Na is 186 pm and Na+ is 95 pm
F is 64 pm and F- is 133 pm
same nuclear charge and repulsion among electrons increases radius
one less electron electrons pulled in by nuclear charge
O < O– < O2–
EXAMPLES
Which is bigger?
Na or Rb Rb higher n, bigger orbitals
K or Ca K poorer screening for Ca
Ca or Ca2+ Ca bigger than cation
Br or Br- Br smaller than anion
QUESTIONThe species F-, Na+,Mg2+ have relative sizes in the order
1 F-< Na+<Mg2+ 2 F-> Na+>Mg2+
3 Na+>Mg2+> F- 4 Na+=Mg2+= F-
5 Mg2+> Na+>F-
QUESTION
1 F-< Na+<Mg2+
2 F-> Na+>Mg2+
3 Na+>Mg2+> F-
4 Na+=Mg2+= F-
5 Mg2+> Na+>F-
Na+ is 95 pm
Mg2+ is 66 pm
F- is 133 pm
ALL 1s22s22p6
ALL are isoelectronic
3. IONIZATION ENERGIES
M(g) M+(g) + e-
energy required to remove an electron from a gas phase atom in its electronic ground state
I1 > 0
first ionization energy(photon)
M+(g) M2+(g) + e-
M2+(g) M3+(g) + e-
second ionization energy
third ionization energy
I2 > 0
I3 > 0
I1 > I2 > I3
Why?
electrons closer to nucleus more tightly held
ION
IZA
TIO
N E
NE
RG
Y
ION
IZA
TIO
N E
NE
RG
Y
first ionization energies decrease
d shell insertion
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9
GROUP NUMBER
ION
IZA
TIO
N E
NE
RG
Y(k
J/m
ol)
1 2 13 14 15 16 17 18
n=1
n=2
n=3
n=4
1. closed shells are energetically most stable
2. half-filled shells are energetically very stable
DERIVATION OF IONIZATION ENERGIES
4. ELECTRON AFFINITIES
the energy change associated with the addition
of an electron to a gaseous atom
X(g) + e– X–(g)
electron affinity can be positive or negative
-200
-100
0
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
ATOMIC NUMBER
-ELE
CT
RO
N A
FF
INIT
Y
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar