1. Modern Theory of the Atom Quantum Mechanical Model Or Wave Mechanical Model Or Schrodinger’s Model

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3. Recap of Bohr Model Electrons treated as particles moving in circular orbits. Specify speed, position, energy. Quantization of energy levels is imposed. Ground state: electrons close to nucleus Electron transitions between energy levels can occur. Higher energy levels are farther from nucleus. –Moving up, electron absorbs energy –Moving down, electron emits light energy Wavelengths of light in H spectrum can be predicted. Depend on energy difference of 2 levels involved in transition.

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5. Problems with Bohr Model Only worked for 1-electron systems. Quantization of energy levels had to be “imposed.”

6. By the end of the 1800’s … Physicists thought they were done! Light or energy was waves. Could come in any frequency or wavelength. No mass. Delocalized. Matter was particles. Have mass. Specify position. Nice packages, everything done. Matter & Energy were DIFFERENT! But there was trouble ahead!

7. Two problems Black body radiation Photoelectric effect

8. Energy of a photon Einstein proposed that light comes in discrete packages called photons.Einstein proposed that light comes in discrete packages called photons. Einstein: E photon = hEinstein: E photon = h All radiation is quantized!All radiation is quantized! Each energy of radiation will have its own frequency.Each energy of radiation will have its own frequency.

9. Photoelectric Effect

10. Photons One photon can give all its energy to one electron. One electron can only accept one photon.One photon can give all its energy to one electron. One electron can only accept one photon. So if the photon is energetic enough, the electron will escape from the metal. If the photon is low energy, the electron can’t escape. (Threshold)So if the photon is energetic enough, the electron will escape from the metal. If the photon is low energy, the electron can’t escape. (Threshold) Brighter light means more photons so more electrons can escape. (Number)Brighter light means more photons so more electrons can escape. (Number)

11. Wave-particle Duality Light can’t be forced into categories like everyday objects.Light can’t be forced into categories like everyday objects. In some situations, light exhibits interference phenomena, like water waves.In some situations, light exhibits interference phenomena, like water waves. In some situations, light shows energy transfers like particles in a collision.In some situations, light shows energy transfers like particles in a collision.

12. E = mc 2 E photon = h = hc/ = mc 2E photon = h = hc/ = mc 2 So m = hc/  c 2So m = hc/  c 2 m = h/ c for a photon.m = h/ c for a photon.

13. Electrons as Waves 1924: Louis de Broglie: Dual nature of MATTER1924: Louis de Broglie: Dual nature of MATTER Suggested that since light can act like a particle, maybe a particle, the electron, can act like a wave.Suggested that since light can act like a particle, maybe a particle, the electron, can act like a wave. m = h/ c for a photon.m = h/ c for a photon. Electrons are not electromagnetic waves. They are “matter waves.”Electrons are not electromagnetic waves. They are “matter waves.” m = h/ v where v = velocity of the particle.m = h/ v where v = velocity of the particle.

14. 2 kinds of waves Traveling wave Wave is not confined to a given space Travels from one location to another Interrupted by a boundary or another wave Standing wave Confined to a given space. (Ends pinned.) Interference between incident & reflected waves. At certain frequencies, certain points seem to be standing still. Other points, displacement changes in a regular way.

15. Standing waves in music Applet with violin string Applet with violin string Wave: reflection of a pulse at a fixed end Wave: reflection of a pulse at a fixed end Interference of two waves traveling through a medium Interference of two waves traveling through a medium So boundary conditions result in only some wavelengths that will fit on the string: “quantization”

16. DeBroglie Electron-Wave The wavelength describing an electron depends on the energy of the electron. At certain energies, electron waves make standing waves in the atom. The wave does not represent electron path. Only certain wavelengths will “fit.”

17. DeBroglie Electron Waves These wavelengths will “work.” This wavelength will not “work.”

18. Bright spots result from constructive interference of waves. The waves are in phase (peaks match). Dark areas result from destructive interference of waves. Waves are out of phase. Only waves make diffraction patterns.

19. Modern Theory Electron is treated as a standing wave.Electron is treated as a standing wave. Cannot specify both position & velocity of electron.Cannot specify both position & velocity of electron. Can determine probability of locating the electron in a given region of space.Can determine probability of locating the electron in a given region of space. Quantized energy levels arise naturally out of wave treatment.Quantized energy levels arise naturally out of wave treatment. Also called Quantum Mechanics or Wave mechanics. Scientist = Schrodinger.Also called Quantum Mechanics or Wave mechanics. Scientist = Schrodinger.

20. Bohr Model vs. Modern Theory Electron = particleElectron = particle OrbitOrbit Holds 2n 2 electronsHolds 2n 2 electrons SphericalSpherical Each orbit has a specific energyEach orbit has a specific energy Can find position, speedCan find position, speed Electron = WaveElectron = Wave OrbitalOrbital Holds 2 electronsHolds 2 electrons Not necessarily sphericalNot necessarily spherical Each orbital has a specific energyEach orbital has a specific energy Probable locationProbable location

21. Schrödinger’s Equation Ĥ  = E  Solve for , the wave functions.  2 gives the probability of finding an electron near a particular point in space. –Represented as probability distribution or electron density map.

22. Heisenberg uncertainty principle Fundamentally impossible to know the velocity and position of a particle at the same time. Impossible to make an observation without influencing the system. –A photon colliding with an electron will knock it off its path.

23. Orbital – Modern Theory Orbital = term used to describe region where an electron might be. Each orbital has a specific energy and a specific shape. Each holds 2 electrons. Described by 4 parameters in the wave function – quantum numbers = n, l, m, s – like an address

24. s orbitals (  2 )

25. p orbitals

26. d orbitals

27. What can orbitals do for us? Physical structure of orbitals explains –Bonding –Magnetism –Size of atoms –Structure of crystals

28. Quantum Numbers Each electron in an atom has a set of 4 quantum numbers – like an address. –3 quantum numbers describe the orbital –1 quantum number gives the electron spin No two electrons can have all 4 quantum numbers the same. (Pauli exclusion principle)

29. Energy level diagram for orbitals of Hydrogen atom. ĤΨ = EΨ can be solved exactly Only 1 electron.

30. Energy Level Diagram Energy Level Diagram Energy levels for Polyelectronic atom

31. n: principal quantum number Related to size and energy of orbital n has integral values: 1, 2, 3, 4, … As n increases, the orbital becomes larger & the electron spends more time farther from the nucleus, which also means higher energy.

32. l = angular momentum quantum number Related to shape of orbital. l has integral values from 0 to n -1 for each value of n. Orbitals with different shapes have slightly different energies. Each type of orbital resides on a different sublevel of the principle energy level.

33. l = angular momentum quantum number Principal energy levels are made up of sublevels. The number of sublevels depends on the principal energy level. – 1 st principal energy level has 1 sublevel – 2 nd “ “ “ “ 2 “ – 3 rd “ “ “ “ 3 “ – 4 th “ “ “ “ 4 “, etc.

34. Naming sublevels Sublevels are usually labeled s, p, d, or f instead of using more numbers. If l = 0, call it an s orbital. If l = 1, call it a p orbital. If l = 2, call it a d orbital. If l = 3, call it an f orbital.

35. m l = magnetic quantum number m l related to orientation of orbital in space relative to other orbitals in the atom. m l has integral values between l and -l, including 0. –For n = 1, l = 0 and m l = 0. –For n = 2, l = 0 or 1. If l = 0 then m l = 0 If l = 1, then m l = -1, 0, or +1.

36. orbitals Sublevels are made up of orbitals Each kind of sublevel has a specific # of orbitals Sublevel# of orbitals s1 p3 d5 f7

37. Spin quantum number, m s m s describes the spin state of the electron in the orbital. m s has two possible values: + ½ and – ½ Pauli exclusion principle: No two electrons in the same atom can have all 4 quantum numbers the same. So each orbital can hold only two electrons.

38. Orbitals Each orbital can hold two electrons with opposite spins. –s sublevels, 1 orbital: 2 e - max capacity –p sublevels, 3 orbitals: 6 e - –d sublevels, 5 orbitals: 10 e - –f sublevels, 7 orbitals: 14 e -

39. Prin.En.LevSublevels# orbitals/slTotal # elec 1s12 2s12 p36 3s12 p36 d510 4s12 p36 d510 f714

40. 1 st principal energy level, 1 sublevel – s 2 nd principal energy level, 2 sublevels – s & p 3 rd principal energy level, 3 sublevels Each box represents an orbital and holds 2 electrons.

41. Order of fill: Aufbau principle Each electron occupies the lowest orbital available Learn sequence of orbitals from lowest to highest energy Is some overlap between sublevels of different principal energy levels

42. Diagonal Rule 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p Sequence of orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, … Follow the arrows Exceptions do occur: half-filled orbitals have extra stability.

43. Hund’s Rule !Distribution of electrons in equal energy orbitals: Spread them out as much as possible! Also, all electrons in singly occupied orbitals must have the same spin state.

44. Electron Configurations

45. Compare Bohr & Schrodinger

46. Frequencies in Chemistry

47. Electron Configuration & P.T.

49. Principle Energy Levels  Sublevels Orbitals Hold 2 Electrons Max   n = 1,2,3,4 Holds 2n 2 Electrons max  1 st energy level has 1 sublevel : s 2 nd “ “ “ 2 sublevels : s and p 3 rd “ “ “ 3 “ : s, p, and d 4 th “ “ “ 4 “ : s, p, d, and f s sublevel holds 1 orbital p sublevel holds 3 orbitals d sublevel holds 5 orbital f sublevel holds 7 orbitals 