Jagiellonian University Institute of PhysicsJacek BierońDepartment of

Atomic Physics

Cracow

Why is Gold YellowRelativistic Effects in Chemistry and in Atomic Physics

Helsingin Yliopisto Laboratoriet forsvensksprakigundervisning

Pekka PyykköKemian Laitos

Relativistiska effekter i kemi och i atomfysik

Varför är guldet gult?Miksi Kulta on Keltaista? Suhteellisuusteoreettisista Ilmiista Kemiassa ja Atomifysiikassa

Uniwersytet Jagielloński Instytut FizykiJacek BierońZakład Optyki

Atomowej

Kraków, 8 kwietnia 2008

Dlaczego złoto jest żółteczyli efekty relatywistyczne w chemii i fizyce atomowej

Quantum Mechanicsof Many-Electron Atoms

relativity ideas [...] are of no importance in the consideration of atomic and molecular structureand ordinary chemical reactions, in which it is,indeed, usually sufficiently accurate if one neg-

lects relativity variation of mass with velocityand assumes only Coulomb forces between the

various electrons and atomic nuclei.

Simple, Bohring algebra …

Speed of a Bohr electronnrmL ...3,2,1n

rm )1( n

2

22

rZe

rm

22 Zerm

cceZZe

22

137/1

Z(Au) = 79

for Z=137 v ~ ccZ

Size of a Bohr atomnrmL ...3,2,1n

rm )1( n

2

22

rZe

rm

2222

Zemrrm

mZer

12

2

m2

0a(Bohr radius)

mZer

12

2

rZem 22 2

Energy of a Bohr atom

cZ

2

42

2meZ

2220

42

1

1

2 c

meZ

for 35.191 U

Relativistic effects

Difference between two models:

22

0 1 cmm

1c skm5103

c

„relativistic”

„nonrelativistic”0mm

„effect” of a model, not a physical effect

Résumé

cZ 22

0

22

0 1/1 Zmcmm

2220

42

2

42

11

22

ZmeZ

meZ

Coulomb Einstein

mm

Za

mZer 00

2

2 1 mm

rNR0

0mmcv NRrrNR

Relativistic effectsin hydrogenic ions

Zfor 82.078

NRrrAu

2222 cZ

1

Aufbau

Non-Rel. Rel.

1s

Orthogonal orbitals

Relativistic aufbau

Non-Rel. Rel. Non-Rel. Rel.

1s

2s

3s

7s

Orthogonal orbitals

Relativistic effectsin the shell structure of heavy atoms

Non-Rel. Rel. Non-Rel. Rel.

f - ekspansiond - ekspansion...s - contraction

1s

2s

3s

7s4d4f

Energies of valence electrons

2.3 eV

3.5 eV

Energy levels inatoms, molecules, and solids

Energy bands in solids

Optical reflectivity

Ag

Au

3.5 eV

2.3 eV

Energy of incident light [eV]

Ref

lect

ivity

inde

x [%

]

Physiology of color

Color wheel

absorbedcolor

colorperceived

inreflected

light

(complementary colors)

Color perceived in reflected lightcolor

absorbedcolor

perceived

temat na seminarium?

Bismuth is trivalent

Relativistic effects in chemistry

Gold is yellow

Mercury is liquid

CsAu exists

Ground state configuration:10d19sd

29110 6565( sdsd forbidden transition, so isolated Au atom is „white”)

Platinum Pt (palladium Pd )

(while CsAg does not)

(while cadmium is solid)

(while antymony – penta-)

(while silver is white)

Thank you for your attention