ch10-1web-Revised

Chem 5 Chapter 10 The Periodic Table and Some Atomic Properties

Part 1 November 1, 2002

“If you had only one sentence to describe the most important scientific knowledge we posses, what would that sentence be? The answer is, everything is made of atoms! ” - Richard Feynman

Joseph Wright of Derby (1734-97)

The Alchemist in Search of the Philosopher’s Stone Discovers Phosphorus (1771)

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.” From Adept Alchemy (Chapter 2) by Robert A. Nelson.

Cavendish Laboratory, Cambridge, UK

Periodic Table When the elements are arranged in order of increasing atomic mass or number, certain sets of properties recur periodically.

Mendeleev (1834-1907)

The explanation of periodic table was the Holy Grail of the early 20th century, 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 1905 1913

Planck Einstein Bohr

Quantization of energy for blackbody radiation Photoelectric effect Bohr model for hydrogen

• • • • • • • • •

1923 1924 1925 1925 1925 1926 1926 1927 1928

de Broglie Bose, Einstein Pauli Heisenberg Schrödinger Born Fermi, Dirac Heisenberg Dirac

Particle-wave duality Bose-Einstein statistics Pauli exclusion principle Matrix mechanics Schrödinger eq. Probability interpretation of wavefunctions Fermi-Dirac statistics Uncertainty principle 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? Uncertainty Principle

∆x∆p ≥ h / 4π The electron cannot be still. Minimum Kinetic Energy

p2

∆p 2

h2 = = Ek = 2m 2m 2ma02

Zero-point energy Bohr orbits of H atom

Estimating the Atomic Radius

h Uncertainty Principle Æ The smallest radius a0 = ∆x ≈ ∆p

Minimum Kinetic Energy

p2

∆p 2

h2 Ek = = = 2m 2m 2ma02

Total Energy For minimum E 2

h2 e2 E = Ek + V = − 2 2 2ma0 a0

dE h2 e2 =− + 2 =0 3 da0 2ma0 a0

h a0 = = 0.53 A = 53 pM 2 me Bohr radius

2 e Potential Energy V = − a0

e2 E=− = −2.179 ×10 −18 J 2 a0

What is the size of a nucleus? Less than one thousandth of the diameter of an atom According to the Uncertainty Principle

∆x∆p ≥ h / 4π ,

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. Electromagnetic interaction is sufficient for understanding chemistry.

Bohr radius

Radial probability distributions Similar to Fig. 9-32 in the text, but y axis not 4πR2(r)r2

R nl2 ( r ) r 2 Z / a0

ψ 1s 2

r a0 / Z

Probability Density ψ 1s 2 dv = R nl2 (r )Ylm2 (θ , φ )r 2 sin θdrdθdφ

Probability

n 2 a0 rnl = Z

 1  l (l + 1)   1 + 1 − 2  2 n   

Screening in Multi-electron Atoms Shielding reduces the apparent nuclear charge. Effective Charge

H-

•e

Zeff = Z - S

• Z=1

e- •

•

H

• Z=1

e-

-

Zeff = 1- 0.3=0.7

He

•

Zeff = 1.0

•e • Z=2 • e-

-

Zeff = 2 - 0.2=1.8

Screening in the excited state of He

1s13p1

0.6

Is

0.5

Radial R2(r) r2 Probability Distributions

0.4 0.3

3p

0.2 0.1 0 0

5

10

15

r (in a0)

20

25

30

What is the Zeff for 1s ? Zeff= Z – S ~ 2 – 0 = 2 What is the Zeff for 3p ? Zeff= Z - S ~ 2 - 1 = 1

The 1s close to the nucleus, not screened by 3p 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 E2s and E2p

2

R nl ( r ) r

V (r ) ∝ −

2

Z eff (r )e 2 r

Z / a0

V (r ) ∝ −

Z eff (r )e 2 r

≠−

Z eff (r ) e 2 r

Large contribution from small r and large Zeff(r)

En = − RH r a0 / Z

Zeff(s) > Zeff(p)

Z eff2 n2

E s < Ep

Penetration In a multi-electron atom, compare E3s,E3p, E3d 0.25

3s

0.2

R 2 r2

Zeff(s) > Zeff(p) > Zeff(d) 3p

0.15 0.1

3d

0.05 0 0

5

10

15

r (in a0)

2 Zeff E n = −R H 2 n

20

25

Es < Ep < Ed

30

For multi-electron Atoms

2 Zeff E n = −R H 2 n

Energy splitting within the same n

Ens