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Why is Gold Yellow
Relativistic Effects in Chemistry and in Atomic Physics
Department of
Jacek Bieroń
Atomic Physics Jagiellonian University Institute of Physics
Cracow
Varför
är on
guldet
gult?
Miksi
Kulta
Keltaista?
Relativistiska effekter
i kemi
och i atomfysik
Suhteellisuusteoreettisista
Ilmiista
Kemiassa
ja Atomifysiikassa
Kemian Laitos
Pekka Pyykkö
Helsingin Yliopisto
Laboratoriet for
svensksprakig
undervisning
Dlaczego złoto jest żółte
czyli efekty relatywistyczne w chemii i fizyce atomowej
Zakład Optyki
Jacek Bieroń
Atomowej
Uniwersytet Jagielloński
Kraków, 8 kwietnia 2008
Instytut Fizyki
Quantum Mechanics
of Many-Electron Atoms
relativity ideas [...] are of no importance in the
consideration of atomic and molecular structure
and ordinary chemical reactions, in which it is,
indeed, usually sufficiently accurate if one neglects relativity variation of mass with velocity
and assumes only Coulomb forces between the
various electrons and atomic nuclei.
Simple, Bohring algebra …
Speed of a Bohr electron
L  m r  n n  1,2,3...
m r   ( n  1)
2
2
m
Ze

2
2

r
r
2
2
m r  Ze
2
  1/ 137
Ze Z e c
for Z=137 v ~ c


 Z c

c
Z(Au) = 79
Size of a Bohr atom
L  m r  n n  1,2,3...
m r   ( n  1)
m
Ze
m
 2
r
r
2

2 2 2
m r
2
 Ze
mr
2
 1
a0   r   2
Ze m
2
(Bohr radius)
2
Energy of a Bohr atom
  m 2  Ze r
2
2
  Z c
2
4
 1
r 2
Ze m
2
2 4
Z e m0
1
Z em
 


2
2
2
2
2
2
1  c
for
U
91
1.35
Relativistic effects
Difference between two models:
„relativistic”
m  m0
c  1   3 10 km s
5
1  c
„nonrelativistic”
2
2
c
m  m0
„effect” of a model, not a physical effect
Résumé
  Z c
1   c  m0 / 1  Z 
m  m0
2
2
4
2
2
2
2
4
Z e
Z e m0
1
   2 m  

2
2 2
2
2
1 Z 
Coulomb
Einstein
m0
 1 a0 m0
 rNR 
r 2  
m
Ze m Z m
2
Relativistic effects
in hydrogenic ions
vc
  NR
m m0
r rNR
1
 Z  c
2
for
Au
2
78
2
2
r rNR  0.82
Z
Aufbau
Non-Rel. Rel.
1s
Orthogonal orbitals
Relativistic aufbau
Rel. Non-Rel.
Non-Rel. Rel.
7s
3s
2s
1s
Orthogonal orbitals
Relativistic effects
in the shell structure of heavy atoms
4f
4d
Rel. Non-Rel.
f - ekspansion
d - ekspansion
...
s - contraction
Non-Rel. Rel.
7s
3s
2s
1s
Energies of valence electrons
3.5 eV
2.3 eV
Energy levels in
atoms, molecules, and solids
Energy bands in solids
Reflectivity index [%]
Optical reflectivity
Ag
3.5 eV
Au
2.3 eV
Energy of incident light [eV]
Physiology of color
Color wheel
color
perceived
in
reflected
light
absorbed
color
(complementary colors)
Color perceived in reflected light
color
perceived
color
absorbed
temat na seminarium?
Relativistic effects in chemistry
Gold is yellow (while silver is white)
(5d 10 6s1  5d 9 6s 2 forbidden transition, so
isolated Au atom is „white”)
Bismuth is trivalent (while antymony – penta-)
Mercury is liquid (while cadmium is solid)
Ground state configuration:
9 1
10
Platinum Pt d s (palladium Pd d )
CsAu exists (while CsAg does not)
Thank you for your attention

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