Download +l - My CCSD

Electronic Structure of Atoms
(i.e., Quantum Mechanics)
Brown, LeMay Ch 6
AP Chemistry
1
6.1: Light is a Wave
• Electromagnetic spectrum:
– A form of radiant energy (can travel without
matter)
– Both electrical and magnetic (properties are
perpendicular to each other)
• Speed of Light: c = 3.0 x 108 m/s (in a
vacuum)
Wavelength (l): distance between wave peaks
(determines “color” of light)
Frequency (n): # cycles/sec (measured in Hz)
c=ln
2
6.2: Light is a Particle (Quantum Theory)
• Blackbody radiation:
* Blackbody: object that absorbs all EM radiation that strikes it; it can radiate
all possible wavelengths of EM; below 700 K, very little visible EM is
produced; above 700 K visible E is produced starting at red, orange, yellow,
and white before ending up at blue as the temperature increases
– discovery that light intensity (energy emitted per unit of time) is proportional
to T4; hotter = shorter wavelengths
“Red hot” < “white hot” < “blue hot”
• Planck’s constant:
Blackbody radiation can be explained if energy can
be released or absorbed in packets of a standard size
he called quanta (singular: quantum).
E  hn 
hc
l
E  hn 
where Planck’s constant (h) = 6.63 x 10-34 J-s
hc
Max Planck
(1858-1947)
l
3
The Photoelectric Effect
• Spontaneous emission of e- from metal
struck by light; first explained by Einstein
in 1905
– A quantum strikes a metal atom and the energy is
absorbed by an e-.
– If the energy is sufficient, e- will leave its orbital,
causing a current to flow throughout the metal.
Albert Einstein
(1879-1955)
4
6.3: Bohr’s Model of the H Atom (and only H!)
Atomic emission spectra:
– Most sources produce light that contains many wavelengths
at once.
– However, light emitted from pure substances may contain
only a few specific wavelengths of light called a line
spectrum (as opposed to a continuous spectrum).
– Atomic emission spectra are inverses of atomic absorption
spectra.
Hydrogen: contains 1 red, 1 blue and 1 violet.
Carbon:
5
Niels Bohr theorized that e-:
– Travel in certain “orbits” around the nucleus, or, are only
stable at certain distances from the nucleus
– If not, e- should emit energy, slow down, and crash into the
nucleus.
Allowed orbital energies are defined by:
 RH
 2.178 10
En 

2
n
n2
18
principal quantum number (n) = 1, 2, 3, 4, …
Rydberg’s constant (RH) = 2.178 x 10-18 J
Johannes Rydberg
(1854-1919)
Niels Bohr
(1888-1962)
6
5
4
E3
3
E2
2
E1
1
Principal Quantum Number, n
Increasing Energy, E
E5
E4
As n approaches ∞, the e- is essentially removed from the atom, and
E∞ = 0.
• ground state: lowest energy level in which an e- is stable
• excited state: any energy level higher than an e-’s ground state
 1
1 
E  R H  2  2 
ni 
 nf
E  R H  1
1 
 2 2
n


h
h  n f
ni 
E R H  1
1 
 2 2
n


h
h  n i
nf 
ni = initial orbital of enf = final orbital of e- in its transition
8
Johann
Balmer
(1825 – 1898)
1
Friedrich
Paschen
(1865 - 1947)
n
5
4
3
2
Theodore
Lyman
(1874 - 1954)
Frederick
Brackett
(1896 – 1988)
?
Figure 1: Line series are transitions from one level to
another.
Series
Transition down to (emitted)
or up from (absorbed)…
Type of EMR
Lyman
1
UV
Balmer
Paschen
Brackett
2
3
4
Visible
IR
Far IR
6.4: Matter is a Wave
Planck said:
E=hc/l
Einstein said:
E = m c2
Louis DeBroglie said (1924): h c / l  m c2
h/lmc
Louis
de Broglie
Therefore:
(1892 - 1987)
Particles (with mass) have an
m = h / cl
associated wavelength
Waves (with a wavelength) have an
l  h / mc
associated mass and velocity
10
IBM – Almaden:
“Stadium Corral”
This image shows a ring of 76 iron atoms on a copper (111) surface. Electrons on this
surface form a two-dimensional electron gas and scatter from the iron atoms but are
confined by boundary or "corral." The wave pattern in the interior is due to the density
distribution of the trapped electrons. Their energies and spatial distribution can be quite
accurately calculated by solving the classic problem of a quantum mechanical particle in a
hard-walled box. Quantum corrals provide us with a unique opportunity to study and
visualize the quantum behavior of electrons within small confining structures.
Heisenberg’s Uncertainty Principle (1927)
It is impossible to determine the exact position
and exact momentum (p) of an electron.
p=mv
• To determine the position of an e-, you have to
detect how light reflects off it.
• But light means photons, which means energy.
When photons strike an e-, they may change
its motion (its momentum).
Werner
Heisenberg
(1901 – 1976)
12
Electron density distribution in H atom
13
6.5: Quantum Mechanics & Atomic Orbitals
Schrödinger’s wave function:
• Relates probability (Y2) of predicting
position of e- to its energy.
h2 d 2Y
dY
E
 UY  ih
2
2m dx
dt
Where:
Erwin
Schrödinger
(1887 – 1961)
U = potential energy
x = position
t = time
m = mass
i =√(-1)
14
Probability plots of 1s, 2s, and 3s orbitals
15
6.6: Representations of Orbitals
s orbital
p orbitals
16
d orbitals
f orbitals: very complicated
Figure 2: Orbital Quantum Numbers
Symbol
Name
n
Principle
Q.N.
l
Angular
Momentum
Q.N.
Description
Energy level
(i.e. Bohr’s
theory)
Meaning
Shell number
n = 1, 2, 3, 4, 5,
6, 7
Subshell
number
l = 0, 1, 2, 3
General
probability
plot (“shape” l = 0 means “s”
of the orbitals) l = 1 means “p”
l = 2 means “d”
l = 3 means “f”
Equations
n = 1, 2, 3,
…
l = 0, 1, 2,
…, n – 1
Ex: If n = 1, l
can only be
0; if n = 2, l
can be 0 or
1.
Symbol
ml
ms
Name
Magnetic
Q.N.
Spin Q.N.
Description
Meaning
3-D orientation
of the orbital
s has 1
p has 3
d has 5
f has 7
Spin of the
electron
Parallel or
antiparallel
to field
Equations
ml = -l, -l +1, …,
0, l, …, +l
There are
(2l + 1) values.
ms = +½ or
-½
* s, p, d, and f come from the words sharp, principal, diffuse, and
fundamental.
Permissible Quantum Numbers
(4, 1, 2, +½)
Not permissible; if l = 1, ml = 1, 0, or –1 (p
orbitals only have 3 subshells)
(5, 2, 0, 0)
Not permissible; ms = +½ or –½
(2, 2, 1, +½)
Not permissible; if n = 2, l = 0 or 1 (there is no
2d orbital)
20
6.7: Filling Order of Orbitals
1. Aufbau principle: e- enter orbitals of lowest
energy first (* postulated by Bohr, 1920)
7p
7s
6s
5s
6p
5p
4p
4s
6d
5f
x7
5d
4f
x7
4d
3d
3p
3s
2s
2p
1s
• Relative stability & average distance of e- from nucleus
21
6.7: Filling Order of Orbitals
1. Aufbau principle: e- enter orbitals of lowest
energy first
7p
7s
6s
5s
6p
5p
4p
4s
6d
5d
5f
x7
4f
x7
4d
3d
3p
3s
2s
2p
1s
• Relative stability & average distance of e- from nucleus
22
Use the “diagonal rule”
(some exceptions do
occur).
1s
2s 2p
3s 3p 3d
Sub-level maxima:
s = 2 ep = 6 ed = 10 ef = 14 e…
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d
7s 7p
23
2. Pauli exclusion principle (1925): no two e- can
have the same four quantum numbers; e- in same
orbital have opposite spins (up and down)
Wolfgang
Pauli
(1900 – 1958)
3. Hund’s rule: e- are added singly to each equivalent
(degenerate) orbital before pairing
Ex: Phosphorus (15 e-) has unpaired e- in
the valence (outer) shell.
1s 2s 2p
3s 3p
Friedrich
Hund
(1896 - 1997)
24
6.9: Periodic Table & Electronic Configurations
s block
s1 s2
1s
2s
3s
4s
5s
6s
7s
f block
d block
p block
s2
p1 p2 p3 p4 p5 p6
2p
d1
d2 d3 d5 d5 d6 d7 d8d10d103p
3d
3d
4p
4d f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f144d
5p
5d 4f
6p
5d
6d 5f
7p
6d
Electronic Configurations
Element
Standard Configuration
Noble Gas
Shorthand
Nitrogen
1s22s22p3
[He] 2s22p3
Scandium
1s22s22p63s23p64s23d1
[Ar] 4s23d1
1s22s22p63s23p64s23d104p1
[Ar] 4s23d104p1
Gallium
26
Noble Gas
Shorthand
Element
Standard Configuration
Lanthanum
1s2 2s22p6 3s23p6 4s23d104p6
5s24d105p6 6s25d1
[Xe] 6s25d1
Cerium
1s2 2s22p6 3s23p6 4s23d104p6
5s24d105p6 6s25d14f1
[Xe] 6s25d14f1`
1s2 2s22p6 3s23p6 4s23d104p6
Praseodymium
5s24d105p6 6s24f3
[Xe] 6s24f3
27
Notable Exceptions
Cr & Mo: [Ar] 4s1 3d5 not [Ar] 4s2 3d4
Cu, Ag, & Au: [Ar] 4s13d10 not [Ar] 4s23d9
28