Download CHAPTER 1. ATOMS: THE QUANTUM WORLD

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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
CHAPTER 1.
담당교수: 신국조
Chapter 1
ATOMS: THE QUANTUM WORLD
Matter – Composed of Atoms
Atomic Structure – Quantum Mechanics (量子力學)
Internal Structure of Atom Æ Electronic Structure
Periodic Variation of Atomic Properties
INVESTIGATING ATOMS
1.1 The Nuclear Atom
Fig. 1.1. Sir Joseph John Thomson (英,1856-1949)
Nobel Prize ‘06 Physics
Fig. 1.2. Cathode ray tube
(His son – George Paget Thomson, Nobel Prize ’37 Physics)
◈ Electron
Discovered by J. J. Thomson in 1897
Æ Measured the value of the ratio, e / me
Oil-drop Experiment by R. Millikan
Æ Measured the value of e = 1.602 x 10 –19 C
Æ 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
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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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
Æ 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
Æ 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
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
Wavelength x frequency = speed of light,
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Chapter 1
λν = c
1.3 Atomic Spectra of Hydrogen Atom
(a) Visible spectrum (white light passing through a prism) (b) Complete spectrum of H atom
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
◈ Rydberg Formula
⎛ 1
1⎞
− 2 ⎟,
2
⎝ n1 n2 ⎠
ν =R ⎜
where
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Chapter 1
Johannes Rydberg (瑞典,1854-1919)
n1 = 1, 2,3,...
n2 = n1 + 1, n1 + 2,...
R = 3.29 × 1015 Hz : Rydberg constant
▶ 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)
(n1 = 4) Frederick Sumner Brackett (美, 1896-1988)
▶ Pfund Series (1924)
IR region
(n1 = 5) August Herman Pfund (美,1879-1949)
From Oxtoby
Fig. 1.11. Absorption spectrum of the Sun due to H around the Sun.
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
QUANTUM THEORY
★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆v★☆★☆
☆ STARS in Quantum Mechanics – Nobel Laureates in Physics ★
★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★ ☆
Max Planck (’18)
Albert Einstein (’21)
Niels Bohr (’22)
(獨,1858-1947)
(獨,1879-1955)
(丁抹,1885-1962)
(佛,1892-1987)
quanta
photoelectric effect
atomic model
matter wave
Werner Heisenberg (’32)
(獨,1901-1976)
uncertainty principle
George P. Thomson (’37)
(英,1892-1975)
diffraction of electron
Erwin Schrödinger (’33)
(墺地利,1887-1961)
Schrödinger equation
Paul A. M. Dirac (’33)
(英,1902-1984)
Dirac equation
Prince Louis de Broglie (’29)
Clinton Davisson (’37)
(美,1881-1958)
diffraction of electron
Wolfgang Pauli (’45)
Max Born (’54)
Eugene Wigner (’63)
(墺地利,1900-1958)
(英,1882-1970)
(洪牙利-美,1902-1995)
exclusion principle
interpretation of
ψ2
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)
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
1.4 Radiation, Quanta, and Photons
Blackbody Radiation
◈ Emission of thermal radiation
◆
Stefan’s law (1879)
Josef Stefan
I T = σ eT 4
(墺,1835-1893)
I T : 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
Wilhelm Wien
Wien’s displacement law (1893)
(獨,1864-1928)
λmaxT = constant (= 2.898 x 10
–3
M⋅K)
Nobel Prize ’11
Physics
Blackbody radiation
Stefan-Boltzmann law
Wien’s displacement law
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
♦ 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 = hν
discrete packet of energy, Quanta
h = 6.626 × 10−34 J ⋅ s 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
1
2
mev2 = hν − Φ
Work function: Φ = hν 0
ν 0 , threshold frequency
Fig. 1.16 Work function in the photoelectric effect
Å characteristic of metal
Fig. 1.17 Different threshold frequencies for different metals
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
Spectral lines of H atom
Transitions between two energy levels of H atom
Frequency of each spectral line:
hν = Eupper − Elower , Bohr frequency condition
High frequency Å Large energy difference
1.5 The Wave-Particle Duality of Matter
Wave nature – Wavelength, Diffraction (回折)
Diffraction Å 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)
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
(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 Æ reflected from a crystal
▶ G. P. Thomson (Nobel’37, diffraction pattern,實)
Fig. 1.21. Thomson’s diffraction pattern
Electrons Æ passing through a thin gold foil
♦ Matter wave – de Broglie relation (1925)
λ=
1.6
h
h
=
mv p
The Uncertainty Principle
Particle – Trajectory Æ localizable
(location & momentum at time t)
Wave – Wavelength Æ delocalized
♦ Uncertainty Principle (1927) – Heisenberg
∆x∆p x ≥ 12 = =
∆y∆p y ≥ 12 = ,
1 h
2 2π
(a) large ∆x, small ∆px
∆z∆pz ≥ 12 =
(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 d 2ψ
−
+ V ( x )ψ = Eψ
2m dx 2
ψ
ψ
Î
H ψ = Eψ
: Wavefunction (or Eigenfunction) – a state of the system
2
or ψ 2 : Probability density of finding a particle (Max Born)
E: Energy eigenvalue
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
H : Hamiltonian operator – Energy operator (KE operator + PE operator)
−
= 2 d 2ψ
: KE operator, V ( x ) : PE operator
2m dx 2
▶ Particle in a box (width: 0 Æ L, height: 0 Æ ∞)
= 2 d 2ψ
= Eψ
Inside the box: V ( x ) = 0 . Æ Schrödinger eq. becomes −
2m dx 2
General solution:
ψ ( x ) = A sin kx + B cos kx
Determination of
Æ
d 2ψ
= −k 2ψ
2
dx
1)
ψ (0) = 0
Æ
ψ (0) = B = 0
2)
ψ ( L) = 0
Æ
ψ ( L) = A sin kL = 0
Î
Å
⎛ nπ x ⎞
⎟,
⎝ L ⎠
ψ ( x ) = A sin ⎜
ψ
is a smooth function
ψ ( x ) = A sin kx
sin kL = 0 . Æ kL = nπ
Since A ≠ 0 ,
E=
k 2=2 k 2h 2
=
2m 8π 2 m
A, B, and k
Boundary conditions at x = 0 and x = L
∴
k 2 = 2mE / = 2 Æ E =
where
with
n = 1,2,... Å quantum number
n = 1, 2,...
k 2h 2
n 2h 2
=
8π 2 m 8mL2
Normalization:
L
∫ ψ ( x)
0
⎛ nπ x ⎞
dx = A ∫ sin 2 ⎜
⎟ dx = 1
⎝ L ⎠
0
L
2
2
A2 ⋅ ( L / 2) = 1
Æ
1/ 2
∴ ψ ( x ) = ⎛⎜ 2 ⎞⎟
⎝L⎠
E=
∴ A = (2 / L)
1/ 2
⎛ nπ x ⎞
sin ⎜
⎟
⎝ L ⎠
k 2h 2
n 2h 2
=
,
8π 2m 8mL2
n = 1,2,...
Energy separation:
∆E = En +1 − En =
Æ
( n + 1) 2 = 2 n 2= 2
h2
−
=
(2
n
+
1)
8mL2
8mL2
8mL2
∆E decreases as m (or L) increases
Fig. 1.26
Small L
Large L
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
From Oxtoby
THE HYDROGEN ATOM
1.7
The Principal Quantum Number
Solve the Schrödinger equation with V ( r ) = −
En = −
where
Æ
hR
n2 ,
R =
e2
4πε 0 r
n = 1, 2,...
me e 4
= 3.29 × 1015 Hz
8h 3ε 02
Same value as Rydberg constant !
e = 2.71828…
For other one-electron ions with atomic number Z,
En = −
Fig. 1.28 Energy levels of a H atom
Z 2 hR
, n = 1, 2,...
n2
Z2-dependence:
1) Field generated by a nucleus of atomic number Z and charge Ze
Æ Z times stronger than that by a proton
2) Electron is drawn Z times closer to the nucleus than it is in hydrogen
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▶ Principal quantum number, n
Ground state energy :
As n increases,
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Chapter 1
Å determines the energy levels of a H atom
E1 = − hR
∆E decreases Æ energy levels come closer together
Bound electrons: E1 = − hR ~ E∞ = 0
Æ Ionization above
E∞
1.8 Atomic Orbitals
Orbitals: (궤도함수,軌道函數)
~
wavefunctions of electrons in atoms
ψ ( r, θ , φ ) = R( r )Y (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
R(r)
Y (θ ,φ )
P
− r / a0
2e
1
e − r / a0
ψ ( r, θ , φ ) = 3/ 2 × 1/ 2 =
1/ 2
a0
2π
(π a03 )
where
a0 =
4πε 0= 2
= 52.9 pm : Bohr radius
mee 2
No angle dependence in Y (θ , φ ) Æ isotropic (spherically symmetric)
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
◈ Quantum numbers in the wavefunctions of hydrogen atom
ψ nlm (r , θ , φ ) = Rnl (r )Ylm (θ , φ )
l
l
▶ Principal quantum number,
Å
n = 1, 2, …
Energy of orbital: En = −
Z 2 hR
, n = 1, 2,...
n2
Orbitals with the same value of n belong to the same shell.
▶ Orbital angular momentum quantum number,
l = 0, 1, 2, …, n–1
Å
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 = {l (l + 1)}1/ 2 =
Degeneracy (축퇴,縮退)
Orbitals with the same value of n (Orbitals of a shell)
Æ
Fall into n subshells with the same energy.
▶ Magnetic quantum number,
ml = l , l − 1,..., −l
Å
Orientation of orbital motion of electron
For each l, there are 2l + 1 values of ml .
Orbital angular momentum around an arbitrary axis is equal to ml =
For l = 1 , ml = 1, 0, −1 .
ml = +1 , orbital angular momentum around an arbitrary axis is += .
Æ
electrons are circulating clockwise
ml = −1 , orbital angular momentum around an arbitrary axis is −= .
Æ
electrons are circulating counterclockwise
ml = 0 , orbital angular momentum around an arbitrary axis is 0.
Æ
electrons are not circulating
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
◈ ns – orbitals : Spherically symmetric
1s – orbital of H :
n = 1 , l = 0 , ml = 0
Æ ψ 2 (r ) =
e −2 r / a0
π a03
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Chapter 1
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
Ex. 1.9. Probability density at r = a0 relative to Probability density at the nucleus for 1s – orbital of H atom
e −2 r / a0
e −2 a0 / a0
e −2
e −20 / a0
1
2
2
ψ (r ) =
Æ ψ (a0 ) =
= 3 , ψ (0) =
= 3
3
3
3
π a0
π a0
π a0
π a0
π a0
2
ψ 2 (a0 ) −2
= e = 0.14
ψ 2 (0)
∴
◈ Radial Distribution Function, P 放射方向 分布函數
P (r ) = r 2 R 2 (r )
For s-orbitals,
∴
Å for any kind of orbital
ψ = RY = R / 2π 1/ 2 ⎯⎯
→ R 2 (r ) = 4πψ 2
P (r ) = 4π r 2ψ 2 (r )
Æ
0 at r = 0
▶ Probability of finding the electron anywhere in a thin shell of radius r and thickness
δ r : P( r )δ r
Fig. 1.32 Radial distribution functions
Fig. 1.33 Spherical boundary surfaces of 1s, 2s, 3s orbitals.
Æ 90% finding probability
Æ Most probable radius for 1s orbital is r = a0 .
☺ Number of radial nodes in the hydrogen wavefunctions increases as n-1.
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
◈ np – orbitals
▶ 2p-orbital
Two lobes with different signs
Æ
∝ sin θ cos φ
A nodal plane between lobes
Fig. 1.35. Radial variation of
2p-orbital along the z-axis
Fig. 1.36
px, py, pz Å linear combination of p+1, p0, p–1
◈ nd – orbitals
Five d-orbitals in a subshell with l = 2
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 l = 3
Å lanthanides, actinides
Fig. 1.38. Seven f-orbitals
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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.
n=4
l = 0, +1, +2, +3
one s-orbital
three p-orbitals
five d-orbitals
seven f-orbitals
Total 16 orbitals
Fig. 1.39
Orbitals in the
n=4
shell
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, ms
+ 12 for ↑
and − 12 for ↓
How do we know…that an electron has spin?
Box 1.1
Otto Stern(美,1888-1969, Nobel Prize’43 Physics) and Walter Gerlach (獨,1889-1979)
Æ
Discovered space quantization in a magnetic field :
Æ
Beam of Ag (one unpaired electron) atoms in a nonuniform magnetic field splits in to two narrow bands
Confirmed two orientations of electron spin
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Chapter 1
1.11 The Electronic Structure of Hydrogen
Ground state of the hydrogen atom :
1s-orbital :
n = 1 , l = 0 , ml = 0 , ms = + 12 or − 12
1st-excited state
2s-orbital :
n = 2 , l = 0 , ml = 0 , ms = + 12 or − 12
2p-orbitals:
n = 2 , l = 1 , ml = +1,0, −1 , ms = + 12 or − 12
MANY-ELECTRON ATOMS
1.12
Orbital Energies
Total potential energy of a helium (He) atom
Attraction of Attraction of
electron 1 to electron 2 to
the nucleus the nucleus
Repulsion
between the
two electrons
2
2
2
2e
2e
e
−
+
V =−
4πε 0 r1 4πε 0 r2 4πε 0 r12
2s, 2p-orbitals : same energy for H atom
but different energies for many electron atoms
(E2p > E2s)
Å Removal of degeneracy
Å Due to electron-electron repulsions
Fig. 1.41. Relative energies of orbitals in
a many-electron atom.
Shielding
En = −
2
Z eff
hR
,
n2
Z eff 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.
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Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008)
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Chapter 1
1.13 The Building-Up Principle (Aufbau Principle)
▶ Electron configuration (電子配置)
Æ
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.
Æ
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.
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▷ Electron configuration of an atom of any element :
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Chapter 1
[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
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
▷
20 Ca: [Ar] 4s2
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
71 Lu : [Xe] 4f145d16s2
72 Hf : [Xe] 4f145d26s2
59 Pr : [Xe] 4f36s2…… 70 Yb : [Xe]4f146s2
1.14 Electronic Structure and the Periodic Table
The development of the periodic table
Box 1.2
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
Æ
Elements fall into families with similar properties
Mendeleev’s prediction of ‘eka-silicon’ Æ Winkler’s discovery of Ge (1886)
1913 Moseley(英) : Resolved the abnormal position for Ar Æ atomic number instead of atomic mass
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Chapter 1
Mendeleev’s Predictions for Eka-Silicon (Germanium)
Property
Eka-Silicon, E
Germanium, Ge
–1
Molar mass
72 g·mol
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
GeO2; white solid; amphoteric; density 4.23
–3
Chloride
g·cm
g·cm–3
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 State Polytechnical University (2001)
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Chapter 1
Mendeleev’s Periodic Table (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 (transition-metal groups)
Group number : # of valence-shell electrons
Each new period : corresponds to occupation of a shell with higher n
Å
lengths of periods
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-orbitals
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
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Chapter 1
THE PERIODICITY OF ATOMIC PROPERTIES
Fig. 1.45 The variation of Zeff for the outermost valence electron with atomic number.
1.15 Atomic Radius
▶ Atomic radius : for metals
Æ half the distance between the centers of
neighboring atoms in a solid sample
▶ Covalent radius : for nonmetals or metalloids
Æ half the distance between nuclei of atoms joined by a chemical bond
▶ van der Waals radius : for noble gas elements
Æ half the distance between the centers of neighboring atoms in a sample of the solidified gas
Æ much larger than covalent radius
Fig. 1.46 The atomic radii of the main-group elements.
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Fig. 1.47 The periodic variation in the atomic radii of the elements with atomic number.
◊ Increase of atomic radii down a group Å valence electrons occupy shells with increasing n
◊ Decrease of atomic radii across a period Å increase of effective nuclear charge
1.16 Ionic Radius
Ionic radius :
Æ Distance between the centers of the neighboring
cation and anion in an ionic solid
Æ Take the radius of oxide ion to be 140 pm
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 compared to their parent atoms.
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◊ All 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 ions with the same charge.
Isoelectronic atoms or ions
Na+, F– , Mg2+ : [He]2s22p6
ionic radii : Mg2+ < Na+ < F–
Ex. 1.11. Arrange pair of ions in order of increasing radius
1.17 Ionization Energy
Ionization energy, I
Æ energy needed to remove an electron from an atom in the gas phase
Æ expressed in eV for a single atom, in kJ ⋅ mol
X(g) ⎯⎯
→ X + (g) + e− (g)
−1
per mole of atoms
I = E (X + ) − E (X)
First ionization energy, I1
Æ energy needed to remove an electron from a neutral atom in the gas phase
Cu(g) ⎯⎯
→ Cu + (g) + e − (g)
energy required = I1 (7.73 eV, 746 kJ ⋅ mol−1 )
Second ionization energy, I2
Æ energy needed to remove an electron from a singly charged gas phase cation
Cu + (g) ⎯⎯
→ Cu 2+ (g) + e − (g)
energy required = I 2 (20.29 eV,1958 kJ ⋅ mol−1 )
Fig. 1.50. The first ionization energies of the main-group elements.
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Fig. 1.51 The periodic variation of the first ionization
담당교수: 신국조
Chapter 1
Fig. 1.52 The successive ionization energies
energies of the elements.
of main-group elements.
◊ First ionization energies decrease down a group.
◊ 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 right
(near He).
◊ Second ionization energy is higher than the first ionization energy.
◊ Low ionization energies at the lower left account for the metallic
character.
◊ High ionization energies at the upper right account for the
nonmetallic character.
1.18 Electron Affinity
Electron affinity, Eea
Æ energy released when an electron is added to the gas phase atom
X(g) + e − (g) ⎯⎯
→ X − (g)
Cl(g) + e − (g) ⎯⎯
→ Cl− (g)
Eea (X) = E (X) − E (X − )
energy released = Eea (3.62 eV,349 kJ ⋅ mol−1 )
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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
Æ Most pronounced for heavy elements in the p-block
Æ
Group 13/III
Al3+
Æ
Group 14/IV
Sn4+, Sn2+
Fig. 1.56 2SnO + O2 Æ 2SnO2
In3+, In+
Pb2+
oxides
Fig. 1.57 Typical ions showing inert-pair effect
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1.20 Diagonal Relationships
A similarity in properties between diagonal neighbors in the main-groups
Fig. 1.58 Diagonal relationship between
diagonal neighbors.
Fig. 1.59 Diagonal relationship between
B(上) and Si(下)
THE IMPACT ON MATERIALS
1.20 The Main-Group Elements
s-block elements : low ionization energies ~ reactive metals Æ form basic oxides
p-block elements : high electron affinities
Æ tend to gain electrons to complete closed shells ~ metals and metalloids
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Fig. 1.60
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Chapter 1
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.
Sc, Ti, V, Cr, Mn
Fe, Co, Ni, Cu, Zn
Fig. 1.64
A sample of a high-temp superconductor.
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Chapter 1
◈ 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 - )
1913
(瑞西,1927 - )
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)
1972
Superconductivity in Hg (Tc = 4 K)
John Bardeen, Leon Cooper and Robert Schrieffer (Nobel Prize ’72 Physics)
"for their jointly developed theory of superconductivity, usually called the BCS-theory"
Bardeen
(美,1908-1991)
1986
Bednorz and Muller,
Cooper
(美,1930 - )
YBCO (Tc = 90 K)
1988
TBCCO (Tc = 125 K)
2006
(美,1931 - )
LaBaCuO (Tc=35 K)
La2-xSrxCuO4
1987
Schrieffer
Hg12Tl3Ba30Ca30Cu45O125 (Tc = 138 K)