המבנה האלקטרוני של האטום:

נושא 7: המבנה האלקטרוני של האטום: Fireworks רקע היסטורי The Electronic Structure of the Atom: Historical Background 1 Prof. Zvi C. Koren 19.07.10 movie

Thomson Millikan Rutherford Maxwell Planck Einstein Balmer Rydberg Bohr de Broglie Heisenberg Schrödinger Born 2 Prof. Zvi C. Koren 19.07.10

Sir Joseph John (J.J.) Thomson 1856 1940, England Nobel Prize in Physics, 1906 Experiment: Cathode Ray Tube, 1897 Cathode Anode e Electric field only Electric + Magnetic fields Conclusion: Calculated e/m, Charge-to-Mass Ratio of e Conclusions: 1. Cathode ray particles ( corpuscles ) are negatively charged 2. Calculated the charge-to-mass ratio, e/m, of this particle ( electron ) from the electric and magnetic forces: (קולון Coulomb, e/m = 1.76 x 10 8 C/g. (C = 3. This e/m ratio is independent of: (a) the cathode material; (b) the residual gas in tube. George Johnstone Stoney 1826 1911, Ireland Coined the name electron in 1874 3 Prof. Zvi C. Koren 19.07.10

Where Are the Electrons in the Atom According to J.J. Thomson? The Famous Plum Pudding (with Raisins) Model 1890 s The Thomson Atom with e s dispersed within a homogeneous positive (+) sphere (note the raisins) 4 Prof. Zvi C. Koren 19.07.10

Robert Andrews Millikan 1868 1953, USA Nobel Prize in Physics, 1923 Experiment: Oil Drop, 1909 Conclusion: Calculated e, the Charge on an e Equating gravitational force with electrical force allows for the calculations of the charges, q, on the oil drops (in units of 10 19 C): 3.20, 1.60, 6.41,... Conclusions: 1. Each q is a multiple of a basic charge: q = n e 2. The basic charge is therefore that for the electron: e = 1.60 x 10 19 C. 3. Thus, the mass m of an electron can be calculated together with Thomson s result for e/m: m = 9.11 x 10 28 g. 5 Prof. Zvi C. Koren 19.07.10

Ernest Rutherford 1871 1937, New Zealand & England Nobel Prize in Chemistry, 1908 3 Experiment: Gold Foil, 1907 1 2 4 רדיד Certain radioactive substances emit particles: 4 α = 2 He 2+ Conclusions: 1. Most of the atom is empty space 2. Electrons ( ) are in that emptiness outside of the center ( nucleus ) 3. The nucleus is miniscule and (+). 4. The nucleus is massive. 4 6 Prof. Zvi C. Koren 19.07.10 e e + e e e 1 2 3

James Clerk Maxwell Electromagnetic Radiation & Wave Properties (1831 1879) Scotland Meaning Amplitude Velocity Speed of light Wavelength Frequency Wavenumber Period Symbol A v c, t Definition Formula, Value Units maximum perpendicular displacement length from axis of propagation speed of the propagating wave length/time (in vacuum) 3.00 x10 8 m/s cycle-length, length of a cycle in the wave length number of cycles per unit time v/ time 1 s 1 = cps (cycles per second)= Hz (Hertz) cycle-number, number of cycles per length 1/ length 1 time per unit cycle 1/ time 7 Prof. Zvi C. Koren 19.07.10

Electromagnetic Spectrum E V iolet I ndigo B lue G reen Y ellow O range R ed 8 Prof. Zvi C. Koren 19.07.10

Blackbody Radiation Blackbody : Perfect absorber and emitter of radiation: Energy absorbed = Energy released Experimental Theoretical If energy is absorbed in a continuous manner: The Ultraviolet Catastrophe, 9 Prof. Zvi C. Koren 19.07.10

Max Planck 1858 1947, Germany Nobel Prize in Physics, 1918 Explained Blackbody Radiation Phenomenon, 1900 Basic (smallest) unit of energy that an atom can absorb (or release): E = h Planck Equation h = Planck s constant = 6.63 x 10 34 J. s = frequency of radiation An atom can absorb or release a number of these energy units: E = n h, n = 1, 2, 3, Conclusions: Energy is quantized; a Quantum of Energy is h An atom can absorb only specific quantities of energy and not a continuum of energies. Planck is the Father of Quantum Theory 10 Prof. Zvi C. Koren 19.07.10

Albert Einstein Conclusions: Photon, Light Particle Electron (1:1) K.E. ejected e = E photon in light E electron in metal ½ mv 2 = h h 0 Planck-Einstein Eqn.: E = h 1879 1955, Germany & USA Nobel Prize in Physics, 1921 Increasing intensity of light irradiation The Photoelectric Effect (with same frequency): light e increases the number of released e s, with same kinetic energy. Increasing the frequency of light irradiation (with same intensity): metal increases the kinetic energy of released e s, not the number of e s. Explained The Photoelectric Effect Phenomenon, 1905: The word photon was coined in 1926 by Gilbert N. Lewis 0 = threshold frequency = f(metal) Planck: Basic (smallest) unit of energy that an atom can absorb or release Einstein: Basic (smallest) unit of energy that a photon of light possesses 11 Prof. Zvi C. Koren 19.07.10

Continuum Spectrum Johann Jakob Balmer 1825 1898, Switzerland Experiment: Atomic Line Spectra of Hydrogen Atoms Recall: white light refraction focusing slits detector Emission Line Spectrum prism visible part of spectrum Balmer Series: gas discharge tube Balmer Series for Visible H Line Spectra: 1 1 1 RH 2 2 2 n R H = Rydberg constant for H = 1.097 x 10 7 m 1 n = 3, 4, 5,... prism H 2 2H H H* H + light ground energy Johannes Robert Rydberg 12 Prof. Zvi C. Koren 19.07.10 Hi V Hi V excited energy

Atomic Line Spectra of Selected Atoms Fantastic Web Sites: http://www.bigs.de/en/shop/htm/termsch01.html http://www.colorado.edu/physics/2000/quantumzone/index.html http://jersey.uoregon.edu/vlab/elements/elements.html 13 Prof. Zvi C. Koren 19.07.10

Generalized Balmer Equation for all Series of Lines in H-Like Atomic Ions: Other Series (or sets) of lines were also found for the H-like atoms in non-visible regions 2 H 1 1 Z R 2 2 Z = Atomic Number n1 n2 n 1 = Series I.D. = 1: Lyman Series Theodore Lyman (1874 1954, USA) 2: Balmer " Johann Jakob Balmer (1825 1898, Switzerland) 3: Paschen " Friedrich Paschen (1865 1947, Germany) 4: Brackett " Frederick Sumner Brackett (1896 1988, USA) 5: Pfund " August Herman Pfund (1879 1949, USA) n 2 = n 1 +1, n 1 +2, 14 Prof. Zvi C. Koren 19.07.10

Niels Bohr 1885 1962, Denmark & Sweden Explained the Occurrence of Atomic Line Spectra in H-Like Atoms: Proposed a Model for the H Atom e in a stationary orbit when e jumps from one orbit to another it absorbs/releases E orbit E = 0 ev e 1 2 n=3 4 r n = a o n 2 /Z a o = Bohr radius = 0.529 Å 1 Å = Ångstrom = 10 10 m E n = (13.6 ev) Z 2 /n 2 E i f = h hc/ 1 ev = 1.60 x 10 19 J E 1 = 13.6 ev 1 1 RH 2 2 n1 n2 15 Prof. Zvi C. Koren 19.07.10 Z 2

Louis de Broglie 1892 1987, France Nobel Prize in Physics, 1929 Theorized the Wave Properties of Electrons (and Matter) For a photon (particle) of light: For a photon (particle) of light: mc 2 E photon = h c/ = = mc 2 /h = h/mc = h/p p = linear momentum = mv Any particle of matter has a wave property: 16 Prof. Zvi C. Koren 19.07.10 h p

Wave-Particle Duality of Light & Matter Matter (e.g.: e - ) Light Particulate Dalton Thomson: e/m Waves de Broglie Particulate Einstein: photons Waves Maxwell Schrödinger: Applied classical wave equation to an electron 17 Prof. Zvi C. Koren 19.07.10

Werner Heisenberg 1901 1976, Germany Nobel Prize in Physics, 1932 Heisenberg s??uncertainty?? Principle Δx Δp x > h Uncertainty in the position of the e Uncertainty in the momentum of the e > 0 The concept of orbitals is correct. (To Be Continued) 18 Prof. Zvi C. Koren 19.07.10

Property 2 E Erwin Scrödinger (1887 1961, Austria & Switzerland) Schrödinger s Wave Equation, 1926 Applied the wave equation to the electron, a particle, in the H atom (recall de Broglie) 2 2 U = Potential Energy = kq 1 q 2 /r, q 1 =q 2 =e (Coulomb s Law) h d U E 2 2 8 m dx Solution of this differential equation yields the following: Name Wave function Probability density Total energy Meaning Orbital ( electron cloud ): Describes the complex path of the electron-wave (see later) Probability of finding the e within a small volume at a certain distance from the nucleus (K.E. + P.E.) of the e in shell n Value Function of: Spatial position; Quantum Numbers (same as above) E n = (13.6 ev) Z 2 /n 2 Most probable Most probable distance of the e in r shell n from the nucleus r mp,n = a o n 2 mp /Z radius (For similar concept of average, recall the Maxwell-Boltzmann distribution.) 19 Prof. Zvi C. Koren 19.07.10

Quantum Numbers and Orbitals Orbital, m l e Subshell, l Shell, n Subshell labels are from the descriptions of the lines of atomic line: s = sharp p = principal d = diffuse f = fundamental Schrödinger Pauli Q.N. n l m l m s Property Name Principal q.n. Angular Momentum q.n. Magnetic q.n. Spin q.n. Structural Name Shell Sub-shell Orbital Electron orientation Questions: How many orbitals are in the 5d subshell? In the 3d? What are their q.n. s? How many subshells are in the 4 th shell? What are their q.n. s? How many total orbitals are there in the 3 rd shell? What are their q.n. s? Allowed Values 1, 2,, 0, 1, 2, 3, 4,, n 1 s, p, d, f, g, l,, 0,,+ l ± ½, or 20 Prof. Zvi C. Koren 19.07.10

Atomic Orbitals: Contour Plots, Surface Boundary Plots, 90% Probability Plots (Schrödinger) Note the Nodes, the nodal surfaces: Angular Planar Nodes. How many in each orbital? s Note: These orbital diagrams do not represent solid physical structures, but only probability distributions: A Good Gambling Game. p x p y p z 21 Prof. Zvi C. Koren 19.07.10

d xy d xz d yz Angular planar(?) surfaces. How many in each orbital? General: What is the # of angular nodes in any orbital? d x 2 y 2 22 Prof. Zvi C. Koren 19.07.10 d z 2

Orbitals in a Subshell in a Shell n, Shell l values Subshells m l values Orbitals 1 0 1s 0 1s 2 0 2s 0 2s 1 2p -1, 0, 1 2p x, 2p y, 2p z 0 3s 0 3s 3 1 3p -1, 0, 1 3p x, 3p y, 3p z 2 3d -2, -1, 0, 1, 2 3dxy, 3dxz, 3dyz, 3d x 2 2 2 z -y, 3d 4 5 (Complete this table) 23 Prof. Zvi C. Koren 19.07.10

Dot Diagram Probability Density = 2 : Probability at a point : Probability of finding the e in a small volume at r a distance r from the nucleus More Orbital Plots D r = Radial Probability Distribution r 2 2 : Probability at a distance : Probability of finding r the e in a thin spherical shell at a distance r from the nucleus. 1s 2s 3s D r The probability density diagrams are problematic because they suggest that the greatest probability of finding the e is in the nucleus. That means that the P.E. U r 1, but the total E of an e is a finite value. K.E.. Impossible! Hence these 2 plots are unrealistic. The radial probability diagrams are better. They indicate that the probability of finding the e in the nucleus is zero. Note also, e.g., for 1s: As r increases, V of shell increases, but 2 decreases. So, D r increases then decreases. 24 Prof. Zvi C. Koren 19.07.10 r mp r r mp,1s =a o n 2 /Z= 0.529 Å (as Bohr for fixed r n=1 ) Note the radial spherical nodes.

Orbital and Probability Plots Radial Probability 1s Boundary Surface or Contour 2s 2p Nodes: Radial Spherical Angular Surface 3s 3p 3d 25 Prof. Zvi C. Koren 19.07.10

Summary of Different Orbital Plots Contour Plots or Boundary Surface Plots z Probability Densities (Probability at a point) Dot Diagram 2p 3d Angular Surface Nodes (planar and conical) = l 3d z 2 Radial Probability Distribution (Probability at a Distance) 1s 2s 3s D r Radial Spherical Nodes = n l 1 r Probability Density Diagram Total # of Nodes for a specific orbital = n 1 26 Prof. Zvi C. Koren 19.07.10