Quantum Mechanical Model and Electronic Structure of Atoms

1. Chapters 7 & 8 Quantum Mechanical Model; Electronic Structure of the Atoms & Periodic Trends

2. Definitions • Atoms - smallest particles of matter • Matter - has mass, volume and specific position • Energy - no mass; a wave function; delocalized

3. Einstein’s Contribution • Energy is related to mass as seen in the equation: E = mc2

4. Law of Conservation of Energy • Energy can never be destroyed. It can only be converted from one form to another.

5. Forms of Energy • Electromagnetic radiation wavelength, frequency and speed • Light • Heat

6. Electromagnetic Spectrum • Radio Waves • Microwaves, Radar Rays • Infrared • Visible • UV • X-rays • Gamma Rays

7. The Wave Nature of Light

8. The Wave Nature of Light

9. Chemistry in Color • Specific elements gave color when heated in flame. • Continuous spectrum - e.g., rainbow • Line Spectrum

10. Line Spectra • Held the key to the structure of the atom!

11. The Bohr Atom • Bohr:suggested that electrons were responsible for the line spectra. Proposed that electrons traveled around the nucleus of the atom in shells

12. The Bohr Atom • Bohr:associated each shell w/ a particular energy level. The farther away, the higher the Energy. Allowed electrons to jump from one shell to another. (ground state excited state)

13. Comparison • Bohr Model similar to model for solar system where the planets revolve in their particular orbits. • Difference: Electrons can jump from one shell to another. The planets do not!

14. Ionization • An electron can absorb so much energy that it can jump completely from the atom!

15. Quantized Energy and Photons The Photoelectric Effect and Photons • If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal. • The electrons will only be ejected once the threshold frequency is reached. • Below the threshold frequency, no electrons are ejected. • Above the threshold frequency, the number of electrons ejected depend on the intensity of the light.

16. Matter and Energy • Matter and Energy are not distinct! • Proof: Matter can absorb or emit energy. • Max Planck’s Postulate: Energy can be gained or lost only in whole numbers or integer multiples, hn.

17. Wrong assumption • Matter was assumed to transfer any amount of energy because E was continuous.

18. Quantum • E can be quantized or delivered in small packets of size hn, called a Quantum. • Quanta = photon

19. Quantum Mechanical Model • De Broglie and Schroedinger • Corrected Bohr’s model • determined that E had wave properties and mass

20. Quantum Mechanical Model • re-evaluated electron as occupying volume of space instead of shells that were like orbits. • Orbital - volume of space occupied by an electron

21. Quantum Mechanics and Atomic Orbitals If we solve the Schrödinger equation, we get wave functions and energies for the wave functions. • We call wave functions orbitals. • Orbitals were located in levels.

22. Quantum Mechanical Model • De Broglie and Schroedinger • Corrected Bohr’s model • determined that E had wave properties and mass

23. Quantum Mechanical Model • re-evaluated electron as occupying volume of space instead of shells that were like orbits. • Orbital - volume of space occupied by an electron

24. Quantum Mechanics and Atomic Orbitals If we solve the Schrödinger equation, we get wave functions and energies for the wave functions. • We call wave functions orbitals.

25. Principal Quantum Number, n • Schrödinger’s equation requires 4 quantum numbers: • Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. N refers to the shell.

26. Azimuthal Quantum Number, l. • This quantum number depends on the value of n. The values of l begin at 0 and increase to (n - 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals.

27. Representations of Orbitals The s-Orbitals

28. Representations of Orbitals

29. Representations of Orbitals The p-Orbitals

31. Magnetic Quantum Number, ml. 3. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. Magnetic quantum numbers give the 3D orientation of each orbital.

32. Shape of Orbitals • s - sphere • p - dumbbell • d - double dumbbell

33. Representations of Orbitals The p-Orbitals • There are three p-orbitals px, py, and pz. • The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system. • The letters correspond to allowed values of ml of -1, 0, and +1. • The orbitals are dumbbell shaped. • As n increases, the p-orbitals get larger. • All p-orbitals have a node at the nucleus.

34. Representations of Orbitals The p-Orbitals

35. Representations of Orbitals The d and f-Orbitals • There are five d and seven f-orbitals. • Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes. • Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes. • Four of the d-orbitals have four lobes each. • One d-orbital has two lobes and a collar.

37. Pauli Exclusion Principle • An orbital with a particular orientation can only hold 2 electrons and they must have opposite spins! In short, NO 2 electrons can have the same 4 quantum numbers. • Example: px, py, pz

38. Rules for Occupancy and Pairing • Opposite spins pair up. • Hund’s Rule: For the same sublevel, each orbital must be occupied singly before pairing can occur. This is the lowest E for an atom configuration.

39. Heisenberg Uncertainty Principle • “There is a fundamental limitation as to how precisely we can determine the position and momentum of a particle at a given time.” • 90-95% probability of finding the electron in the orbital

40. Magnetic Spin Quantum Number, ms • Gives insight into the spin of the electron • 2 Possible Values: ½ and – ½

41. Many-Electron Atoms Orbitals and Their Energies • Orbitals of the same energy are said to be degenerate. • For n 2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other. • Therefore, the Aufbau diagram looks slightly different for many-electron systems.

42. Energy Levels • The electrons are found at a certain distance from nucleus in their shell(s). • energy level = shell (interchangeable terms) • Electrons in the same shell have the same E.

43. Heisenberg Uncertainty Principle • “There is a fundamental limitation as to how precisely we can determine the position and momentum of a particle at a given time.” • 90-95% probability of finding the electron in the orbital

44. Shorthand Notation • Uses the closest noble gas before the given element to represent the inner electrons. • Al = 13 electrons 1s2 2s2 2p6 3s2 3p1 • Shorthand Notation: [Ne] 3s2 3p1 • Neon represents the 10 inner electrons

45. Periodicity • Valence electrons determined the position of the atoms in the periodic table and predicted the reactivity of the elements.

46. Periodic Table • Organized according to Electronic Configuration of elements • Based on the Aufbau Principle of building up the number of electrons and protons

47. Definitions • Core Electrons - inner electrons • Valence Electrons - electrons on the outermost energy level of an atom

48. Valence Electrons • Are the electrons in the outermost shell • Determines the group where the element belongs in the periodic table. • For ex., 1s22s22p3 = element belongs to Grp V. Outermost level is 2. Add the electrons in 2s and 2p orbitals.

49. Sample Problem • What is the largest principal quantum number in the ground state electron configuration of iodine ?

50. Sample Problem • What is the azimuthal quantum number for the orbitals being filled in the Lanthanide series?