המבנה האלקטרוני של האטום:

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

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

3 Sir Joseph John (J.J.) Thomson , 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 , Ireland Coined the name electron in Prof. Zvi C. Koren

4 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

5 Robert Andrews Millikan , 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 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 C. 3. Thus, the mass m of an electron can be calculated together with Thomson s result for e/m: m = 9.11 x g. 5 Prof. Zvi C. Koren

6 Ernest Rutherford , New Zealand & England Nobel Prize in Chemistry, Experiment: Gold Foil, 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 e e + e e e 1 2 3

7 James Clerk Maxwell Electromagnetic Radiation & Wave Properties ( ) 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

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

9 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

10 Max Planck , 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 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

11 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 , 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

12 Continuum Spectrum Johann Jakob Balmer , 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: RH n R H = Rydberg constant for H = 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 Hi V Hi V excited energy

13 Atomic Line Spectra of Selected Atoms Fantastic Web Sites: Prof. Zvi C. Koren

14 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 ( , USA) 2: Balmer " Johann Jakob Balmer ( , Switzerland) 3: Paschen " Friedrich Paschen ( , Germany) 4: Brackett " Frederick Sumner Brackett ( , USA) 5: Pfund " August Herman Pfund ( , USA) n 2 = n 1 +1, n 1 +2, 14 Prof. Zvi C. Koren

15 Niels Bohr , 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 = Å 1 Å = Ångstrom = m E n = (13.6 ev) Z 2 /n 2 E i f = h hc/ 1 ev = 1.60 x J E 1 = 13.6 ev 1 1 RH 2 2 n1 n2 15 Prof. Zvi C. Koren Z 2

16 Louis de Broglie , 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 h p

17 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

18 Werner Heisenberg , 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 Property 2 E Erwin Scrödinger ( , 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 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

20 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

21 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

22 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 d z 2

23 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 z -y, 3d 4 5 (Complete this table) 23 Prof. Zvi C. Koren

24 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 r mp r r mp,1s =a o n 2 /Z= Å (as Bohr for fixed r n=1 ) Note the radial spherical nodes.

25 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

26 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