Chem 5
Chapter 10
The Periodic Table and Some
Atomic Properties
Part 1
“If you had only one sentence to
describe the most important scientific
knowledge we posses, what would
that sentence be? The answer is,
”
- Richard Feynman
Joseph Wright of Derby (1734-97)
The Alchemist in Search
of the Philosopher’s Stone
Discovers Phosphorus
Modern physicists have accomplished one of the
goals of alchemy: the production of artificial gold.
“In 1980, a group of researchers at Lawrence Berkeley
Laboratory (Glen T. Seaborg, et. al.) reported the
production of a few billion atoms of gold…. A bismuth
target was bombarded with a ‘relativistic projectile’ that
chipped some protons from the Bi nuclei, forming gold.
The experiment produced less than one-billionth of a cent
worth of gold.”
When the elements are
arranged in order of
increasing atomic mass or
number, certain sets of
properties recur periodically.
Periodic Table
The explanation of periodic table was the Holy Grail of the
early 20
thcentury, one of the triumphs of quantum mechanics.
Quantum mechanics is the most successful theory in the history
of science, providing a quantitative understanding of the microscopic world.
Time line of the birth of quantum mechanics:
• 1900 Planck Quantization of energy for blackbody radiation • 1905 Einstein Photoelectric effect
• 1913 Bohr Bohr model for hydrogen
• 1923 de Broglie Particle-wave duality • 1924 Bose, Einstein Bose-Einstein statistics • 1925 Pauli Pauli exclusion principle • 1925 Heisenberg Matrix mechanics
• 1925 Schrödinger Schrödinger eq.
• 1926 Born Probability interpretation of wavefunctions • 1926 Fermi, Dirac Fermi-Dirac statistics
• 1927 Heisenberg Uncertainty principle
• 1928 Dirac Relativistic wave equation and quantum field theory
What is the diameter of the electron in a H atom?
Your text book assumes 10
-14m – and that is wrong!
What is the approximate size of the wave function?
π
4
/
h
p
x
∆
≥
∆
Uncertainty Principle
The electron cannot be still.
Minimum
Kinetic
Energy
02 2 2 22
2
2
ma
h
m
p
m
p
E
k=
=
∆
=
Zero-point energy
Estimating the Atomic Radius
p
h
x
a
∆
≈
∆
=
0 0 2a
e
−
=
The smallest radius
Uncertainty Principle Æ
Minimum
Kinetic
Energy
02 2 2 22
2
2
ma
h
m
p
m
p
E
k=
=
∆
=
Potential Energy
V
2 0 2 2 0 22
a
e
ma
h
V
E
E
=
k+
=
−
Total Energy
0
2
02 2 3 0 2 0=
+
−
=
a
e
ma
h
da
dE
For minimum E
J
a
e
E
18 0 210
179
.
2
2
−×
−
=
−
=
pM
A
me
h
a
20
.
53
53
2 0=
=
=
Bohr radius
What is the size of a nucleus?
Less than one thousandth of the diameter of an atom
According to the Uncertainty Principle
π
4
/
h
p
x
∆
≥
∆
, p ~ ∆p
∆x
p
Why don’t the protons and neutrons fall apart?
Because of the strong interaction!
There are three kinds of forces in the universe:
Gravitational, electromagnetic, and strong interactions.
φ θ θ φ θ ψ d drd r Y r R dv lm nl s sin ) , ( ) ( 2 2 2 2 1 =
Probability
Probability Density
2 1sψ
−
+
+
=
0 2 2(
1
)
1
2
1
1
n
l
l
Z
a
n
r
nl 0 2 2 / ) ( a Z r r R nlSimilar to Fig. 9-32 in the text, but y axis not 4πR2(r)r2
Bohr radius Z a r / 0
Screening
in Multi-electron Atoms
Shielding reduces the apparent nuclear charge.
H
-Effective Charge
Z
eff= Z - S
e
-• Z=1
•
•
Z
eff= 1- 0.3=0.7
e
-• Z=1
•
e
-•
H
He
Z=2
e
-•
e
•
-•
Z
eff= 2 - 0.2=1.8
Z
eff= 1.0
Screening
in the excited state of He 1s
13p
1 0 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 25 30Is
3p
r (in a0) R2(r) r2Radial
Probability
Distributions
What is the Z
efffor 1s ?
Z
eff= Z – S ~ 2 – 0 = 2
The 1s close to the nucleus, not screened
by 3p
Z
eff= Z - S ~ 2 - 1 = 1
The 3p far away from the nucleus, well
screened by 1s
This He 3p orbital is like an H-atom 3p!
Penetration
- The ability to circumvent screening
In a multi-electron atom, compare E
2sand E
2pZ
eff(s) > Z
eff(p)
E
s< E
p 0 2 2 / ) ( a Z r r R nl Z a r / 0r
e
r
Z
r
V
eff 2)
(
)
(
∝
−
r
e
r
Z
r
e
r
Z
r
V
eff eff 2 2(
)
)
(
)
(
∝
−
≠
−
Large contribution from small r and large Zeff(r)
2 2
n
Z
R
E
n=
−
H effPenetration
In a multi-electron atom, compare E
3s,E
3p, E
3d0 0.05 0.1 0.15 0.2 0.25 0 5 10 15 20 25 30
r (in a
0)
3s
3p
3d
R
2r
2Z
eff(s)
>
Z
eff(p)
>
Z
eff(d)
2 2 eff H n
n
Z
R
E
=
−
E
s<
E
p<
E
dEnergy crossover for different n
E
4s<E
3dE
5s<E
4dE
6s<E
4f<E
5d<E
6pE
7s<E
5f<E
6d<E
7p2 2 eff H n
n
Z
R
E
=
−
Energy splitting within the same n
For certain but not all atomic No.
2
e
For multi-electron Atoms
Electron Configuration and the Periodic Table
1. Minimizing energy
2. Paul exclusion principle 3. Hund’s rule
The essence of periodicity is that elements in the same group of the table have similar electronic configurations.
The Aufbau Process
Periodic Properties: Atomic radii Inonic radii Ionization energies Electron affinities Chemical reactivity
Interaction of Electromagnetic Waves with Matter
Mechanisms for color generation
Why does your credit card give rainbow
colors?
What gives rise to a rainbow?
Dispersion
- Light velocity is frequency dependent.Diffraction
- A grating has a periodic structure at the dimension of the light wavelength.Scattering
Rayleigh Scattering
-
Elastic scattering has higher efficiency at higher frequenciesWhy is the sky blue or red?
Mie Scattering
- Scattering by metallic particles
Raman Scattering
-
Inelastic scattering, characteristic of molecular vibrationsWhy is the church glass
so colorful?
What substance in the church glass gives
rise to these colors?
Southwark Cathedral, London,
where John Harvard was baptized in 1607.
Mie scattering by
gold particles of
different diameters
Emission
Spontaneous Emission (Fluorescence)
Blackbody Radiation
LASER Emission
What do you see from the lamps?
The Noble Gases
http://home.achilles.net/~jtalbot/data/elements/
Greek Argos –The lazy one
William Ramsay 1852-1916
Summary of Electromagnetic
Interactions with Matter
• Dispersion
• Diffraction
• Scattering
• Rayleigh scattering
• Mie scattering
• Raman scattering
• Absorption
• Emission
• Fluorescence
• Blackbody radiation
• Laser
Cecilia Payne-Gaposchkin (1900-1979)
Harvard College Observatory had a vast amount of spectroscopic data. Every star has many spectral lines. Different spectra among stars seemed to
suggest different stars’ compositions. Her thesis project was to figure out what the spectral lines meant.
In 1923, Cecilia Payne came to Harvard as a graduate student from England. As an undergraduate, she had heard lectures by Bohr and Rutherford that interested her in astrophysics. At that time, however, the best an
educated woman could hope to do was to teach high school.
She found that the spectral lines have the same
frequencies but different intensities. She realized that the compositions of the stars are the same; the only
difference is their temperatures. She was not only able to determine the temperatures of the stars, but also came to the conclusion that most stars are composed of hydrogen and helium.
At first, her thesis committee did not believe her conclusions, but before long they and other scientists hailed her work as the greatest thesis in astrophysics. She later became the first woman professor at Harvard.
