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 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) 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 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 – 31 Æ me = 9.109 x 10 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 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 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 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 Wavelength x frequency = speed of light, λν = c 1.3 Atomic Spectra of Hydrogen Atom (a) Visible spectrum (white light passing through a prism) (b) Complete spectrum of H atom 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 ◈ Rydberg Formula Johannes Rydberg (瑞典,1854-1919) ⎛⎞11 ν =−R ⎜⎟22, nn12=1,2,3,... =n1+1,n1+2,... ⎝⎠nn12 where 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) 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. 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 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 ψ 2 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) 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 1.4 Radiation, Quanta, and Photons Blackbody Radiation ◈ Emission of thermal radiation ◆ Stefan’s law (1879) 4 Josef Stefan IT = σeT (墺,1835-1893) IT : 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) –3 λmaxT = constant (= 2.898 x 10 M⋅K) Nobel Prize ’11 Physics Blackbody radiation Stefan-Boltzmann law Wien’s displacement law 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) 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 ! Eh= ν 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 2 mhev =ν −Φ Work function: Φ=hν 0 ν 0 , threshold frequency Å characteristic of metal Fig. 1.16 Work function in the photoelectric effect Fig. 1.17 Different threshold frequencies for different metals 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 Spectral lines of H atom Transitions between two energy levels of H atom Frequency of each spectral line: hEν =upper −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) 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) 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) hh λ == mpv 1.6 The Uncertainty Principle Particle – Trajectory Æ localizable (location & momentum at time t) Wave – Wavelength Æ delocalized ♦ Uncertainty Principle (1927) – Heisenberg ∆∆xp≥11= = h x 222π (a) large ∆x, small ∆px 1 1 ∆∆ypy ≥2 = , ∆zp∆≥z 2 = (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) =22d ψ −+Vx()ψ =Eψ Hψ = Eψ 2mdx2 Î ψ : Wavefunction (or Eigenfunction) – a state of the system 2 ψ or ψ 2 : Probability density of finding a particle (Max Born) E: Energy eigenvalue 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 H : Hamiltonian operator – Energy operator (KE operator + PE operator) =22d ψ − : KE operator, Vx(): PE operator 2mdx2 ▶ Particle in a box (width: 0 Æ L, height: 0 Æ ∞) =22d ψ Inside the box: Vx()= 0. Æ Schrödinger eq. becomes −=Eψ 2mdx2 General solution: d 2ψ kk22= 2h2 ψ ()x =+AksinxBcoskx Æ =−k 2ψ where km22= 2E/= Æ E == dx2 28mmπ 2 Determination of A, B, and k Boundary conditions at x = 0 and x = L Å ψ is a smooth function 1) ψ (0) = 0 Æ ψ (0) =B =0 Î ψ ()x = Aksinx 2) ψ ()L = 0 Æ ψ ()LA==sinkL0 Since A ≠ 0 , sin kL = 0 . Æ kL = nπ with n = 1, 2, ... Å quantum number ⎛⎞nxπ ∴ ψ ()xA= sin⎜⎟, n = 1,2,... ⎝⎠L kh22 n22h E == 88π 22mmL Normalization: LL 2 22⎛⎞nxπ ∫∫ψ ()xdx==Asin⎜⎟dx1 00⎝⎠L Æ AL2 ⋅(/2)=1 ∴ AL= (2/ )1/2 1/2 ∴ ⎛⎞2 ⎛nxπ ⎞ ψ ()x = ⎜⎟sin⎜ ⎟ ⎝⎠LL⎝ ⎠ kh22 n2h2 E == , n = 1, 2, ... 88π 22mmL Energy separation: (1nn+ )22==22 h2 ∆=EEnn+1 −E= 22− =(2n+1) 2 88mL mL 8mL Small L Large L Æ ∆E decreases as m (or L) increases Fig. 1.26 2009년도 제1학기 화 학 1 담당교수: 신국조 Textbook: P. Atkins / L. Jones, Chemical Principles, 4th ed., Freeman (2008) Chapter 1 From Oxtoby THE HYDROGEN ATOM 1.7 The Principal Quantum Number e2 Solve the Schrödinger equation with Vr()=− 4πε0r hR E =− n n2 , n = 1,2,..