CHAPTER 1. ATOMS: THE QUANTUM WORLDrhbestsh.x-y.net/.../Chemistry/Lecture_Note/Ch.01.pdf · 2010-04-12 · Atomic Structure – Quantum Mechanics (量子力學) Internal Structure

2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1

CHAPTER 1. ATOMS: THE QUANTUM WORLD

Matter – Composed of Atoms

Atomic Structure – Quantum Mechanics (量子力學)

Internal Structure of Atom Electronic Structure

Periodic Variation of Atomic Properties

INVESTIGATING ATOMS 1.1 The Nuclear Atom

Fig. 1.1. Sir Joseph John Thomson (英,1856-1949) Fig. 1.2. Cathode ray tube

Nobel Prize ‘06 Physics (His son – George Paget Thomson, Nobel Prize ’37 Physics)

◈ Electron

Discovered by J. J. Thomson in 1897

Measured the value of the ratio, e / me

Oil-drop Experiment by R. Millikan

Measured the value of e = 1.602 x 10 –19 C

me = 9.109 x 10 – 31 kg

Robert Millikan (美,1868-1953) Fig. 1.3. Oil-drop experiment

Nobel Prize ‘23 Physics

R.A. Millikan, On the Elementary Electric charge and the Avogadro Constant, Phys. Rev. II, 2(1913), p. 109

http://en.wikipedia.org/wiki/George_Paget_Thomson

2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 ◈ Nuclear Model

Fig. 1.4. Ernest Rutherford Hans Geiger Ernest Marsden

(英--新西蘭,1871-1937) (獨,1882–1945) (英--新西蘭,1871-1937)

Nobel Prize ‘08 Chemistry Geiger-Müller counter

▶ Geiger-Marsden Experiment : Shooting α -particles toward thin metal (Au, Pt,…) foils Hans Geiger and Ernst Marsden, “On a Diffuse Reflection of the α-Particles.”

Proceedings of the Royal Society 82 (1909): 495-500.

♦ There is a dense pointlike center of positive charge, nucleus.

♦ Surrounding large empty space in which electrons are located

♦ Nucleons : Protons + Neutrons

♦ Atomic Number, Z : Number of protons in the nucleus

♦ Total charge on an atomic nucleus of atomic number Z : +Ze

There must be Z electrons around it to ensure total atomic neutrality

The Characteristics of Electromagnetic Radiation

Spectroscopy (分光法) : analysis of the light emitted or absorbed by substances

Electromagnetic radiation : Oscillating electric and magnetic field that travel through empty space

at the speed of light c = 3.00 x 108 m·s–1

Frequency, ν : # of wave peaks per second passing over a fixed point Unit: 1 Hz = 1 s–1 ~1015 Hz for visible light

Intensity : Square of the amplitude

Wavelength, λ : 400 ~ 700 nm for visible light


Wavelength x frequency = speed of light, cλν =

1.3 Atomic Spectra of Hydrogen Atom

(a) Visible spectrum (white light passing through a prism) (b) Complete spectrum of H atom


◈ Rydberg Formula Johannes Rydberg (瑞典,1854-1919)

1 2 1 12 21 2

1 1 , 1,2,3,... 1, 2,... n n n nn n

ν⎛ ⎞

= − = = + +⎜ ⎟⎝ ⎠

R

where : Rydberg constant 153.29 10 Hz= ×R

▶ Lyman Series (1906) UV region (n1 = 1) Theodore Lyman (美,1874-1954)

▶ Balmer Series (1885) Visible region (n1 = 2) Johann Balmer (瑞西,1825-1898)

▶ Paschen Series (1908) Near IR region (n1 = 3) Friedrich Paschen (獨,1865-1947)

▶ Brackett Series (1922) IR region (n1 = 4) Frederick Sumner Brackett (美, 1896-1988)

▶ Pfund Series (1924) (n1 = 5) August Herman Pfund (美,1879-1949)

From Oxtoby

Fig. 1.11. Absorption spectrum of the Sun due to H around the Sun.


QUANTUM THEORY

★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆v★☆★☆

☆ STARS in Quantum Mechanics – Nobel Laureates in Physics ★

★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★ ☆

Max Planck (’18) Albert Einstein (’21) Niels Bohr (’22) Prince Louis de Broglie (’29)

(獨,1858-1947) (獨,1879-1955) (丁抹,1885-1962) (佛,1892-1987)

quanta photoelectric effect atomic model matter wave

Werner Heisenberg (’32) Erwin Schrödinger (’33) Paul A. M. Dirac (’33) Clinton Davisson (’37)

(獨,1901-1976) (墺地利,1887-1961) (英,1902-1984) (美,1881-1958)

uncertainty principle Schrödinger equation Dirac equation diffraction of electron

George P. Thomson (’37) Wolfgang Pauli (’45) Max Born (’54) Eugene Wigner (’63)

(英,1892-1975) (墺地利,1900-1958) (英,1882-1970) (洪牙利-美,1902-1995)

diffraction of electron exclusion principle interpretation of 2ψ group theory

“What is Life? Mind and Matter”, by E. Schrödinger, Cambridge Univ Press (1944).

“Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik”, by W. Heisenberg, Piper (1969).

“The Part and the Whole: Talks about Atomic Physics”

– “부분(部分)과 전체(全體)”, 김용준 역, 지식산업사 (1982)


1.4 Radiation, Quanta, and Photons

Blackbody Radiation

◈ Emission of thermal radiation

◆ Stefan’s law (1879)

4TI eTσ=

Josef Stefan

(墺,1835-1893)

TI : Total energy emitted over the entire range of frequencies,

per second and per m2 from the object at temperature T (K)

σ : Stefan-Boltzmann constant, measure of the efficiency of converting

thermal energy of the particle motion into thermal radiation.

σ = 5.67 x 10–8 J m–2 K–4 s–1 = 5.67 x 10–8 W m–2 K–4

e : emissivity, 0 < e < 1 , an empirical parameter depending on surfaces

◆ Wien’s displacement law (1893)

λmaxT = constant (= 2.898 x 10–3 M⋅K)

Wilhelm Wien

(獨,1864-1928)

Nobel Prize ’11

Physics

Blackbody radiation Stefan-Boltzmann law Wien’s displacement law


♦ Ultraviolet Catastrophe : Predicted by Rayleigh-Jeans using classical theory

----- classcal theory (5000K) ----- classical theory (7000K) ___ experiment (5000K) ___ experiment (7000K)

▶ Planck’s Quantization of EM radiation (1900) ~ successful explanation of blackbody radiation !

E h ν= discrete packet of energy, Quanta

346.626 10 J sh −= × ⋅ Planck’s constant

Photoelectric Effect (光電效果) – Energy quanta, Particle nature of radiation

1. No electrons ejected below the threshold frequency

2. Immediate ejection of electrons, however low the intensity

3. KE of ejected electrons increases linearly with the frequency

Einstein (1904) Photon (光子) with a packet of energy E hν=

212 em hν= −Φv

Work function: 0hνΦ = 0ν , threshold frequency characteristic of metal

Fig. 1.16 Work function in the photoelectric effect Fig. 1.17 Different threshold frequencies for different metals


Spectral lines of H atom

Transitions between two energy levels of H atom

Frequency of each spectral line:

upper lowerh E Eν = − , Bohr frequency condition

High frequency Large energy difference

1.5 The Wave-Particle Duality of Matter

Wave nature – Wavelength, Diffraction (回折)

Diffraction Constructive and destructive interferences of incident light waves

X-ray diffraction – Determination of crystal structures

Figs. 1.19 & 20 Constructive and destructive interferences of the waves of EM radiation

◈ Wave-Particle Duality

(1) Electromagnetic radiation

Particle ? – Yes! Einstein (Nobel’21, Photoelectric effect)

Wave ? – Yes! X-ray diffraction

X-ray : Discovered – Röntgen, Nobel’01

Diffraction : Discovered – Laue, Nobel’14

Structures – Braggs父子, Nobel’15 (Crystals); Hodgkin, Nobel’64 (biomolecules)


(2) Electron

Particle ? – Yes! J. J. Thomson e / me (Nobel’06)

Wave ? – Yes ! de Broglie (Nobel’29, matter wave,理)

▶ Davisson (Nobel ’37 ) & Germer (diffraction pattern,實)

Electrons reflected from a crystal

▶ G. P. Thomson (Nobel’37, diffraction pattern,實)

Electrons passing through a thin gold foil

Fig. 1.21. Thomson’s diffraction pattern

♦ Matter wave – de Broglie relation (1925)

h h

m pλ = =

v

1.6 The Uncertainty Principle

Particle – Trajectory localizable

(location & momentum at time t)

Wave – Wavelength delocalized

♦ Uncertainty Principle (1927) – Heisenberg

1 12 2 2 hxx p π∆ ∆ ≥ =

12yy p∆ ∆ ≥ , 12zz p∆ ∆ ≥

(a) large ∆x, small ∆px

(b) small ∆x, large ∆px

Note! Complementarity of x and px

1.7 Wavefunctions and Energy Levels

◈ Quantum Mechanics: Matrix Mechanics (Heisenberg), Wave Mechanics (Schrödinger)

◈ Schrödinger equation (1927)

2 2

2 ( )2d V x E

m dxψ ψ ψ− + = Eψ ψ=H

ψ : Wavefunction (or Eigenfunction) – a state of the system 2 2 or ψ ψ : Probability density of finding a particle (Max Born)

E: Energy eigenvalue


H : Hamiltonian operator – Energy operator (KE operator + PE operator)

2 2

22d

m dxψ

− : KE operator, : PE operator ( )V x

▶ Particle in a box (width: 0 L, height: 0 ∞)

Inside the box: ( ) 0V x = . Schrödinger eq. becomes 2 2

22d E

m dxψ ψ− =

General solution:

( ) sin cosx A kx B kxψ = + 2

22

d kdxψ ψ= − where 2 22 /k mE=

2 2 2 2

22 8k k hE

m mπ= =

Determination of A, B, and k

Boundary conditions at and 0x = x L= ψ is a smooth function

1) (0) 0ψ = (0) 0Bψ = = ( ) sinx A kxψ =

2) ( ) 0Lψ = ( ) sin 0L A kLψ = =

Since , si . kL0A ≠ n 0kL = nπ= with 1,2,...n = quantum number

∴ ( ) sin n xx ALπψ ⎛ ⎞= ⎜ ⎟

⎝ ⎠, 1,2,...n =

2 2 2 2

2 28 8k h n hE

m mLπ= =

Normalization:

2 2 2

0 0

( ) sin 1L L n xx dx A dx

Lπψ ⎛ ⎞= =⎜ ⎟

⎝ ⎠∫ ∫

∴ 2 ( / 2) 1A L⋅ = 1/ 2(2 / )A L=

∴ 1/ 22 ( ) sin n xx

L Lπψ ⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

2 2 2 2

2 2 8 8k h n hE

m mLπ= = , 1,2,...n =

Energy separation:

2 2 2 2 2

1 2 2

( 1) (2 1)8 8 8n n

n nE E E nmL mL mL++

∆ = − = − = + 2h

decreases as m (or L) increases Fig. 1.26 E∆

Small L Large L


From Oxtoby

THE HYDROGEN ATOM

1.7 The Principal Quantum Number

Solve the Schrödinger equation with 2

0

( )4

eV rrπε

= −

2nhE = − Rn , 1,2,...n =

where 4

153 2

0

3.29 10 Hz8

em eh ε

= = ×R

Same value as Rydberg constant !

e = 2.71828…

For other one-electron ions with atomic number Z,

2

2nZ hE

n= −

R, 1,2,...n =

Fig. 1.28 Energy levels of a H atom

Z2-dependence:

1) Field generated by a nucleus of atomic number Z and charge Ze

Z times stronger than that by a proton

2) Electron is drawn Z times closer to the nucleus than it is in hydrogen


▶ Principal quantum number, n determines the energy levels of a H atom

Ground state energy : 1E h= − R

As n increases, E∆ decreases energy levels come closer together

Bound electrons: ~ 1E h= − R 0E∞ = Ionization above E∞

1.8 Atomic Orbitals

Orbitals: (궤도함수,軌道函數)

~ wavefunctions of electrons in atoms

( , , ) ( ) ( , )r R r Yψ θ φ θ φ=

( )R r : radial wavefunction

( , )Y θ φ : angular wavefunction

Fig. 1.29 Spherical polar coordinates

θ : polar angle, φ: azimuthal angle

Ground-state (n=1) wavefunction of H atom

( )

0 0

( ) ( , )/ /

1/ 23/ 2 1/ 2 30 0

2 1( , , )2

R r Yr a r ae er

a a

θ φ

ψ θ φπ π

− −

= × = where 2

00 2

4 52.9 pme

am eπε

= = : Bohr radius

No angle dependence in ( , )Y θ φ isotropic (spherically symmetric)


◈ Quantum numbers in the wavefunctions of hydrogen atom

( , , ) ( ) ( , )nlm nl lmr R r Yl lψ θ φ θ φ=

▶ Principal quantum number, n = 1, 2, … Energy of orbital: 2

2nZ hE

n= −

R, 1,2,...n =

Orbitals with the same value of n belong to the same shell.

▶ Orbital angular momentum quantum number, l = 0, 1, 2, …, n–1 Shape of orbital

For each n, there are n values of l.

Orbitals with the same value of l belong to the same subshell.

Value of l 0 1 2 3

Orbital type s p d f

sharp principal diffuse fundamental

Orbital angular momentum 1/ 2{ ( 1)}l l= +

Degeneracy (축퇴,縮退)

Orbitals with the same value of n (Orbitals of a shell)

Fall into n subshells with the same energy.

▶ Magnetic quantum number, , 1,...,lm l l l= − − Orientation of orbital motion of electron

For each l, there are values of . 2 1l + lm

Orbital angular momentum around an arbitrary axis is equal to lm

For , 1l = 1,0, 1lm = − .

1lm = + , orbital angular momentum around an arbitrary axis is . +

electrons are circulating clockwise

1lm = − , orbital angular momentum around an arbitrary axis is . −

electrons are circulating counterclockwise

0lm = , orbital angular momentum around an arbitrary axis is 0.

electrons are not circulating


◈ ns – orbitals : Spherically symmetric

1s – orbital of H : , , 1n = 0l = 0lm =02 /

230

( )r aera

ψπ

−

=


Ex. 1.9. Probability density at relative to Probability density at the nucleus for 1s – orbital of H atom 0r a=

02 /2

30

( )r aera

ψπ

−

= 0 02 / 2

20 3 3

0 0

( )a ae eaa a

ψπ π

− −

= = , 020 /

23 30 0

1(0)ae

a aψ

π π

−

= =

∴ 2

202

( ) 0.14(0)a eψ

ψ−= =

◈ Radial Distribution Function, P 放射方向分布函數

2 2( ) ( )P r r R r= for any kind of orbital

For s-orbitals, 1/ 2 2 2/ 2 ( ) 4RY R R rψ π π= = ⎯⎯→ = ψ

∴ 0 at r = 0 2 2( ) 4 ( )P r r rπ ψ=

▶ Probability of finding the electron anywhere in a thin shell of radius r and thickness rδ : ( )P r rδ

Fig. 1.32 Radial distribution functions Fig. 1.33 Spherical boundary surfaces of 1s, 2s, 3s orbitals.

Most probable radius for 1s orbital is . 90% finding probability 0r a=

☺ Number of radial nodes in the hydrogen wavefunctions increases as n-1.


◈ np – orbitals

▶ 2p-orbital

Two lobes with different signs sin cosθ φ∝

A nodal plane between lobes

Fig. 1.35. Radial variation of Fig. 1.36 px, py, pz linear combination of p+1, p0, p–1 2p-orbital along the z-axis

◈ nd – orbitals

Five d-orbitals in a subshell with 2l =

Fig. 1.37. Five d-orbitals. Dark orange for the positive lobes and light orange for the negative lobes.

◈ nf – orbitals

Seven f-orbitals in a subshell with lanthanides, actinides 3l =

Fig. 1.38. Seven f-orbitals

2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 ▶ Total number of orbitals in a shell with principal quantum number n is n2.

Orbital quantum number l has n integer values from 0 to n – 1 .

Number of orbitals in a subshell for a given value of l is 2l + 1

(2x0 +1) + (2x1 +1) +… + [2x(n – 1) + 1] = 1 + 3 + 5 +… + 2n-1 = n2

Ex. 4n = 0, 1, 2, 3l = + + +

one s-orbital

three p-orbitals

five d-orbitals

seven f-orbitals

Total 16 orbitals

Fig. 1.39 Orbitals in the shell 4n =

1.10 Electron Spin

Slight deviations from the prediction of spectral lines by Schrödinger equation !

1925 Samuel Goudsmit and George Uhlenbeck

(和-美,1902-1978) (和-美,1900-1988)

Electron has an intrinsic property, “spin”

There are two spin states:

↑ (up, counterclockwise spin)

↓ (down, clockwise spin) Fourth quantum number:

▶ Spin magnetic quantum number, sm

1+ 2 for ↑ and 1− 2 for ↓

Box 1.1 How do we know…that an electron has spin? Otto Stern(美,1888-1969, Nobel Prize’43 Physics) and Walter Gerlach (獨,1889-1979)

Discovered space quantization in a magnetic field :

Beam of Ag (one unpaired electron) atoms in a nonuniform magnetic field splits in to two narrow bands Confirmed two orientations of electron spin


1.11 The Electronic Structure of Hydrogen

Ground state of the hydrogen atom :

1s-orbital : , , 1n = 0l = 0lm = , 1 12 2or sm = + −

1st-excited state

2s-orbital : , , 2n = 0l = 0lm = , 1 12 2or sm = + −

2p-orbitals: , , 2n = 1l = 1,0, 1lm = + − , 1 12 2or sm = + −

MANY-ELECTRON ATOMS

1.12 Orbital Energies

Total potential energy of a helium (He) atom

Attraction of Attraction ofelectron 1 to electron 2 tothe nucleus the nucl

Repulsionbetween thetwo electrons

2

0 12

er

eus

2 2

0 1 0 24 4 42 2e eV

r r πε+

πε πε−= −

2s, 2p-orbitals : same energy for H atom

but different energies for many electron atoms

(E2p > E2s) Removal of degeneracy Due to electron-electron repulsions

Fig. 1.41. Relative energies of orbitals in

a many-electron atom.

Shielding

2eff

2nZ hE

n= −

R, effZ e : effective nuclear charge

Penetration of electrons through the inner shells: s > p > d

from Oxtoby

Fig. Radial distribution functions for s-, p-, and d-orbitals in the first three shells of a H atom.


1.13 The Building-Up Principle (Aufbau Principle)

▶ Electron configuration (電子配置)

a list of all occupied orbitals of an atom with the numbers of electrons that each one contains

◈ Pauli’s Exclusion Principle (排他原理) 1925 Wolfgang Pauli (’45)

No more than two electrons may occupy any given orbital. When two electrons do occupy one orbital,

their spins must be paired.

No two electrons in an atom can have the same set of quantum numbers.

Fig. 1.43 (a) Two electrons are paired. (Opposite spins)

(b) Two electrons have parallel spins (Same direction)

closed shell 2s1: valence electron(原子價電子)

◈ Building-Up Principle

(1) Add Z electrons, one after the other, to the orbitals in the order shown in Fig. 1.44 but with no

more than two electrons in any one orbital.

(2) (Hund’s Rule) If more than one orbital in a subshell is available, add electrons with parallel spins to different orbitals of that subshell rather than pairing two electrons in one of the orbitals.

Fig. 1.44 The order in which atomic orbitals are occupied according to the building-up principle.


▷ Electron configuration of an atom of any element :

[A noble gas core] + Valence shell (原子價껍질) ▷ All the atoms of the main-group elements in a given period have a valence shell

with the same principal quantum number, which is equal to the period number.

▷ All the atoms of a given group have analogous valence electron configurations

that differ only in the value of n.

▷ Fourth period elements :

energy of 4s-orbital < energy of 3d-orbital until 20 19 K: [Ar]4s1 20 Ca: [Ar] 4s2

energy of 4s-orbital > energy of 3d-orbital after 20 21 Sc: [Ar] 3d14s2 22 Ti: [Ar]3d24s2

except 24 Cr: [Ar] 3d54s1 and 29 Cu: [Ar] 3d104s1

▷ Fifth period elements

37 Rb: [Kr]5s1 38 Sr: [Kr]5s2 39 Y [Kr] 4d15s2 40 Zr [Kr] 4d25s2

▷ Sixth period elements

55 Cs : [Xe]6s1 56 Ba : [Xe]6s2

57 La : [Xe] 5d16s2 58 Ce : [Xe] 4f15d16s2 59 Pr : [Xe] 4f36s2…… 70 Yb : [Xe]4f146s2

71 Lu : [Xe] 4f145d16s2 72 Hf : [Xe] 4f145d26s2

1.14 Electronic Structure and the Periodic Table

Box 1.2 The development of the periodic table

1860 Congress of Karlsruhe

Avogadro’s Principle : # of molecules in samples of different gases of equal P, V, T are the same

1869 Mendeleev(露) and Meyer(獨) discovered the primitive form of periodic table independently

Arrange elements in order of increasing atomic mass Elements fall into families with similar properties

Mendeleev’s prediction of ‘eka-silicon’ Winkler’s discovery of Ge (1886)

1913 Moseley(英) : Resolved the abnormal position for Ar atomic number instead of atomic mass

2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 Mendeleev’s Predictions for Eka-Silicon (Germanium)

Property Eka-Silicon, E Germanium, Ge

Molar mass 72 g·mol–1 72.59 g·mol–1

Density 5.5 g·cm–3 5.32 g·cm–3

Melting point High 937oC

Appearance Dark gray Gray-white

Oxide EO2; white solid; amphoteric; density 4.7

g·cm–3GeO2; white solid; amphoteric; density 4.23

g·cm–3

Chloride ECl4; boils below 100oC; density 1.9 g·cm–3 GeCl4; boils at 84oC; density 1.84 g·cm–3

멘델레예프의 꿈 … Periodic Table (1869)

Dmitriy Ivanovich Mendeleyev (1834-1907) Md (101) Mendelevium

Robin McKown, “Mendeleev and his Periodic Table” (1965)

St. Petersburg S nical University (2001)

tate Polytech


Mendeleev’s Periodic T

transition-metal groups)

f a shell with higher n lengths of periods

als

able (1869)

Organization of periodic table : Closely related to electronic configuration

Division into s, p, d, f -blocks : s, p-blocks (main groups) d, f-blocks (

Group number : # of valence-shell electrons

Each new period : corresponds to occupation o

Period 1 a single 1s-orbital 2 elements

Period 2 one 2s- , three 2p-orbitals 8 elements

Period 3 one 3s- , three 3p-orbitals 8 elements

Period 4 one 4s- , three 4p- , five 3d-orbit 18 elements

Period 5 one 5s- , five 4d- , three 5p-orbitals 18 elements

Period 6 one 6s- , five 5d-, three 6p-, seven 4f-orbitals 32 elements


THE PERIODICITY OF ATOMIC PROPERTIES

Fig. 1.45 The variation of Zeff for the outermost valence electron w mber.

1.15

tals

he centers of

▶ Co alloids

ith atomic nu

Atomic Radius

▶ Atomic radius : for me

half the distance between t

neighboring atoms in a solid sample

valent radius : for nonmetals or met

half the distance between nuclei of atoms joined by a chemical bond

oring atoms in a sample of the solidified gas

▶ van der Waals radius : for noble gas elements

half the distance between the centers of neighb

much larger than covalent radius

Fig. 1.46 The atomic radii of the main-group elements.


Fig. 1.47 The periodic variation in the atomic radii of the elements with atomic number.

◊ Inc

n the centers of the neighboring

140 pm

rease of atomic radii down a group valence electrons occupy shells with increasing n

◊ Decrease of atomic radii across a period increase of effective nuclear charge

1.16 Ionic Radius

Ionic radius :

Distance betwee

cation and anion in an ionic solid

Take the radius of oxide ion to be

Fig. 1.48 The ionic radii of the ions of the main-group elements.

Fig. 1.49 The relative sizes of some cations and anions comp red to their parent atoms. a


◊ Al

ns with the same charge.

22p6 ionic radii : Mg2+ < Na+ < F–

l cations are smaller than their parent atoms.

Li : 1s22s1 (r = 152 pm), Li+ : 1s2 (r = 76 pm)

◊ All anions are larger than their parent atoms.

◊ Atoms in the same main group tend to form io

Isoelectronic atoms or ions

Na+, F– , Mg2+ : [He]2s

Ex. 1.11. Arrange pair of ions in order of increasing radius

1.17 Ionization Energy

energy needed to remove an electron from an atom in the gas phase

Ionization energy, I

expressed in eV for a single atom, in 1kJ mol−⋅ per mole of atoms

(X )E− +=

rst ioni energy, I1 energy needed to remove an electron from a neutral atom in the gas phase

mol )− −⋅

Second ionization energy, I2 energy needed to remove an electron from a singly charged gas phase cation

8 kJ mol )− −⋅

X(g) X (g) e (g) (X)I E⎯⎯→ + − +

Fi zation

+ 11Cu(g) Cu (g) e (g) energy required (7.73 eV,746 kJI⎯⎯→ + =

2+ 12Cu (g) Cu (g) e (g) energy required (20.29 eV,195I⎯⎯→ + =

+

Fig. 1.50. The first ionization energies of the main-group elements.


Fig. 1.51 The periodic variation of the first ionization 52 The successive ion nergies

First ionization energies decrease down a group.

◊

ight

◊ zation energy is higher than the first ionization energy.

c

◊ ation energies at the upper right account for the

Fig. 1. ization e

energies of the elements. of main-group elements.

◊

◊ First ionization energies increase across a period.

Then it falls back to a lower value at the start of the next period.

◊ Lowest value at the bottom left (Cs), the highest at the upper r

(near He).

Second ioni

◊ Low ionization energies at the lower left account for the metalli

character.

High ioniz

nonmetallic character.

1.18 Electron

Electron affinity, Eeaed when an electron is added to the gas phase atom

+ ⎯⎯→ = −

⋅

Affinity

energy releas

eaX(g) e (g) X (g) (X) (X) (X )E E E− − −

1eaCl(g) e (g) Cl (g) energy released (3.62 eV,349 kJ mol )E

− − −+ ⎯⎯→ =


Fig. 1.54 The variation in the electron affinities of the main-group elements.

◇ With the exception of the noble gases, Eea are highest toward the (upper) right side of the periodic table.

◇ Difference between electron affinities of C (+122) : [He]2s22p2 and N(-7) : [He]2s22p3

Fig. 1.55 The energy change when an electron is added to C and N atoms.

1.19 The Inert-Pair Effect Inert-pair effect: Tendency to form ions two units lower in charge than expected from the group number

Most pronounced for heavy elements in the p-block

Group 13/III Al3+ In3+, In+

Group 14/IV Sn4+, Sn2+ Pb2+ oxides

Fig. 1.56 2SnO + O2 2SnO2 Fig. 1.57 Typical ions showing inert-pair effect


1.20 Diagonal Relationships

A similarity in properties between diagonal neighbors in the main-groups

Fig. 1.58 Diagonal relationship between Fig. 1.59 Diagonal relationship between

diagonal neighbors. B(上) and Si(下)

THE IMPACT ON MATERIALS

1.20 The Main-Group Elements

s-block elements : low ionization energies ~ reactive metals form basic oxides

p-block elements : high electron affinities

tend to gain electrons to complete closed shells ~ metals and metalloids


Fig. 1.60 All alkali metals are soft (Na).

Fig. 1.61 Group 14/IV elements (C,Si,Ge,Sn,Pb) Fig. 1.62 Group 16/VI elements (O2,S8,Se,Te)

1.22 The Transition Metals All d-block elements are transition metals.

Transition metals form ions with different oxidation states.

Fe2+, Fe3+ (in hemoglobin) Cu+, Cu2+ (in protein responsible for electron transport)

Catalysts, Alloys, High-temp superconductors (lanthanides).

Fig. 1.63 Elements in the 1st row of the d-block. Fig. 1.64 A sample of a high-temp superconductor.

Sc, Ti, V, Cr, Mn

Fe, Co, Ni, Cu, Zn


◈ High Temperature Superconductor (High Tc Superconductor)

1987 Nobel Prize ’87 Physics “for their important breakthrough in the discovery of superconductivity in ceramic materials”

Johannes Georg Bednorz Karl Alexander Müller

(獨,1950 - ) (瑞西,1927 - )

1913 Heike Kamerlingh-Onnes (Nobel Prize ’13 Physics)

"for his investigations on the properties of matter at low temperatures which led, inter alia,

to the production of liquid helium"

(和,1853-1926) Superconductivity in Hg (Tc = 4 K)

1972 John Bardeen, Leon Cooper and Robert Schrieffer (Nobel Prize ’72 Physics)

"for their jointly developed theory of superconductivity, usually called the BCS-theory"

Bardeen Cooper Schrieffer

(美,1908-1991) (美,1930 - ) (美,1931 - )

1986 Bednorz and Muller, LaBaCuO (Tc=35 K)

La2-xSrxCuO4

1987 YBCO (Tc = 90 K)

1988 TBCCO (Tc = 125 K)

2006 Hg12Tl3Ba30Ca30Cu45O125 (Tc = 138 K)
http://nobelprize.org/nobel_prizes/physics/laureates/1972/index.html

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CHAPTER 1. ATOMS: THE QUANTUM WORLDrhbestsh.x-y.net/.../Chemistry/Lecture_Note/Ch.01.pdf · 2010-04-12 · Atomic Structure – Quantum Mechanics (量子力學) Internal Structure