New Tutorial Center Schedule

1. New Tutorial Center Schedule

2. Problems with the Wave Theory of Light Blackbody Radiation The Photoelectric Effect Emission Spectra of Atoms By the mid-1800s, the wave theory became predominant, but…… When light interacted with matter, the wave theory failed. The important examples are:

3. Problem #2Photoelectric Effect Animation

4. Problem #3. Atomic Line Spectra • Periodic Table of Line Spectra

5. Problem #3. Atomic Line Spectra Emission spectra for pure elements • Periodic Table of Line Spectra

6. Niels Bohr (1885-1962) Danish physicist who worked with J.J. Thomson at Cambridge University in 1911. He didn’t agree with Thomson’s atomic model, so worked for Rutherford in 1912. • In 1912, in a bold step, he suggested that the classical laws of physics cannot be applied to matter as small as atoms and electrons. Instead, new laws are needed • Bohr sought to solve the problem with Rutherford’s atomic model and explain the phenomenon of atomic spectra, by applying the quantum theory of light to atoms and electrons

7. Bohr’s Quantum Atomic Model Postulated that the energy of the electron must be quantized. Only certain electron energies are possible. Orbit radii (energy levels) correspond to definite energies Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy level to another n= energy level number or principal quantum number Why does an electron possess energy? 1) 2)

8. Stairstep analogy How do quantized energy levels explain spectral lines? Atoms “place” electrons in lowest possible energy levels (“ground state”) When electrons are provided with enough energy, they “jump” to higher energy levels, where they are unstable (“excited state”) The electrons then fall back down to the lower possible energy levels, releasing absorbed energy as a photon of light We see these photons as the spectral lines emitted by excited atoms Energy of H electron = E = -RH/n2 n = 1, 2, 3, … ∞ RH = 2.179 x 10-18 J

9. energy levels

10. H emission spectrum “quantum jump” ∆E4→2 = E2 - E4= h4→2

11. A “quantum jump” Emission ∆E = E2 - E4= h4→2 Absorption ∆E = E4 – E2= h2→4

12. Simulations of Bohr Model Visible emission spectral lines of hydrogen

13. Success & Limitation of Bohr’s Quantum Model Explained the existence of spectral lines Solved the problem with Rutherford’s model of the hydrogen atom But, the mathematics only worked for atoms with 1 electron! How can this model be made to work for all elements?

14. de Broglie’s Novel Notion Light was “known” (thought) to be a wave, but Einstein showed that it also acts particle-like. Electrons were “known” to be particles mass & charge. French physicist: What if …… 1923 electrons behaved as waves also Diffraction pattern obtained by firing a beam of electrons through a crystal.

15. Dr. Quantum video

16. Werner Heisenberg In 1927, German physicist, proposed that the dual nature of the electron places limitations on how precisely we can know both the location and speed of the electron Instead, we can only describe electron behavior in terms of probability The Uncertainty Principle speed position

17. Heisenberg’sUncertainty Principle Wave behavior limits what can be known! What if the particle has a small mass? What if the electron’s position is known very precisely? What if the electron’s speed is known very precisely? h 4m ± speed ± position (±x)(±vx) Can the electron’s orbit be precisely defined?

18. Erwin Schrodinger In 1926, Austrian physicist, proposed an equation that incorporates both the wave and particle behavior of the electron When applied to hydrogen’s 1 electron atom, solutions provide the most probable location of finding the electron in the first energy level Can be applied to more complex atoms too! Wave Equation & Wave Mechanics

19. Extremely small mass Located outside the nucleus Moving at very high speeds Have specific energy levels Standing wave behavior Electron Characteristics

20. Baseball v. Electron A baseball behaves as a particle and follows a predictable path. BUT Anelectron behaves as a wave,and its path cannot be predicted. All we can do is to calculate theprobabilityof the electron following a specific path.

21. What if a baseball behaved like an electron? =h/(mu) speed mass • Characteristic wavelength () • baseball  10-34 m • electron  0.1 nm So, all we can predict is…..

22. “deterministic” “probabilistic”

23. Bohr Model v. Quantum Mechanics BohrQuantum Mechanics Energy Electron Position/Path Elements

24. “Most Successful Theory of the 20th Century” Matter Dalton Thomson Rutherford Quantum Mechanics Bohr & de Broglie Heisenberg Einstein Plank Schrödinger Maxwell Wave Mechanics Newton Light

25. Implication of Heisenberg’sUncertainty Principle Wave behavior of electron limits what can be known! The electron’s trajectory (speed, position, etc.) cannot be known with any certainty. So, we can only describe electron behavior in terms of probability. h 4m ± speed ± position (±x)(±vx) 25

26. Quantum Mechanics ModelDescribes the energy, arrangement & space occupied by electrons Electron’s energy is quantized Quantum Mechanics Mathematics of waves to define orbitals (wave mechanics) 26

27. Dartboard Analogy 27

28. From “Physical Chemistry” by Tinoco, Sauer and Wang 28

29. Results from Schrodinger’s Wave Equation ● Electron is modeled with standing wave behavior at quantized energy levels. ●Solution gives the probability of an electron at a given location in the 3-D space around nucleus. ● Probability maps are called orbitals. ● Orbitals are defined to contain the location of the electron 99% of the time. “probability map” 29

30. Probability Distributions:Point (A) versus Volume (B) Probability per unit volume at a given point Probability at a given point 30

31. Representing s orbitals: density shading 31

32. 1s and 2s orbitals compared What is the biggest difference? 32

33. Representing s Orbitals 33

34. Quantum Mechanics Model The electron's movement cannot be known precisely. We can only map the probability of finding the electron at various locations outside the nucleus. The probability map is called anorbital. The orbital is calculated to confine 99% of electron’s range. Energy of the electron is quantized into sublevels.

35. Energy levels in the hydrogen atom 35

36. Concept Check In which transition is the energy of photon emission greatest for an atom of neon. A) 2p 2sB) 2s 1sC) 3s 2s Follow-up Which transition would have the lowest wavelength of photon emission? 36

37. Principal Quantum Number & Energy Sublevels Principal quantum number (n) = number of subshells 37

38. Representing 2p orbitals density map Do these orbitals have different electron energies? ____ How do they differ from one another? ______________ 38

39. Shapes of d orbitals (probability maps in 3-D space) How many “orientations” of d orbitals are possible? ____ When combined together, the shape is roughly _______. 39

40. Shapes of f orbitals Do these have different electron energies? _____ How many “orientations” of f orbitals are possible? ____ When combined together, the shape is roughly _______. 40

41. Why are atoms spherical? Tro, Chemistry: A Molecular Approach 41

42. Quantum numbers and orbital energiesEach electron in an atom has a unique set of quantum numbers to define it{ n, l, ml, ms } • n = principal quantum number • electron’s energy depends principally on this • l = azimuthal quantum number • for orbitals of same n, l distinguishes different shapes (angular momentum) • ml = magnetic quantum number • for orbitals of same n & l, ml distinguishes different orientations in space • ms = spin quantum number • for orbitals of same n,l & ml, ms identifies the two possible spin orientations

43. Energy levelSublevel# of orbitals/sublevel n = 1 1s (l = 0) 1 (ml has one value) n = 22s (l = 0) 1 (ml has one value) 2p (l = 1) 3 (ml has three values) n = 33s (l = 0) 1 (ml has one value) 3p (l = 1) 3 (ml has three values) 3d (l = 2) 5 (ml has five values) Quantum numbers and orbital energies Each atom’s electron has a unique set of quantum numbers to define it{ n, l, ml, ms } n = principal quantum number (energy) l = azimuthal quantum number (shape) ml = magnetic quantum number (orientation)

44. Concept: Each electron in an atom has a unique set of quantum numbers to define it{ n, l, ml, ms } 44

45. What is the reason that the periodic table organizes elements according to similarities in chemical properties?

46. multi-electron atoms H atom All other atoms As n increases, the difference in energy level _______. 46