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Electronic Structure of AtomsElectronic Structure of Atoms(i.e., Quantum Mechanics)(i.e., Quantum Mechanics)
Brown, LeMay Ch 6
AP Chemistry
2
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 (): distance between wave peaks
(determines “color” of light)Frequency (): # cycles/sec (measured in Hz)
c =
3
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”
ch
h E
ch h E
Max Planck(1858-1947)
• 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).
where Planck’s constant (h) = 6.63 x 10-34 J-s
4
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)
5
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:
6
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:
principal quantum number (n) = 1, 2, 3, 4, …
Rydberg’s constant (RH) = 2.178 x 10-18 J
2
18
2H
n n
10178.2
n
RE
Niels Bohr(1888-1962)
Johannes Rydberg(1854-1919)
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
Incr
easi
ng E
nerg
y, E
Pri
ncip
al Q
uant
um N
umbe
r, n
54
3
2
1
E5
E4
E3
E2
E1
8
ni = initial orbital of e-
nf = final orbital of e- in its transition
2
i2
f
Hn
1
n
1RE
2
i2
f
H
n
1
n
1
h
R
h
E
2
f2
i
H
n
1
n
1
h
R
h
E
Figure 1: Line series are transitions from one level to another.
SeriesTransition down to (emitted)
or up from (absorbed)…Type of EMR
Lyman 1 UV
Balmer 2 Visible
Paschen 3 IR
Brackett 4 Far IR
5432
1
n
Theodore Lyman
(1874 - 1954)
JohannBalmer
(1825 – 1898)
FriedrichPaschen
(1865 - 1947)
FrederickBrackett
(1896 – 1988)?
10
6.4: Matter is a Wave
Planck said: E = h c /
Einstein said: E = m c2
Louis DeBroglie said (1924): h c / m c2
h / m c
Therefore:
m = h / c Particles (with mass) have an associated wavelength
h / mcWaves (with a wavelength) have an associated mass and velocity
Louisde Broglie
(1892 - 1987)
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.
12
Heisenberg’s Uncertainty Principle (1927)
It is impossible to determine the exact position and exact momentum (p) of an electron.
p = m v
• 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).
WernerHeisenberg
(1901 – 1976)
13
Electron density distribution in H atom
14
6.5: Quantum Mechanics & Atomic Orbitals
Schrödinger’s wave function:• Relates probability () of predicting
position of e- to its energy.
dt
dihU
dx
d
m
hE
2
22
2
Where: U = potential energy
x = position t = time
m = mass i =√(-1)
ErwinSchrödinger(1887 – 1961)
15
Probability plots of 1s, 2s, and 3s orbitals
16
6.6: Representations of Orbitals
s orbital
p orbitals
d orbitals
f orbitals: very complicated
Figure 2: Orbital Quantum NumbersSymbol Name Description Meaning Equations
nPrinciple
Q.N.
Energy level
(i.e. Bohr’s theory)
Shell number
n = 1, 2, 3, 4, 5, 6, 7
n = 1, 2, 3, …
lAngular
Momentum Q.N.
General probability
plot (“shape” of the orbitals)
Subshell number
l = 0, 1, 2, 3
l = 0 means “s”
l = 1 means “p”
l = 2 means “d”
l = 3 means “f”
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 Name Description Meaning Equations
mlMagnetic
Q.N.3-D orientation of the orbital
s has 1
p has 3
d has 5
f has 7
ml = -l, -l +1, …,
0, l, …, +l
There are
(2l + 1) values.
ms Spin Q.N.Spin of the electron
Parallel or antiparallel
to field
ms = +½ or
-½
* s, p, d, and f come from the words sharp, principal, diffuse, and fundamental.
20
Permissible Quantum Numbers
(4, 1, 2, +½)
(5, 2, 0, 0)
(2, 2, 1, +½)
Not permissible; if l = 1, ml = 1, 0, or –1 (p orbitals only have 3 subshells)
Not permissible; ms = +½ or –½
Not permissible; if n = 2, l = 0 or 1 (there is no 2d orbital)
21
1. Aufbau principle: e- enter orbitals of lowest energy first (* postulated by Bohr, 1920)
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
6d
4f x 7
5f x 7
Increasing Energy
7p
6.7: Filling Order of Orbitals
• Relative stability & average distance of e- from nucleus
22
1. Aufbau principle: e- enter orbitals of lowest energy first
Increasing Energy
1s
2s
3s
4s
5s
6s
7s
3d
4d
5d
6d
4f x 7
5f x 7
2p
3p
4p
5p
6p
7p
• Relative stability & average distance of e- from nucleus
6.7: Filling Order of Orbitals
23
Use the “diagonal rule” (some exceptions do occur).
Sub-level maxima: s = 2 e-
p = 6 e-d = 10 e-f = 14 e-…
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d
7s 7p
24
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)
3. Hund’s rule: e- are added singly to each equivalent (degenerate) orbital before pairing
Ex: Phosphorus (15 e-) has unpaired e- inthe valence (outer) shell.
1s 2s 2p 3s 3p
WolfgangPauli
(1900 – 1958)
FriedrichHund
(1896 - 1997)
6.9: Periodic Table & Electronic Configurations
s block p blockd blockf block
s1 s2
p1p2p3p4p5 p6
d2 d3 d5 d5 d6 d7 d8d10d10
f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14
s2
1s2s3s4s5s6s7s
2p3p4p5p6p7p
4f5f
3d4d5d6d
3d4d5d6d
d1
26
Electronic Configurations
Element Standard ConfigurationNoble Gas Shorthand
Nitrogen
Scandium
Gallium
[He] 2s22p3
[Ar] 4s23d1
[Ar] 4s23d104p1
1s22s22p3
1s22s22p63s23p64s23d1
1s22s22p63s23p64s23d104p1
27
Element Standard ConfigurationNoble Gas Shorthand
Lanthanum
Cerium
Praseodymium
[Xe] 6s25d1
[Xe] 6s25d14f1`
1s2 2s22p6 3s23p6 4s23d104p6
5s24d105p6 6s25d1
1s2 2s22p6 3s23p6 4s23d104p6
5s24d105p6 6s25d14f1
[Xe] 6s24f31s2 2s22p6 3s23p6 4s23d104p6
5s24d105p6 6s24f3
28
Notable Exceptions
Cr & Mo: [Ar] 4s1 3d5 not [Ar] 4s2 3d4
Cu, Ag, & Au: [Ar] 4s13d10 not [Ar] 4s23d9