MIT 麻省理工學院線上課程
http://ocw.mit.edu/courses/
atomic model
: based on 200 years’ experimental evidence (1800-2011)
for chemists:
periodic repetition of properties
classical physics (developed by Isaac Newton and many others)
During the first 30 years of the 20th century, the results of many
physical experiments could be not explained by the theories of
classical physics
quantum mechanics: to explain the behavior of light and atoms
This “new physics” provides many surprises for humans who are used to the
macroscopic world, but it seems to account flawlessly (within the bounds of
necessary approximations) for the behavior of matter.
outline:
electromagnetic radiation, nature of matters, simplified models,
quantum mechanical model, periodic table
1
electromagnetic radiation:
one way for energy to travel through space
examples: microwave, sunlight, X-ray, heat, …
travel speed in a vacuum: speed of light
wave-like behavior
waves:
wavelength
λ (lambda)
frequency
speed
ν (nu)
c
c: 2.9979 x 108 m/s
 : # of waves per second,
cycles/sec (1/sec = s-1)= Hz (hertz)
λν=c
relationship between
λ and ν
λ and c
ν and c
Since all types of electromagnetic radiation travel at the speed of
light, short-wavelength radiation must have a high frequency.
For light, c = 2.9979 × 108 m/s
2
λν=c
relationship
between
λ and ν
λ and c
ν and c
classification of EM radiation
4x 10-7
λ (m)
10-12
10-10
X-ray
7x 10-7
10-8
UV
10-4
vis
10-2
IR microwave
UV : ultraviolet
VIS : visible 400-700nm
IR : infrared
1
102
104
FM
SW
AM
radio waves
sunlight: UV and vis reach earth
microwave: H2O in food absorb MW radiation
energy of H2O
energy transfer to other molecules
temperature of food
3
matter & energy
19th century
matter: particles
energy: electromagnetic radiation
20th century
Max Planck ∆E = nhν
n = 1, 2, 3, …
h: Planck’s s constant
= 6.626 x 10-34 J.s
ν: emitted or absorbed EM radiation
Energy is quantized (not continuous)
(each unit : quantum (pl. quanta))
energy : have particle properties
Albert Einstein Ephoton = hν = hc/λ
energy : stream of particles
E = mc2
energy has mass
energy vs. particle
(Albert Einstein)
energy has mass
m = E/c2 = (hc/λ)/c2 = h/λc
photon: no rest mass
Summary from Planck & Einstein’s results:
* energy : quantized – occurs only in discrete units
* dual nature of light
(EM radiation : particle and wave properties)
energy: particle & wave properties
matter: particle & wave properties? YES!
Louis de Broglie
λ = h/mv
λ: wavelength for a particle
v: velocity of a particle
5
diffraction
Diffraction : scattering light from a regular array of points or lines
Example of diffraction:
CD (compact disc): rainbow colors
-- various wavelengths of visible light: scattered differently
by regularly arranged ridges and grooves of a CD
X-ray
X’al
film
CCD detector
bright spot: constructive interference
dark area: destructive interference
diffraction pattern
6
diffraction
electron: if speed is 107 m/s
λ = 10-10 m = 10-8 cm = 1 Å
Most efficient diffraction : λ ~ spacing between scattering points
X-ray diffraction: structural determination
Conclusion:
EM radiation: wave-like and particulate properties
electron:
particulate and wave-like properties
matter & energy – not distinct
all matters exhibit particulate and wave properties
size of matter:
Large (e.g. baseball) particulate properties dominates
Intermediate (e.g. electron) both properties
Small (e.g. photon) wave properties dominates
7
E
H2
2H
-E
Excited state
2H
Emit energy
Excited state
Ground state
absorb energy
Absorb energy
emit energy: quantized
Ground state
emission spectrum – line spectrum
E wave properties spectrometer
hydrogen emission spectrum:
only certain energies are allowed for the e- in the hydrogen atom
8
continuous vs. line spectrum
continuous spectrum:
white light
prism
line spectrum:
E
energy level
∆E1 = hc/λ1
9
in H:
Electron moves around the nucleus in certain allowed circular orbits
quantized energies
circular movement
attraction between e- (-) and nucleus (+)
angular momentum (product of mass, velocity, orbital radius):
to maintain the e- in the orbit
a model that can explain the experimental results
the model is incorrect but leads to the current theory
11
Bohr Model:
quantum mechanical model:
10
Bohr model?
Bohr model:
only works for hydrogen
does not work for other elements
electrons: do not move around the nucleus in circular orbits
14
Werner Heisenberg
Louis de Broglie
Erwin Schrödinger
quantum mechanics (wave mechanics)
electron in atoms: similar to a standing wave
fastened
side-ways
½
1
node: points of zero lateral
standing wave: whole number of half-waves
15
solutions of Schrödinger’s equation
Schrodinger’s equation : many solutions
Each solution : a wave function with a particular E
A wave function : an orbital
not a Bohr’s orbit (circular)
a wave function: no information about the pathway of e(an orbital)
17
solutions of Schrödinger’s equation
Solutions to Schrödinger eq.:
each function corresponds to a given energy state
n
1
2
function
ψ = √(2/L)sin(πx/L)
ψ= √(2/L)sin(2πx/L)
energy
E1 = h2/8mL2
18
solutions of Schrödinger’s equation
19
Heisenberg uncertainty principle
Heisenberg uncertainty principle:
∆x • ∆(mv) ≥ h/4π
∆ x: uncertainty in position
∆(mv): uncertainty in momentum
The limitation is very important for small particles (e.g. e-)
small for big objects
electron density map
electron probability
ψ : not easy to visualize
ψ2 : probability of finding e-
probability (R2)
(intensity)
distance from nucleus (r)
20
radial probability
maximum probability
Radial probability (4πr2R2)
distance from nucleus (r)
H: 1s orbital r = 0.529 Å
max. radial probability
radius of Bohr’s innermost orbit of H
21
size of orbital
size of an orbital: ? probability never becomes zero!
define relative orbital size!
for chemists, size of a orbital:
radius of the sphere that enclosed 90% of the total electron probability
orbital: 3-D electron density map
many solutions for Schrödinger’s equation
many wave functions
Use quantum numbers to represent them (4 number)
Principle quantum number (主量子數
主量子數)
主量子數
Angular momentum quantum number (角
角(動
動)量子數
量子數)
量子數
Magnetic quantum number (磁量子數
磁量子數)
磁量子數
Spin quantum number (自旋量子數
自旋量子數)
自旋量子數
23
principle quantum number (n)
values: integral (1, 2, 3, ….)
related to the size and energy of the orbital (決定大小與能量)
n↗ size of orbital↗ energy ↗
(e- & nucleus interaction↘)
angular momentum quantum number (l)
• values: integral, 0 to n-1
• shape of orbital (形狀)
l =0
s; l = 1
p; l = 2
d; l = 3
f; l = 4
g
magnetic quantum number (ml)
• values: integral, -l to l
• orientation of orbital (決定方向)
24
n
l
ml
1
2
0
0
1
0
1
1s
2s
2p
3s
3p
2
3d
0
1
2
3
4s
4p
4d
4f
3
4
# of orbitals
1
0
1
0
-1, 0, 1(px,py,pz) 3
1
0
3
-1, 0, 1
(px,py,pz)
5
-2 , -1 , 0, 1, 2
(dxy, dyz, dxz, dx2-y2, dz2 )
0
-1, 0, 1
-2, -1, 0, 1, 2
-3, -2, -1, 0, 1, 2, 3
1
3
5
7
max # of e2
2
6
2
6
10
2
6
10
14
25
characteristics of hydrogen orbitals
s orbitals:
1s, 2s, 3s, …
sizes : surface contains 90% electron probability
1s
2s
e- probability distribution
3s
Nodal surface
: zero probability
26
2p orbitals
2p orbital:
27
3d orbitals
3d orbital: two types
four lobes
two lobes and a belt
energy of orbitals
energy level diagram of H
ame n same energy
ame n same energy
E
3s
3p
2s
2p
For H , same n same energy
Orbital with same energy degenerate (簡併)
electron in 1s ground state
electron in other orbital excited state
3d
energy
En = nh2/8mL2
electron spin
electron spin: *fourth quantum number
*developed to explain the details of emission
spectra of atoms by y Goudsmit and Uhlenbeck
when they were graduate students
in external magnetic field
magnetic moment of a electron
: two possible orientations
from a spinnig charge
two oppositely directed spin states
electron spin quantum number : ms (+1/2 or -1/2)
30
Pauli principle
Pauli exclusion principle:
in an atom, no two electrons can have the same set of four quantum numbers
(n, l, ml, ms) of eA- ≠ (n, l, ml, ms) of eBone orbital can hold only two electrons
the two electrons: opposite spins
one orbital: n, l, ml are set
Pauli exclusion principle
(n, l, ml, ms) of eA- ≠ (n, l, ml, ms) of eB-
(2,1,-1,+1/2) 2px (up electron)
2s
3px
(?,?,?,?)
3dxy
(?,?,?,?)
(?,?,?,?)
polyelectronic atoms: more than one electron, more than one proton
e- -- nucleus: attraction
Potential energy
e- -- e-: repulsion
electrons: moving around nucleus
Kinetic energy
e- pathways: unknown
e- -- e- repulsions: cannot be exactly solved
net result of
example: Na (11 electrons)
nuclear attraction
average repulsions of all other electrons
one of the 11 electrons
10 other electrons and nucleus
32
shielding effect
Na
11+
e11-
10-
Electron is screened or shielded
from the nuclear charge (11+)
11+
11+
e-
by the repulsions of other electrons (10-)
33
orbital energy level diagram
orbitals for
hydrogen
polyelectronic atom
relative energies of orbitals
polyelectronic atom
H
3 3s
3p
3d
3p
3s
3d
E
E
2s
1s
2p
2p
2s
1s
Ens < Enp < End < Enf
34
relative energies of orbitals
Penetration effect : e- penetrates to the nucleus (more penetration for 2s than 2p)
larger e- -- nucleus attraction
lower energy
(attraction: 2s > 2p)
(2s lower than 2p)
E2s < E2p < E3s < E3p < E3d
35
Aufbau principle
Aufbau: build up in German
Aufbau principle: building up elements
protons are added one by one
electrons
H: ground state
He:
lowest orbital 1s
1s1
1s2
Electron configurations
36
configuration & orbital diagram
electron configuration
H
1s1
He
1s2
C
1 1s22 2s22 2p2
N
1s22s22p3
O
1s22s22p4
F
1s22s22p5
Ne
1s22s22p6
orbital diagram
1s
2s
2p
3s
Na
37
Hund’s rule : lowest energy configuration max. number of unpaired electrons
configuration & orbital diagram
electron configuration
C
1s22s22p2
N
1s22s22p3
O
1s22s22p4
orbital diagram
1s
2s
2p
Valence electrons(價電子)
Core electrons(核電子)
Most important electrons : involved in bonding
38
valence electrons & groups
in periodic table
elements in the same group: same valence electron configuration similar chemical behavior (like 1A)
K (potassium)
1s22s22p63s23p64s1
= [Ar]4s1
Ca (calcium)
[Ar]4s2
Sc (scandium)
[Ar]4s23d1
Ti (titanium)
[Ar]4s23d2
transition metals (elements)
39
transition elements
d-transition elements: e-’s in 3d, 4d, 5d, 6d
f-transition elements: lanthanides & actinides
e- filling:
* (n+1)s before nd (penetration effect: s penetrates better)
* La (lanthanide): [Xe]6s25d1
Hf (hafnium): [Xe]4f146s25d2
Ce ([Xe]6s24f15d1), Pr ([Xe]6s24f35d0), Nd ([Xe]6s24f45d0), …
lanthanide series (lanthanides)
40
filling the electrons
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d
5d
6d
4f
5f
Energy series : 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, ……
41
periodic trends
Ionization energy : energy to remove an electron from a gaseous atom or ion
X(g)
highest energy
X(g)+ + e- I 12stndee--
I1
I2
within a period
within a group
I1: decreases with increasing Z
∵Z ↗
e- farther away from nucleus
easier to remove (less attracted)
ionization energy
atomic number
I1: increases with increasing Z
∵Z ↗
stronger e- -- nulceus attraction
(nuclear charge ↗
and shielding is not efficient)
more energy t to remove e-
ionization energy
atomic number
42
group & period
a group (a family): a vertical column
a period : a horizontal row
43
electron affinity
X(g) + e-
within a group
∆E: change is small
less negative with increasing Z
X(g)-
∆E
within a period
∆E: more negative with increasing Z
more stable
more positive
44
atomic radius
size of an orbital:
size of an atom: cannot be specified exactly
arbitrary choice
atomic radius (pl. radii; diameter = 2 X radius):
Example:
Br-Br: dBr-Br = 228 pm = 2.28 Å
rBr = 114 pm = 1.14 Å
2r
covalent r ≤ r of 90% of e- density of an atom
∵
nonmetallic atoms:
1. r from diatomic molecules
2. r from various covalent compounds
metal atoms:
from solid metal crystals
45
atomic radius
within a group
r: increase with increasing Z
∵increasing in orbital size (n↗)
within a period
r: decrease with increasing Z
∵increasing nuclear charge
(relatively, shielding is decreasing )
attraction between e- -- nucleus ↗
smaller size
46
periodic table
metals & nonmetals
metals: *tend to give up electron(s) to form cations
*tend to have low ionization energies
*left-hand side of the table
*most reactive metals: lower left-hand portion
nonmetals: *tend to gain electron(s) when react with metal
*large ionization energies
*right-hand side of the table
*most reactive nonmetals: upper right-hand portion
(noble gases are excluded)
metalloids (= semimetals): exhibit both metallic and nonmetallic properties
47
periodic table
for representative elements:
in a group: same valence electron configuration
similar properties
*IA (1A), IIA (2A), IIIA (3A), ….., VIIIA (8A)
number of the group: number of valence electrons
*
electron configurations – predictable
*transition metals: many exceptions (e.g. Cr & Cu)
special names for certain groups
: alkali metals, alkaline earth metals, transition metals, …, noble gases
48
periodic table
special names of the groups
chalcogens
alkali metals
halogens
noble gases
alkaline earth metals
IA
VIIIA
transition elements
IIIA IVA VA VIA VIIA
IIA
VIIIB
IIIB IVB VB VIBVIIB
Lanthanides
Actinides
IB IIB
49
Summary
wave character of energy
quantum mechanics: H and polyelectronic atoms
periodic table: *valence electron configuration
*periodic trends in atomic properties
*group and period
50